结合边界约束网络和分水岭分割算法的建筑物提取
- Building detection based on a boundary-regulated network and watershed segmentation
- 2022年26卷第7期 页码：1459-1468
纸质出版日期： 2022-07-07
- DOI： 10.11834/jrs.20219335
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结合边界约束网络和分水岭分割算法的建筑物提取 Building detection based on a boundary-regulated network and watershed segmentation 1 first-author 罗壮，研究方向为计算数学、数据科学。E-mail： luozhuang726995@163.com 罗壮，研究方向为计算数学、数据科学。E-mail： luozhuang726995@163.com luozhuang726995@163.com 2 corresp 李明，研究方向为计算数学、数据科学。E-mail： liming01@tyut.edu.cn 李明，研究方向为计算数学、数据科学。E-mail： liming01@tyut.edu.cn liming01@tyut.edu.cn 3 太原理工大学 数学学院, 晋中 030600 太原理工大学 数学学院, 晋中 030600 College of Mathematics, Taiyuan University of Technology, Jinzhong 030600, China College of Mathematics, Taiyuan University of Technology, Jinzhong 030600, China 太原理工大学 大数据学院, 晋中 030600 太原理工大学 大数据学院, 晋中 030600 College of Data Science, Taiyuan University of Technology, Jinzhong 030600, China College of Data Science, Taiyuan University of Technology, Jinzhong 030600, China 清华大学 地球系统科学系, 北京 100084 清华大学 地球系统科学系, 北京 100084 Department of Earth System Science, Tsinghua University, Beijing 100084, China Department of Earth System Science, Tsinghua University, Beijing 100084, China 城市作为高密度建筑区域，在较小范围内有大量结构相似的建筑紧密分布。当前从高分辨率图像中准确检测建筑仍然是一个挑战，本文受边缘检测网络启发，提出一种强化边界精度的建筑物提取新方案，根据建筑物及边界特点改进深度网络，结合自下而上分组的分水岭分割提高分类精度和建筑边界的准确度。首先对数据预处理，生成建筑边界和建筑分割线两类辅助标签；改进性能较优的建筑检测框架ICT-Net网络，修改网络结构和损失函数，针对两类辅助标签，强化边界影响，提高网络性能；最后对网络预测结果应用结合分水岭分割和梯度提升回归树的后处理，实现高精度的建筑提取。结果表明，数据预处理、改进深度学习算法可提高建筑检测像素精度IOU（Intersection over Union）约1%。后处理能充分利用网络输出的概率信息，有效优化建筑边界，在网络预测结果的基础上提高建筑实例召回率10.5%。本文方案与原始的ICT-Net网络相比，提高建筑实例召回率22.9%。 High-density urban cities contain numerous similar buildings positioned in close proximity. Building detection from high-spatial-resolution remote sensing imagery in such scenes remains a challenge in computer vision and remote sensing urban applications. The integration of traditional segmentation algorithms and a novel neural network is an effective approach for such challenging settings. Inspired by the recent success of deep-learning-based edge detection, a new building detection method aiming at accurate boundaries is proposed. In accordance with the characteristics of buildings and their border, this study improves the network structure and integrates the network with bottom-up watershed segmentation to improve boundary precision and classification accuracy. First, two auxiliary labels, namely, the building boundary and parting line, are derived from the original dataset through data preprocessing. Second, the newly proposed building detection frame called ICT-Net is improved by modifying its structure and loss function in accordance with the two auxiliary labels to obtain the probability of three classes. Lastly, a post-process integrating watershed segmentation with gradient-boosted regression trees is employed to achieve high-accuracy building detection. Specifically, a probability feature map is generated by merging the probability of three classes. Watershed segmentation with building marker thresholds is applied to obtain building instances from the probability feature map. Then, the building probability of each building instance predicted by gradient-boosted regression trees is used to select building instances, resulting in building detection results. Parameter selection is also implemented. The performance of the proposed method is validated on the INRIA dataset, which provides aerial orthorectified color imagery with a spatial resolution of 0.3 m and with corresponding ground truth labels for two semantic classes: building and not building. Experimental results suggest that data preprocessing and the application of boundary loss can obtain an improvement of 1% in terms of the Intersection over Union (IOU) of building detection. The post-process can take full advantage of probability information from the network, thereby effectively optimizing the building boundary. The post-process brings an improvement of 10.5% in terms of building instance recall compared with the results of the neural network. Our study achieves a building instance recall rate that is 22.9% higher than that of the original ICT-Net. A novel building detection method based on a boundary-regulated network and watershed segmentation is proposed in this study. Experimental results reveal the advantages of the enhanced-boundary-oriented data preprocessing and modified neural network and demonstrate that the proposed method can further improve prediction accuracy on a network basis. However, the excellent performance of the proposed method largely depends on parameter selection, and further improvements should be made in the future. 遥感 建筑检测 深度网络 边界损失 分水岭分割 实例分割 remote sensing building detection deep neural network boundary loss watershed segmentation instance segmentation 1 引言 1 建筑信息广泛应用于灾害监测，数字城市建设和流行病监控等。高分辨率光学影像是建筑提取的重要数据源。高分辨率影像提供丰富的光谱特征，突出物体的结构、纹理等信息。同时高空间分辨率也带来了更多的图像噪声和“异物同谱”等问题（ 明冬萍 等，2005 明冬萍 等，2005 ）。此外因建筑结构的多样性和背景环境的复杂性，从高分辨率图像中准确检测建筑仍然是一个挑战。 中小尺寸的建筑物是城市的主体，在因人口聚集而土地稀缺的城市密集排列，常表现为大量大小相似的建筑物，位置非常接近。这类场景的遥感影像建筑物提取主要有两个问题：（1）精度不高，受建筑物结构的多样化和周边环境（特别是相邻建筑）的影响，容易误判，降低分类结果精度。（2）建筑边界不清晰，常出现多个建筑物“粘连”为一个。使用带掩模分支的目标识别框架（如Mask R-CNN（ He等，2017） He等，2017） ）和语义分割网络（如U-net（ Ronneberger等，2015） Ronneberger等，2015） ）识别时各有不足。目标识别允许对象之间有重叠（ Goldman等，2019 Goldman等，2019 ），不适合建筑实例提取。不加约束和处理的单纯语义分割算法，常将多个建筑分割为一个区域对象。 建筑检测的算法和理论，可以分为传统面向对象的图像分析方法和深度学习方法。传统方法使用光谱、纹理（ 谭衢霖，2010 谭衢霖，2010 ； Wu等，2014 Wu等，2014 ）、形态轮廓（ Lv等，2014 Lv等，2014 ）等特征提取建筑，用多尺度方法（ Tian等，2016 Tian等，2016 ； Liu等，2005 Liu等，2005 ）、先验知识（如阴影（ Dosovitskiy等，2015 Dosovitskiy等，2015 ； Liow和Pavlidis，1990） Liow和Pavlidis，1990） ）提升精度。相较于传统方法，深度学习的主要优势是学习特征表达的自适应性及较强的泛化能力。如DeepGlobe挑战（ Demir等，2018 Demir等，2018 ）和INRIA建筑检测比赛（ Maggiori等，2017 Maggiori等，2017 ）的前5名方案均基于神经网络。当前建筑检测技术在精度上还有较大进步空间，特别是边界定位准确度需要提高。 针对密集建筑区域内，建筑提取精度不足和边界模糊两个问题，根据文献成果，加入边缘检测网络（ Wu等，2018 Wu等，2018 ）或边缘检测分支（ Marmanis等，2018 Marmanis等，2018 ），优化边界损失函数（ Bokhovkin和Burnaev，2019 Bokhovkin和Burnaev，2019 ）可改进遥感影像的语义分割，受其启发，本文提出了一个完整的建筑检测方案。结合神经网络和自下而上分组的分水岭算法，对数据标签预处理，生成两类辅助标签-边界标签和相邻建筑分割线标签，在性能较优的建筑检测框架ICT-Net网络（ Chatterjee和Poullis，2019 Chatterjee和Poullis，2019 ）基础上改进，使用更适合建筑特性和3类标签的新损失函数，提升精度，以基于分水岭算法和梯度提升回归树（ Ke等，2017 Ke等，2017 ）的后处理，从“粘连”的多个建筑掩模中，提取单体建筑。实验证明本文检测方案容易训练，既显著提高建筑检测精度，又使提取的建筑边界更准确。 2 方法 1 本文的建筑检测总流程如 图1 图1 所示，分3个阶段，数据预处理、监督分类和后处理。数据预处理就是转换原始建筑样本标签，生成建筑、边界和相邻建筑分割线3类标签。监督分类使用转换后的训练样本训练本文网络，预测3类别概率。后处理阶段，对网络预测结果应用基于分水岭算法和梯度提升回归树的后处理，从密集建筑掩模中提取建筑实例。 2.1 数据集与预处理 2 本文使用的数据源是INRIA数据集中的芝加哥（ Maggiori等，2017 Maggiori等，2017 ），共36张0.3 m空间分辨率的彩色正射校正航空影像和对应的建筑掩模标签，每景影像为5000像素×5000像素，面积约81 km 2 。 数据预处理就是对数据标签的预处理，形成3类标签：原建筑标签、边界标签、相邻建筑分割线标签，前两类存在于每一个建筑，第3类分割线仅存在于紧凑相邻的建筑物之间。 图2 图2 为数据与预处理示例，每个建筑标签区域（建筑像素为1，非建筑像素为0）对应一个单体建筑，数据预处理的流程如下（其中形态学腐蚀尺寸、膨胀尺寸和邻域范围是根据图像特点设置的经验值）： 1,2,3,4; （1）对建筑标签应用形态学腐蚀操作（腐蚀尺寸设置为3×3），腐蚀后的建筑掩模与原建筑掩模的差，作为边界标签； （2）对建筑标签应用形态学膨胀操作（膨胀尺寸设置为9×9），并减去原建筑标签区域，形成分割线标签的候选点集合； （3）对原建筑标签做区域标号，遍历候选点集合，若该像素邻域范围（尺寸设置为7×7）内存在至少2个不同建筑物，则该像素作为分割线标签。 2.2 网络结构与损失函数 2 本文考虑建筑物的特点，改进原ICT-Net网络。ICT-Net（ Chatterjee和Poullis，2019 Chatterjee和Poullis，2019 ）属于完全卷积网络，基于U-net网络（ Ronneberger等，2015 Ronneberger等，2015 ），结合Dense blocks与Squeeze-and-Excitation的组合（这里简称FRDB模块， 图3 图3 显示ICT-Net网络结构，细节参考 Chatterjee和Poullis（2019） Chatterjee和Poullis（2019） 。 首先修改网络最后一层为三通道，分别对应建筑、边界、分割线3个类，应用Sigmoid激活函数获得每个类的概率，并裁剪预测结果的4条边各24个像素宽的边缘，以避免边界效应（ Iglovikov等，2017 Iglovikov等，2017 ），被裁剪的边缘不参与网络优化，减少后向传播的计算量。 其次，本文使用了更适合建筑提取和更有利于边界准确的损失函数，焦点损失（ Lin等，2017 Lin等，2017 ）、骰子损失和 <math id="M1"><mi mathvariant="normal">J</mi><mi mathvariant="normal">a</mi><mi 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id="M10"><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">B</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">y</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019109&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019107&type= 9.48266602 3.72533321 ，计算如下： <math display="block" id="M11"><mtable columnalign="left"><mtr><mtd><msubsup><mrow><mi mathvariant="bold-italic">Y</mi></mrow><mrow><mi mathvariant="bold">g</mi><mi mathvariant="bold">t</mi></mrow><mrow><mi mathvariant="bold-italic">b</mi></mrow></msubsup><mo>=</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi mathvariant="bold-italic">Y</mi></mrow><mrow><mi mathvariant="bold">g</mi><mi mathvariant="bold">t</mi></mrow></msub><mo>,</mo><mtext> </mtext><mn mathvariant="normal">3</mn></mrow></mfenced><mo>-</mo><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi mathvariant="bold-italic">Y</mi></mrow><mrow><mi mathvariant="bold">g</mi><mi mathvariant="bold">t</mi></mrow></msub></mrow></mfenced><mo>,</mo></mtd></mtr><mtr><mtd><msubsup><mrow><mi mathvariant="bold-italic">Y</mi></mrow><mrow><mi mathvariant="bold">p</mi><mi mathvariant="bold">d</mi></mrow><mrow><mi mathvariant="bold-italic">b</mi></mrow></msubsup><mo>=</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi mathvariant="bold-italic">Y</mi></mrow><mrow><mi mathvariant="bold">p</mi><mi mathvariant="bold">d</mi></mrow></msub><mo>,</mo><mtext> </mtext><mn mathvariant="normal">3</mn></mrow></mfenced><mo>-</mo><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><msub><mrow><mi mathvariant="bold-italic">Y</mi></mrow><mrow><mi mathvariant="bold">p</mi><mi mathvariant="bold">d</mi></mrow></msub></mrow></mfenced></mtd></mtr></mtable></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019114&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019112&type= 51.22333527 12.27666664 <math display="block" id="M12"><msubsup><mrow><mi mathvariant="bold-italic">Y</mi></mrow><mrow><mi mathvariant="bold">g</mi><mi mathvariant="bold">t</mi></mrow><mrow><mi mathvariant="bold-italic">b</mi><mo>,</mo><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">x</mi><mi mathvariant="bold-italic">t</mi></mrow></msubsup><mo>=</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi><mfenced separators="|"><mrow><msubsup><mrow><mi mathvariant="bold-italic">Y</mi></mrow><mrow><mi mathvariant="bold">g</mi><mi mathvariant="bold">t</mi></mrow><mrow><mi mathvariant="bold-italic">b</mi></mrow></msubsup><mo>,</mo><mn mathvariant="normal">5</mn></mrow></mfenced><mo>,</mo><mtext> </mtext><msubsup><mrow><mi mathvariant="bold-italic">Y</mi></mrow><mrow><mi mathvariant="bold">p</mi><mi mathvariant="bold">d</mi></mrow><mrow><mi mathvariant="bold-italic">b</mi><mo>,</mo><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">x</mi><mi mathvariant="bold-italic">t</mi></mrow></msubsup><mo>=</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi><mfenced separators="|"><mrow><msubsup><mrow><mi mathvariant="bold-italic">Y</mi></mrow><mrow><mi mathvariant="bold">p</mi><mi mathvariant="bold">d</mi></mrow><mrow><mi mathvariant="bold-italic">b</mi></mrow></msubsup><mo>,</mo><mn mathvariant="normal">5</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019118&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019116&type= 57.65800095 5.24933338 <math display="block" id="M13"><mi>P</mi><mo>=</mo><mfrac><mrow><msub><mrow><mfenced open="<" close=">" separators="|"><mrow><msubsup><mrow><mi mathvariant="bold-italic">Y</mi></mrow><mrow><mi mathvariant="bold">p</mi><mi mathvariant="bold">d</mi></mrow><mrow><mi mathvariant="bold-italic">b</mi></mrow></msubsup><mo>,</mo><mtext> </mtext><msubsup><mrow><mi mathvariant="bold-italic">Y</mi></mrow><mrow><mi mathvariant="bold">g</mi><mi mathvariant="bold">t</mi></mrow><mrow><mi mathvariant="bold-italic">b</mi><mo>,</mo><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">x</mi><mi mathvariant="bold-italic">t</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><mi>F</mi></mrow></msub></mrow><mrow><msub><mrow><mfenced open="‖" close="‖" separators="|"><mrow><msubsup><mrow><mi mathvariant="bold-italic">Y</mi></mrow><mrow><mi mathvariant="bold">p</mi><mi mathvariant="bold">d</mi></mrow><mrow><mi mathvariant="bold-italic">b</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac><mo>,</mo><mtext> </mtext><mi>R</mi><mo>=</mo><mfrac><mrow><msub><mrow><mfenced open="<" close=">" separators="|"><mrow><msubsup><mrow><mi mathvariant="bold-italic">Y</mi></mrow><mrow><mi mathvariant="bold">g</mi><mi mathvariant="bold">t</mi></mrow><mrow><mi mathvariant="bold-italic">b</mi></mrow></msubsup><mo>,</mo><mtext> </mtext><msubsup><mrow><mi mathvariant="bold-italic">Y</mi></mrow><mrow><mi mathvariant="bold">p</mi><mi mathvariant="bold">d</mi></mrow><mrow><mi mathvariant="bold-italic">b</mi><mo>,</mo><mi mathvariant="bold-italic">e</mi><mi mathvariant="bold-italic">x</mi><mi mathvariant="bold-italic">t</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><mi>F</mi></mrow></msub></mrow><mrow><msub><mrow><mfenced open="‖" close="‖" separators="|"><mrow><msubsup><mrow><mi mathvariant="bold-italic">Y</mi></mrow><mrow><mi mathvariant="bold">g</mi><mi mathvariant="bold">t</mi></mrow><mrow><mi mathvariant="bold-italic">b</mi></mrow></msubsup></mrow></mfenced></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019122&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019119&type= 53.84799957 13.71599960 <math display="block" id="M14"><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">B</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">y</mi></mrow></msub><mo>=</mo><mn mathvariant="normal">1</mn><mo>-</mo><mfrac><mrow><mn mathvariant="normal">2</mn><mi>P</mi><mi>R</mi></mrow><mrow><mi>P</mi><mo>+</mo><mi>R</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019125&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019123&type= 30.14133072 7.36600018 式中，掩模标签 <math id="M15"><msub><mrow><mi mathvariant="bold-italic">Y</mi></mrow><mrow><mi mathvariant="bold">g</mi><mi mathvariant="bold">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019127&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019126&type= 3.97933316 3.72533321 由元素 <math id="M16"><msub><mrow><mi>y</mi></mrow><mrow><mi mathvariant="normal">g</mi><mi mathvariant="normal">t</mi></mrow></msub><mo>∈</mo><mfenced open="{" close="}" separators="|"><mrow><mn mathvariant="normal">0,1</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019129&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019128&type= 15.83266735 4.23333359 构成，预测掩模 <math id="M17"><msub><mrow><mi mathvariant="bold-italic">Y</mi></mrow><mrow><mi mathvariant="bold">p</mi><mi mathvariant="bold">d</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019132&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019130&type= 4.57200003 3.72533321 由元素 <math id="M18"><msub><mrow><mi>y</mi></mrow><mrow><mi mathvariant="normal">p</mi><mi mathvariant="normal">d</mi></mrow></msub><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">0,1</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019138&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019135&type= 16.34066582 4.23333359 构成， <math id="M19"><msub><mrow><mfenced open="<" close=">" separators="|"><mrow><mi mathvariant="normal">*</mi><mo>,</mo><mi mathvariant="normal">*</mi></mrow></mfenced></mrow><mrow><mi>F</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019142&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019140&type= 10.15999985 4.91066647 表示矩阵点积求和运算， <math id="M20"><mi mathvariant="normal">p</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi><mfenced separators="|"><mrow><mi mathvariant="normal">*</mi><mo>,</mo><mi mathvariant="normal">p</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi><mo>_</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">z</mi><mi mathvariant="normal">e</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019144&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019143&type= 26.67000008 4.57200003 表示最大池化， <math id="M21"><mi>p</mi><mi>o</mi><mi>o</mi><mi>l</mi><mo>_</mo><mi>s</mi><mi>i</mi><mi>z</mi><mi>e</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019146&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019145&type= 12.69999981 3.47133350 为池化尺寸。建筑类、边界类、分割线类的损失分别是 <math display="block" id="M22"><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">b</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi></mrow></msub><mo>=</mo><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">F</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi></mrow></msub><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">e</mi></mrow></msub><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">J</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">d</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019148&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019147&type= 50.12266922 4.48733330 <math display="block" id="M23"><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">b</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></msub><mo>=</mo><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">F</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi></mrow></msub><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">e</mi></mrow></msub><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">J</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">d</mi></mrow></msub><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">B</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">y</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019150&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019149&type= 68.07199860 4.48733330 <math display="block" id="M24"><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi></mrow></msub><mo>=</mo><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">F</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi></mrow></msub><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">D</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">e</mi></mrow></msub><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">J</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">d</mi></mrow></msub><mo>+</mo><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">B</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">y</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019152&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019151&type= 65.95532990 4.48733330 式中， <math id="M25"><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019155&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019153&type= 20.31999969 4.57200003 为各损失项的权重。权衡建筑类和两个辅助类的重要性，网络总损失为 <math display="block" id="M26"><mi>L</mi><mo>=</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">b</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi></mrow></msub><mo>+</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">b</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></msub><mo>+</mo><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019157&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019156&type= 45.04266739 3.72533321 式中， <math id="M27"><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019159&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019158&type= 15.40933418 4.23333359 表示3个类的权重。 2.3 后处理 2 后处理是将网络输出的建筑、分割线和边界3类概率值转化为建筑区域标记的过程。首先合成3类概率为一个值，使预测结果合成为一个灰度图，合成公式为 <math display="block" id="M28"><mi>G</mi><mi>p</mi><mo>=</mo><mi>P</mi><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">b</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi></mrow></msub><mo>×</mo><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>P</mi><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi></mrow></msub></mrow></mfenced><mo>×</mo><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>k</mi><mi>P</mi><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">b</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019162&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019160&type= 62.39933777 5.24933338 式中， <math id="M29"><mi>P</mi><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">b</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi></mrow></msub><mo>,</mo><mtext> </mtext><mi>P</mi><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi></mrow></msub><mo>,</mo><mtext> </mtext><mi>P</mi><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">b</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></msub><mo>∈</mo><mfenced open="[" close="]" separators="|"><mrow><mn mathvariant="normal">0</mn><mo>,</mo><mtext> </mtext><mn mathvariant="normal">1</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019165&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019164&type= 44.11133575 4.23333359 分别表示建筑概率、分割线概率和边界概率； <math id="M30"><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>P</mi><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">e</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019170&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019168&type= 16.25600052 5.24933338 表示分割线约束，建筑不应与分割线重叠； <math id="M31"><mfenced separators="|"><mrow><mn mathvariant="normal">1</mn><mo>-</mo><mi>k</mi><mi>P</mi><msub><mrow><mi>d</mi></mrow><mrow><mi mathvariant="normal">b</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></mrow></msub></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019175&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019173&type= 19.98133469 5.24933338 表示边界约束，处于建筑边界的像素属于建筑的可能性较小，参数 <math id="M32"><mi>k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020251&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020249&type= 1.69333339 2.62466669 控制边界约束的权重。 后处理也分为训练和预测两个部分。训练阶段的流程如下： （1）对 <math id="M33"><mi>G</mi><mi>p</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019954&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019949&type= 3.97933316 3.47133350 图，以较小的阈值 <math id="M34"><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019924&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019921&type= 2.20133328 3.72533321 二值化，形成建筑标记 <math id="M35"><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019201&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019199&type= 3.04800010 3.72533321 （像素值大于 <math id="M36"><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019924&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019921&type= 2.20133328 3.72533321 标记为建筑，其余标为非建筑）。对建筑标记 <math id="M37"><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019201&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019199&type= 3.04800010 3.72533321 和 <math id="M38"><mi>G</mi><mi>p</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019954&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019949&type= 3.97933316 3.47133350 图采用基于标记的分水岭分割算法，获得预测图 <math id="M39"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019965&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019962&type= 3.47133350 3.72533321 。 （2）在 <math id="M40"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019215&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019212&type= 3.47133350 3.72533321 建筑标记范围内，分别以从小到大的阈值 <math id="M41"><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019220&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019218&type= 12.02266598 4.23333359 对 <math id="M42"><mi>G</mi><mi>p</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019954&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019949&type= 3.97933316 3.47133350 图二值化，形成初步建筑标记 <math id="M43"><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019229&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019227&type= 14.56266594 4.23333359 ，并分别结合 <math id="M44"><mi>G</mi><mi>p</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019954&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019949&type= 3.97933316 3.47133350 图分水岭分割，形成相应的分割结果 <math id="M45"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019241&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019237&type= 15.74800014 4.23333359 ，都是在 <math id="M46"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019965&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019962&type= 3.47133350 3.72533321 建筑标记范围内的建筑细分。 （3）对分割结果 <math id="M47"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019252&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019249&type= 21.92866707 4.23333359 中每一个连通区域（视作一个建筑），计算与真实标签的 <math id="M48"><mi>I</mi><mi>O</mi><mi>U</mi><mo>=</mo><mfrac><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi><mo>+</mo><mi mathvariant="normal">F</mi><mi mathvariant="normal">P</mi><mo>+</mo><mi mathvariant="normal">F</mi><mi mathvariant="normal">N</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019258&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019256&type= 33.18933105 7.36600018 ，若 <math id="M49"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020161&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020159&type= 6.18066692 2.70933342 小于0.5的， <math id="M50"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020161&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020159&type= 6.18066692 2.70933342 值改为0；其中 <math id="M51"><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019275&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019272&type= 4.14866638 2.62466669 表示正确检测（ <math id="M52"><mi mathvariant="normal">T</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">e</mi><mtext> </mtext><mi mathvariant="normal">P</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">e</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019286&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019281&type= 19.04999924 2.79399991 ）； <math id="M53"><mi mathvariant="normal">F</mi><mi mathvariant="normal">P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019294&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019290&type= 4.14866638 2.62466669 表示误检（ <math id="M54"><mi mathvariant="normal">F</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mtext> </mtext><mi mathvariant="normal">P</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">e</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019497&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019495&type= 20.06599998 2.79399991 ）； <math id="M55"><mi mathvariant="normal">F</mi><mi mathvariant="normal">N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019310&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019305&type= 4.57200003 2.70933342 表示漏检（ <math id="M56"><mi mathvariant="normal">F</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mtext> </mtext><mi mathvariant="normal">N</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">e</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019513&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019510&type= 21.33600044 3.47133350 ）。 （4）以上一步的建筑区域的 <math id="M57"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020161&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020159&type= 6.18066692 2.70933342 为目标值，对每个建筑区域，分别经验性选取面积、面积周长比、长短轴、邻域信息等41个常用区域及邻域相关的描述特征，训练梯度提升回归树。特征计算依赖于skimge库（Van Der Walt等，2014）的regionprops函数，该函数为每一个连通区域计算囊括上述特征的数十个属性值。 预测阶段，后处理流程如下： （1）对 <math id="M58"><mi>G</mi><mi>p</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019954&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019949&type= 3.97933316 3.47133350 图，经训练阶段的第1—2步处理，获得分割结果 <math id="M59"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019334&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019332&type= 21.92866707 4.23333359 ，对结果的每一个连通区域，用训练阶段第4步的同样特征和训练好的回归树预测 <math id="M60"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020161&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020159&type= 6.18066692 2.70933342 。 （2）对于 <math id="M61"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019965&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019962&type= 3.47133350 3.72533321 的每一个连通区域，选取 <math id="M62"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019352&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019351&type= 21.92866707 4.23333359 中的 <math id="M63"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020161&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020159&type= 6.18066692 2.70933342 平均值最大的分割结果，替换原连通区域，形成最终分割结果。 （3）对最终分割结果的每一个区域，若对应的 <math id="M64"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020161&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020159&type= 6.18066692 2.70933342 大于接受阈值 <math id="M65"><msub><mrow><mi>t</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019370&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019366&type= 2.20133328 3.72533321 ，或该区域概率均值大于概率阈值 <math id="M66"><msub><mrow><mi>t</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019379&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019375&type= 2.20133328 3.72533321 ，则该区域标记为建筑。 3 实验结果与分析 1 本论文实验环境是Linux系统下以Tensorflow为后端的keras框架（Chollet，2015）。根据多次实验结果，设置建筑、边界、分割线的损失权重 <math id="M67"><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>α</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">1</mn><mo>,</mo><mtext> </mtext><mn mathvariant="normal">0.4</mn><mo>,</mo><mtext> </mtext><mn mathvariant="normal">0.4</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019386&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019382&type= 35.81399918 4.23333359 ，焦点损失、骰子损失、Jaccard损失、边界损失的权重 <math id="M68"><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">1</mn><mo>/</mo><mn mathvariant="normal">3</mn><mo>,</mo><mtext> </mtext><mn mathvariant="normal">1</mn><mo>/</mo><mn mathvariant="normal">3</mn><mo>,</mo><mtext> </mtext><mn mathvariant="normal">1</mn><mo>/</mo><mn mathvariant="normal">3</mn><mo>,</mo><mtext> </mtext><mn mathvariant="normal">1</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019394&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019390&type= 48.25999832 4.57200003 。网络使用Nadam（ Dozat，2016 Dozat，2016 ）优化器，初始学习率设置为5×10 -4 ，在第10、50个周期，学习率除以5。网络总共训练80个周期，每个周期迭代250次，共2万次迭代。网络的输入尺寸为196×196，批尺寸为16。后处理中，融合处理参数 <math id="M69"><mi>k</mi><mo>=</mo><mn mathvariant="normal">1</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019400&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019396&type= 7.70466709 2.62466669 ，建筑标记阈值 <math id="M70"><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">0.55</mn><mo>,</mo><mtext> </mtext><mn mathvariant="normal">0.65</mn><mo>,</mo><mtext> </mtext><mn mathvariant="normal">0.75</mn><mo>,</mo><mtext> </mtext><mn mathvariant="normal">0.85</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019407&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019404&type= 54.94866943 4.23333359 ，阈值 <math id="M71"><msub><mrow><mi>t</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>t</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>t</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">0.45</mn><mo>,</mo><mtext> </mtext><mn mathvariant="normal">0.5</mn><mo>,</mo><mtext> </mtext><mn mathvariant="normal">0.85</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019414&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019411&type= 39.03133011 4.23333359 。实验数据已在2.1节介绍。本文采用四折交叉验证比较实验效果，即每一次交叉验证使用27张尺寸5000×5000的图像为训练集，剩余9张为测试集，分别训练和评估，并且所有实验使用相同的随机数。 3.1 指标 2 根据经验（ Maggiori等，2017 Maggiori等，2017 ），本文使用召回率 <math id="M72"><mi mathvariant="normal">R</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">l</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019422&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019419&type= 9.48266602 2.70933342 ，准确率 <math id="M73"><mi mathvariant="normal">P</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019427&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019424&type= 13.54666710 2.70933342 ， <math id="M74"><msub><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019432&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019429&type= 15.57866764 3.80999994 和 <math id="M75"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020161&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020159&type= 6.18066692 2.70933342 等指标衡量网络性能，计算公式如下： <math display="block" id="M76"><mi mathvariant="normal">R</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">l</mi><mo>=</mo><mtext> </mtext><mfrac><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi><mo>+</mo><mi mathvariant="normal">F</mi><mi mathvariant="normal">P</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019445&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019441&type= 27.43199921 7.28133297 <math display="block" id="M77"><mi mathvariant="normal">P</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi><mo>=</mo><mfrac><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi><mo>+</mo><mi mathvariant="normal">F</mi><mi mathvariant="normal">N</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019452&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019449&type= 31.91933441 7.36600018 <math display="block" id="M78"><msub><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mo>=</mo><mfrac><mrow><mn mathvariant="normal">2</mn><mo>×</mo><mi mathvariant="normal">P</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi><mo>×</mo><mi mathvariant="normal">R</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">l</mi></mrow><mrow><mi mathvariant="normal">P</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi><mo>+</mo><mi mathvariant="normal">R</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">l</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019460&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019456&type= 54.61000061 7.36600018 <math display="block" id="M79"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi><mo>=</mo><mfrac><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi></mrow><mrow><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi><mo>+</mo><mi mathvariant="normal">F</mi><mi mathvariant="normal">P</mi><mo>+</mo><mi mathvariant="normal">F</mi><mi mathvariant="normal">N</mi></mrow></mfrac></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019468&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019463&type= 33.18933105 7.36600018 式中， <math id="M80"><mi mathvariant="normal">T</mi><mi mathvariant="normal">P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019476&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019473&type= 4.14866638 2.62466669 表示正确检测（ <math id="M81"><mi mathvariant="normal">T</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">e</mi><mtext> </mtext><mi mathvariant="normal">P</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">e</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019484&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019479&type= 19.04999924 2.79399991 ）； <math id="M82"><mi mathvariant="normal">F</mi><mi mathvariant="normal">P</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019492&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019489&type= 4.14866638 2.62466669 表示误检（ <math id="M83"><mi mathvariant="normal">F</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mtext> </mtext><mi mathvariant="normal">P</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">e</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019497&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019495&type= 20.06599998 2.79399991 ）； <math id="M84"><mi>F</mi><mi>N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019507&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019503&type= 4.74133301 2.62466669 表示漏检（ <math id="M85"><mi mathvariant="normal">F</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mtext> </mtext><mi mathvariant="normal">N</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">e</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019513&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019510&type= 21.33600044 3.47133350 ）。召回率反映真实样本遗漏比率，准确率反映预测结果误检比率。 <math id="M86"><msub><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019520&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019516&type= 15.40933418 3.80999994 是精确度和召回率的综合测量值。 <math id="M87"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019528&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019523&type= 6.18066692 2.70933342 是预测结果与真实标签的重叠比率。 本文使用新指标评估后处理结果。对建筑标签中每一个建筑，计算其与预测结果中每一个建筑的 <math id="M88"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020161&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020159&type= 6.18066692 2.70933342 ，并将最大值作为该建筑实例的 <math id="M89"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020161&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020159&type= 6.18066692 2.70933342 ，若 <math id="M90"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019546&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019542&type= 6.18066692 2.70933342 > 0.5，视为该建筑实例被检测；计算其与预测结果中每一个建筑的重叠面积，占该建筑面积的比例，并将最大值记为该建筑实例的 <math id="M91"><mi mathvariant="normal">C</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019554&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019551&type= 8.46666718 2.70933342 值。由此延伸实例召回率Recallc（ Hosang等，2016 Hosang等，2016 ）、覆盖比例P c 及 <math id="M92"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><msub><mrow><mi mathvariant="normal">U</mi></mrow><mrow><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020105&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020104&type= 9.39799976 3.80999994 指标： <math display="block" id="M93"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><msub><mrow><mi mathvariant="normal">U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><munder><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi>j</mi></mrow></munder><mfenced separators="|"><mrow><mfrac><mrow><mi mathvariant="bold-italic">g</mi><msub><mrow><mi mathvariant="bold-italic">t</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub><mo>⋂</mo><mi mathvariant="bold-italic">p</mi><msub><mrow><mi mathvariant="bold-italic">d</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msub></mrow><mrow><mi mathvariant="bold-italic">g</mi><msub><mrow><mi mathvariant="bold-italic">t</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub><mo>⋃</mo><mi mathvariant="bold-italic">p</mi><msub><mrow><mi mathvariant="bold-italic">d</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msub></mrow></mfrac></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019570&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019567&type= 35.56000137 10.15999985 <math display="block" id="M94"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><msub><mrow><mi mathvariant="normal">U</mi></mrow><mrow><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi></mrow></msub><mo>=</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi>N</mi></mrow></mfrac><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi></mrow><mrow><mi>N</mi></mrow></munderover></mstyle><mrow><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><msub><mrow><mi mathvariant="normal">U</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mo>,</mo></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019576&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019573&type= 30.31066895 8.29733276 <math display="block" id="M95"><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">c</mi></mrow></msub><mo>=</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi>N</mi></mrow></mfrac><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi></mrow><mrow><mi>N</mi></mrow></munderover></mstyle><mrow><mi mathvariant="double-struck">I</mi></mrow><mfenced separators="|"><mrow><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><msub><mrow><mi mathvariant="normal">U</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>></mo><mn mathvariant="normal">0.5</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019583&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019580&type= 36.74533463 8.29733276 <math display="block" id="M96"><mi mathvariant="normal">C</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">e</mi><msub><mrow><mi mathvariant="normal">r</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><munder><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">x</mi></mrow><mrow><mi>j</mi></mrow></munder><mfenced separators="|"><mrow><mfrac><mrow><mi mathvariant="bold-italic">g</mi><msub><mrow><mi mathvariant="bold-italic">t</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub><mo>⋂</mo><mi mathvariant="bold-italic">p</mi><msub><mrow><mi mathvariant="bold-italic">d</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msub></mrow><mrow><mi mathvariant="bold-italic">g</mi><msub><mrow><mi mathvariant="bold-italic">t</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub></mrow></mfrac></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019590&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019586&type= 37.84600067 9.90600014 <math display="block" id="M97"><msub><mrow><mi>P</mi></mrow><mrow><mi mathvariant="normal">c</mi></mrow></msub><mo>=</mo><mfrac><mrow><mn mathvariant="normal">1</mn></mrow><mrow><mi>N</mi></mrow></mfrac><mstyle displaystyle="true"><munderover><mo largeop="true">∑</mo><mrow><mi>i</mi></mrow><mrow><mi>N</mi></mrow></munderover></mstyle><mrow><mi mathvariant="double-struck">I</mi><mfenced separators="|"><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">e</mi><msub><mrow><mi mathvariant="normal">r</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>></mo><mn mathvariant="normal">0.5</mn></mrow></mfenced></mrow></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019595&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019593&type= 38.86199951 8.29733276 式中， R c 为实例召回率， P c 为覆盖比例， <math id="M98"><mi mathvariant="bold-italic">g</mi><msub><mrow><mi mathvariant="bold-italic">t</mi></mrow><mrow><mi mathvariant="bold-italic">i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019602&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019600&type= 4.06400013 4.57200003 表示真实标签的第 <math id="M99"><mi>i</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019609&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019605&type= 1.10066664 2.62466669 个建筑掩模， <math id="M100"><mi mathvariant="bold-italic">p</mi><msub><mrow><mi mathvariant="bold-italic">d</mi></mrow><mrow><mi mathvariant="bold-italic">j</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019616&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019612&type= 4.40266657 4.57200003 表示预测结果的第 <math id="M101"><mi>j</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019625&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019619&type= 0.84666669 3.47133350 个建筑掩模， <math id="M102"><mi>N</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019632&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019629&type= 2.53999996 2.62466669 为建筑总数， <math id="M103"><mi mathvariant="double-struck">I</mi><mfenced separators="|"><mrow><mi>*</mi></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019640&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019636&type= 6.51933336 3.72533321 为示性函数。根据 <math id="M104"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><msub><mrow><mi mathvariant="normal">U</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019650&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019644&type= 6.94266701 3.80999994 与 <math id="M105"><mi mathvariant="normal">C</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">v</mi><mi mathvariant="normal">e</mi><msub><mrow><mi mathvariant="normal">r</mi></mrow><mrow><mi>i</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019661&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019656&type= 9.14400005 3.80999994 的定义，若真实标签的建筑 <math id="M106"><mi>A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019695&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019692&type= 2.11666679 2.62466669 与预测结果的建筑 <math id="M107"><mi>B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019682&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019675&type= 2.28600001 2.62466669 的 <math id="M108"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019691&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019686&type= 6.18066692 2.70933342 > 0.5，则建筑 <math id="M109"><mi>A</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019695&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019692&type= 2.11666679 2.62466669 至少50%像素与建筑 <math id="M110"><mi>B</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019709&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019703&type= 2.28600001 2.62466669 重叠，即覆盖比例是实例召回率的上界。 3.2 数据预处理与边界损失 2 本节探究数据预处理、边界损失与网络性能的关系，比较建筑类网络，无边界损失的网络，本文网络和基准网络的建筑预测图。由 Chatterjee和Poullis（2019） Chatterjee和Poullis（2019） ，基准网络使用原始的ICT-Net，网络最后一层仅预测建筑类别，使用交叉熵作为损失函数；建筑类网络，与基准网络结构相同，使用 <math id="M111"><msub><mrow><mi>L</mi></mrow><mrow><mi mathvariant="normal">u</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">b</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019719&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019713&type= 6.51933336 3.72533321 作为损失函数；未应用边界损失的网络，与本文网络结构相同，修改边界损失权重 <math id="M112"><msub><mrow><mi>β</mi></mrow><mrow><mn mathvariant="normal">4</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019727&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019723&type= 3.04800010 4.48733330 为0。 表1 表1 显示比较结果，与基准、建筑类和无边界损失的网络相比，本文网络在 <math id="M113"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020161&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020159&type= 6.18066692 2.70933342 、召回率和 <math id="M114"><msub><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019743&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019738&type= 15.57866764 3.80999994 表现较优，其中本文网络相比基准网络提高 <math id="M115"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020161&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020159&type= 6.18066692 2.70933342 约1%，对于 <math id="M116"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><msub><mrow><mi mathvariant="normal">U</mi></mrow><mrow><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020105&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020104&type= 9.39799976 3.80999994 和实例召回率，本文网络高于前三者至少2.8%和5.7%，表明应用了数据预处理和边界损失的本文网络能更准确地检测建筑实例。 注： 黑体表示最优值。 指标\方案 基准网络 建筑类网络 无边界损失网络 本文网络 <math id="M117"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020175&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020174&type= 4.74133301 2.03200006 0.762 0.766 0.769 0.772 准确率 <math id="M118"><mi mathvariant="normal">P</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020168&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020166&type= 10.32933331 2.03200006 0.873 0.869 0.874 0.873 召回率 <math id="M119"><mi mathvariant="normal">R</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">l</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019784&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019781&type= 7.19666624 2.03200006 0.856 0.865 0.864 0.869 <math id="M120"><msub><mrow><mi>F</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019792&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019788&type= 12.02266598 2.87866688 0.864 0.867 0.869 0.871 <math id="M121"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><msub><mrow><mi mathvariant="normal">U</mi></mrow><mrow><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019799&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019795&type= 7.53533268 2.87866688 0.547 0.532 0.581 0.609 实例召回率Recallc/% 57.2 53.6 63.9 69.6 本节选取两个子区域进一步比较，如 图4 图4 ，相较于其他3种网络，本文网络提取的建筑边界形态更接近真实标签。 1,2,3,4,5,6; 3.3 后处理 2 本文选取一典型示例，阐明后处理的具体步骤。 如 图5 图5 ，将 图5（a） 图5（a） 遥感影像输入网络，预测3类概率，其中对 图5（c） 图5（c） 网络预测的建筑类概率，以0.5二值化形成 图5（d） 图5（d） 建筑预测图。同时合成3类概率形成 图5 图5 （e） <math id="M122"><mi>G</mi><mi>p</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019954&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019949&type= 3.97933316 3.47133350 图，以标记阈值 <math id="M123"><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019924&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019921&type= 2.20133328 3.72533321 形成 图5（f） 图5（f） 预测图 <math id="M124"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019965&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019962&type= 3.47133350 3.72533321 。以标记阈值 <math id="M125"><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019939&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019933&type= 2.20133328 3.72533321 形成 图5（g） 图5（g） 建筑标记 <math id="M126"><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019959&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019956&type= 3.04800010 3.72533321 。采用基于标记的分水岭分割算法以 <math id="M127"><mi>G</mi><mi>p</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019954&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019949&type= 3.97933316 3.47133350 图和 <math id="M128"><msub><mrow><mi>L</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019959&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019956&type= 3.04800010 3.72533321 分割 <math id="M129"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019965&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33019962&type= 3.47133350 3.72533321 ，形成建筑实例，每个实例以回归树预测 <math id="M130"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020161&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020159&type= 6.18066692 2.70933342 。将每一个 <math id="M131"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020161&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020159&type= 6.18066692 2.70933342 大于接受阈值的实例标记为建筑，形成 图5（h） 图5（h） 后处理预测图，其中不同颜色表示不同建筑实例。 1,2,3,4;5,6,7,8; 为验证后处理性能，比较本文网络、合成处理和后处理的结果：建筑预测图、预测图 <math id="M138"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020098&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020096&type= 3.47133350 3.72533321 和后处理预测图，并与基准网络的建筑预测图比较。对比结果如 表2 表2 ，后处理与本文网络相比，提高实例召回率10.5%，提高 <math id="M139"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><msub><mrow><mi mathvariant="normal">U</mi></mrow><mrow><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020102&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020099&type= 9.39799976 3.80999994 4.5%，与基准网络相比，提高实例召回率22.9%，提高 <math id="M140"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><msub><mrow><mi mathvariant="normal">U</mi></mrow><mrow><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020105&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020104&type= 9.39799976 3.80999994 10.7%，表明后处理在本文网络的基础上进一步提高建筑检测精度。 注： 黑体表示最优值。 指标\阶段 基准网络 本文网络 合成处理 后处理 <math id="M141"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><msub><mrow><mi mathvariant="normal">U</mi></mrow><mrow><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020109&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020107&type= 7.53533268 2.87866688 0.547 0.609 0.628 0.654 实例召回率/% 57.2 69.6 74.4 80.1 本文以两个典型例子展示本文方法各阶段的结果，进一步说明后处理的作用，如 图6 图6 ，红色框展示结果改善的区域。 图6（e） 图6（e） 中蓝色建筑显示后处理从“粘连”的掩模中区分建筑实例，其检测结果与参考标签基本吻合。绿色建筑处于阴影或树荫下，未能被本文网络和后处理检测。 1,2,3,4,5;6; 4 讨论 1 4.1 网络结构 2 本节讨论网络结构的性能差异，选用U-net和FC-DenseNet56（ Jégou等，2017 Jégou等，2017 ），如2.2节对ICT-Net修改，改变网络最后一层结构，并应用3类标签和边界损失。 表3 表3 ，显示ICT-Net相较于U-net和FC-DenseNet56，在准确率、 <math id="M142"><msub><mrow><mi>F</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020158&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020155&type= 15.57866764 3.80999994 和 <math id="M143"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020161&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020159&type= 6.18066692 2.70933342 上较优， 图7 图7 呈现训练过程中的损失和指标，间接证明了上述结论。 注： 黑体表示最优值。 方法 召回率 <math id="M144"><mi mathvariant="normal">R</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">l</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020165&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020163&type= 7.19666624 2.03200006 准确率 <math id="M145"><mi mathvariant="normal">P</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020168&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020166&type= 10.32933331 2.03200006 <math id="M146"><msub><mrow><mi>F</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>-</mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020172&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020170&type= 12.02266598 2.87866688 <math id="M147"><mi mathvariant="normal">I</mi><mi mathvariant="normal">O</mi><mi mathvariant="normal">U</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020175&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020174&type= 4.74133301 2.03200006 U-net 0.859 0.859 0.859 0.754 FC-DenseNet56 0.872 0.859 0.865 0.763 ICT-Net 0.869 0.873 0.871 0.772 4.2 参数选取 2 由2.3节所述，合成公式参数 <math id="M148"><mi>k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020251&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020249&type= 1.69333339 2.62466669 和建筑标记阈值 <math id="M149"><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020196&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020194&type= 17.01799965 4.23333359 对后处理性能有较大影响，本节讨论参数的选取。 针对建筑标记阈值 <math id="M150"><mi mathvariant="normal">t</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">d</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020201&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020198&type= 13.54666710 2.70933342 ，固定合成公式参数 <math id="M151"><mi>k</mi><mo>=</mo><mn mathvariant="normal">1</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020204&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020202&type= 8.04333401 2.62466669 ，选取建筑标记阈值 <math id="M152"><mi mathvariant="normal">t</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">d</mi><mo>∈</mo><mfenced open="{" close="" separators="|"><mrow><mn mathvariant="normal">0.05</mn><mo>,</mo><mtext> </mtext><mn mathvariant="normal">0.1</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020208&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020206&type= 32.76599884 3.89466691 ， <math id="M153"><mo>…</mo><mo>,</mo><mtext> </mtext><mn mathvariant="normal">0.95</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020212&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020211&type= 12.86933327 3.13266683 共19个值，生成预测图 <math id="M154"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020217&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020215&type= 3.47133350 3.72533321 ，计算实例召回率和覆盖比例。如 图8（a） 图8（a） 所示，随着建筑标记阈值的提高，覆盖比例逐渐减小，实例召回率逐渐增大。当建筑标记阈值较小时，实例召回率较低，后处理无法充分利用网络输出的概率信息，且覆盖比例与召回率的差距过大，易带来过多噪音和预测负担；当建筑标记阈值过大时，后处理倾向于对预测图过度分割，覆盖比例衰减较大，覆盖比例作为实例召回率的上界限制了后处理的提升。权衡实例召回率和覆盖比例，本文选取四个建筑标记阈值 <math id="M155"><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">0.55</mn><mo>,</mo><mtext> </mtext><mn mathvariant="normal">0.65</mn><mo>,</mo><mtext> </mtext><mn mathvariant="normal">0.75</mn><mo>,</mo><mtext> </mtext><mn mathvariant="normal">0.85</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020222&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020220&type= 52.74732971 4.23333359 ，以 <math id="M156"><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">0.55</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020226&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020224&type= 13.20800018 3.80999994 对应的建筑标记形成预测图 <math id="M157"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020229&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020228&type= 3.47133350 3.72533321 ，以 <math id="M158"><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">1</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">2</mn></mrow></msub><mo>,</mo><mtext> </mtext><msub><mrow><mi>l</mi></mrow><mrow><mn mathvariant="normal">3</mn></mrow></msub><mo>=</mo><mn mathvariant="normal">0.65</mn><mo>,</mo><mtext> </mtext><mn mathvariant="normal">0.75</mn><mo>,</mo><mtext> </mtext><mn mathvariant="normal">0.85</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020233&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020231&type= 41.23266602 4.23333359 形成的建筑标记对预测图 <math id="M159"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020238&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020236&type= 3.47133350 3.72533321 进一步分割。 针对参数 <math id="M160"><mi>k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020240&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020239&type= 1.69333339 2.62466669 ，固定建筑标记阈值 <math id="M161"><mi mathvariant="normal">t</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">d</mi><mo>=</mo><mn mathvariant="normal">0.55</mn></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020242&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020241&type= 24.46866608 2.70933342 ，选取 <math id="M162"><mi>k</mi><mo>∈</mo><mfenced open="{" close="}" separators="|"><mrow><mn mathvariant="normal">0</mn><mo>,</mo><mtext> </mtext><mn mathvariant="normal">0.1</mn><mo>,</mo><mtext> </mtext><mo>…</mo><mo>,</mo><mtext> </mtext><mn mathvariant="normal">1</mn></mrow></mfenced></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020244&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020243&type= 28.44799995 3.89466691 共11个值，生成预测图 <math id="M163"><msub><mrow><mi>P</mi></mrow><mrow><mn mathvariant="normal">0</mn></mrow></msub></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020246&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020245&type= 3.47133350 3.72533321 ，计算实例召回率和覆盖比例。如 图8（b） 图8（b） ，实例召回率随 <math id="M164"><mi>k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020251&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020249&type= 1.69333339 2.62466669 逐渐增大，而覆盖比例下降较小，本文选取 <math id="M165"><mi>k</mi></math> http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020251&type= http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=33020249&type= 1.69333339 2.62466669 =1。 1,2;3; 5 结论 1 本文针对密集建筑区域的建筑检测，提出了一种结合神经网络自下而上分组的分水岭算法。该方法通过数据预处理，利用原建筑标签生成两类辅助掩模标签；在性能较优的ICT-Net基础上，修改网络结构和损失函数，针对两类辅助标签添加边界损失；然后在网络预测结果的基础上，通过一个结合分水岭算法和梯度提升回归树的后处理完成建筑实例的准确检测。实验表明，在中小建筑密集的城市区域，本文检测方案能有效解决密集建筑掩模“粘连”的问题，准确定位建筑边界，检测建筑实例，检测效果明显优于原始的ICT-Net网络。本文方法的优势如下： （1）数据预处理生成的两类辅助标签，注重边界特征，可丰富边界信息。 （2）经修改的网络结构、添加的边界损失函数充分考虑建筑物特点和边界优化的需要，相较于基准网络，本文网络提取的建筑边界形态更接近真实标签。 （3）后处理借助分水岭分割算法可利用网络预测的概率信息进一步优化建筑边界，采用梯度提升回归树可筛选最优的分割结果，因此后处理在本文网络的基础上可使建筑实例的检测精度更高。 本文方法目前仅引入了建筑边界信息，未考虑建筑的内部结构，今后将在这一方面深入探索。 参考文献（References） Bokhovkin A and Burnaev E . 2019 . 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杨必胜 武汉大学 测绘遥感信息工程国家重点实验室;时空数据智能获取技术与应用教育部工程研究中心
韩旭 武汉大学 测绘遥感信息工程国家重点实验室;时空数据智能获取技术与应用教育部工程研究中心
董震 武汉大学 测绘遥感信息工程国家重点实验室;时空数据智能获取技术与应用教育部工程研究中心
郑超磊 中国科学院空天信息创新研究院 遥感科学国家重点实验室
贾立 中国科学院空天信息创新研究院 遥感科学国家重点实验室
胡光成 中国科学院空天信息创新研究院 遥感科学国家重点实验室
张虎 中国科学院空天信息创新研究院 遥感科学国家重点实验室;中国科学院大学资源与环境学院
李静 中国科学院空天信息创新研究院 遥感科学国家重点实验室;中国科学院大学资源与环境学院
相关机构
武汉大学 测绘遥感信息工程国家重点实验室
时空数据智能获取技术与应用教育部工程研究中心
中国科学院空天信息创新研究院 遥感科学国家重点实验室
中国科学院空天信息创新研究院 遥感科学国家重点实验室
中国科学院大学 资源与环境学院
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