{ "source_file": "0930", "source_platform": "知乎专栏", "author": "stone", "title_listed": "语义分割之 U-Net", "keywords": "语义分割,U-Net", "domain": "图像处理", "content_type": "论文精读", "is_paid_flag": "否", "url": "https://zhuanlan.zhihu.com/p/37804107", "publish_date": "2018", "corpus_stage": "应用", "notes": "U-Net 语义分割论文解读", "id": "3fb832a93bd4", "collected_at": "2026-10-02T18:43:59", "title": "语义分割之U-net - 知乎", "body_markdown": "[![](https://zhuanlan.zhihu.com/p/37804107)](javascript:void\\(0\\))\n![ZhiHu logo](../images/body-e1fa91dbdb48b8055184.png)\n[](https://www.zhihu.com)\n[关注](https://www.zhihu.com/signin?next=%2Ffollow)[推荐](https://www.zhihu.com/signin?next=%2F)[热榜](https://www.zhihu.com/signin?next=%2Fhot)[专栏](https://www.zhihu.com/signin?next=%2Fcolumn-square)[圈子](https://www.zhihu.com/signin?next=%2Fring-feeds)[AI WorksBeta ](https://www.zhihu.com/project-square)[故事](https://www.zhihu.com/fiore/h5/vip-web)\n​\n[直答](https://zhida.zhihu.com/)\n切换模式\n登录/注册\n语义分割之U-net\n首发于[图像语义分割](https://www.zhihu.com/column/c_197474183)\n切换模式\n![语义分割之U-net](../images/000.img)\n# 语义分割之U-net\n[![stone](../images/013.jpg)](https://www.zhihu.com/people/big-big-stone)\n[stone](https://www.zhihu.com/people/big-big-stone)\n收藏之前点个赞呗\n[收录于 · 图像语义分割](https://www.zhihu.com/column/c_197474183)\n28 人赞同了该文章\n## 更多语义分割文章，请看专栏：[图像语义分割](https://zhuanlan.zhihu.com/c_197474183)\n## U-Net\n## 论文信息\n论文地址：[U-Net: Convolutional Networks for Biomedical Image Segmentation](https://zhuanlan.zhihu.com/p/37804107/edit)\n发表时间：18 May 2015\n## 创新点\n深度网络通常需要大量的数据进行训练，当样本量较少的情况下，[深度网络](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=2&q=%E6%B7%B1%E5%BA%A6%E7%BD%91%E7%BB%9C&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLmt7HluqbnvZHnu5wiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjIsInpkX3Rva2VuIjpudWxsfQ.cNQq22OGBk9BANq-dyKgrzrOdABIeTkP7PKotTtS_mA&zhida_source=entity)可能表现没那么好。对于这个问题，本文提出了新的[网络架构](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E7%BD%91%E7%BB%9C%E6%9E%B6%E6%9E%84&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLnvZHnu5zmnrbmnoQiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.o_mSWjlg_g_3YtyR3AzbDrRfSAc74S-jpiLnNcTe8LE&zhida_source=entity)和图像增强策略。网络架构包括encoder和[decoder](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=decoder&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiJkZWNvZGVyIiwiemhpZGFfc291cmNlIjoiZW50aXR5IiwiY29udGVudF9pZCI6NzMxMjg5OSwiY29udGVudF90eXBlIjoiQXJ0aWNsZSIsIm1hdGNoX29yZGVyIjoxLCJ6ZF90b2tlbiI6bnVsbH0.hQlCZEc8dHa5XvjBb1wanjxtfnM6j99q7fGS8O0EwZw&zhida_source=entity)（论文中称为浓缩路径(contracting path)和扩展路径(expanding path)，实际上就是encoder和decoder），encoder可以有效地捕捉上下文信息，而decoder可以较好地预测位置信息。\n## 模型\n## 1. 模型设计思想\nU-net是基于[FCN](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=FCN&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiJGQ04iLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.On5AO9_vhtOMlsrCmiwsNd4M4tIjhvDV6FNaLJ-Ygo4&zhida_source=entity)网络的思想设计的，整个网络只有[卷积层](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E5%8D%B7%E7%A7%AF%E5%B1%82&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLljbfnp6_lsYIiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.o9yeEdW8iFD9oU6bRbIieoOLZHFsHgtq3kHfeFazaDE&zhida_source=entity)，而没有[全连接层](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E5%85%A8%E8%BF%9E%E6%8E%A5%E5%B1%82&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLlhajov57mjqXlsYIiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.YSzKILAVD6vH07DWi28BNcj3XMcUgpA8lw8jDoZSMmU&zhida_source=entity)。\n在FCN中：网络的浓缩路径，图像分辨率逐渐降低，上下文信息会逐渐增强。在扩展路径中，通过[上采样](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E4%B8%8A%E9%87%87%E6%A0%B7&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLkuIrph4fmoLciLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.x5T8LCqsnw-BzNj6hRe1bMRhwXVmhOTmpsYWjT9h7Zc&zhida_source=entity)的方式，让[特征图](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E7%89%B9%E5%BE%81%E5%9B%BE&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLnibnlvoHlm74iLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.f91_1Zl6sbvbOgDU7g1Uv3wJrzhbHqw3NKWAtDA31Go&zhida_source=entity)的分辨率逐渐增大。同时，为了结合低层feature map的强位置信息，将浓缩路径中的相应部分结合到扩展路径中。这种架构可以较好地进行位置定位。\n![](../images/004.jpg)\nU-net做的修改有：\n 1. 在上采样部分，feature map的通道数非常大，作者认为这样可以将上下文信息传递到分辨率更高的层当中。这样做的一个结果就是它基本上和浓缩路径对称了，因此看上去像一个U形的结构。\n 2. 为了预测图像边界区域的像素点，采用[overlap-tile策略](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=overlap-tile%E7%AD%96%E7%95%A5&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiJvdmVybGFwLXRpbGXnrZbnlaUiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.ib6gX4EQmjA1dd1WxgUbikbs_hQHG8IiBg8wQ1FpKsk&zhida_source=entity)补全缺失的context。\n 3. 由于训练数据太少，采用大量弹性形变的方式增强数据。这可以让模型更好学习形变不变性。这种增强方式对于医学图像来说很重要。\n 4. 在[细胞分割](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E7%BB%86%E8%83%9E%E5%88%86%E5%89%B2&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLnu4bog57liIblibIiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.PHOo97dPhx7ZegI3uuVtyRQh2YqZs0pqUirQ0eOcbfM&zhida_source=entity)任务中的另一个挑战是，如何将同类别的相互接触的目标分开。本文提出了使用一种带权重的损失([weighted loss](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=weighted+loss&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiJ3ZWlnaHRlZCBsb3NzIiwiemhpZGFfc291cmNlIjoiZW50aXR5IiwiY29udGVudF9pZCI6NzMxMjg5OSwiY29udGVudF90eXBlIjoiQXJ0aWNsZSIsIm1hdGNoX29yZGVyIjoxLCJ6ZF90b2tlbiI6bnVsbH0.W3WipArjO8SSR-P04yYhF0qkLgWas9z4T0YBHn28oBQ&zhida_source=entity))。在[损失函数](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E6%8D%9F%E5%A4%B1%E5%87%BD%E6%95%B0&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLmjZ_lpLHlh73mlbAiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.u1yzS2xHe75Aw4fUGyS3d4o5_pgsK2ov4fxu5r66rq8&zhida_source=entity)中，分割相互接触的细胞像素获得了更大的权重。\n\n\n![](../images/005.jpg)\n## 2. 网络结构\n网络结构包括浓缩路径和扩展路径。\n浓缩路径：\n 1. 注意图像输入是经过tile的。因此网络的输出是和图像的输入大小是不一样的。\n 2. 每经过两个3x3conv（没有padding）之后，会跟上一个2x2的max-pooling进行[下采样](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E4%B8%8B%E9%87%87%E6%A0%B7&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLkuIvph4fmoLciLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.GDgioToaOSmKGQ5M1FkSXK9_1Rxe6C7eXWYzHjKhQCw&zhida_source=entity)。\n\n\n扩展路径：\n 1. 使用2x2的[deconv](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=deconv&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiJkZWNvbnYiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.edl7eafFoT-zGJg0IG7ROO_Om9tFmXvJDbWJK_O3NE8&zhida_source=entity)来进行上采样，上采样的过程中，通道数减半。同时，将上采样的[feature map](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=3&q=feature+map&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiJmZWF0dXJlIG1hcCIsInpoaWRhX3NvdXJjZSI6ImVudGl0eSIsImNvbnRlbnRfaWQiOjczMTI4OTksImNvbnRlbnRfdHlwZSI6IkFydGljbGUiLCJtYXRjaF9vcmRlciI6MywiemRfdG9rZW4iOm51bGx9.TW4bILlT-j0BKl7-bDTX7Fx9vkdU21F1WMKXpvcKxqY&zhida_source=entity)和浓缩路径中相应的feature map进行concatenate（注意：由于浓缩路径中的conv都是没有做padding动作的，这会导致扩展路径中的feature map和浓缩路径中相应位置的feature map大小不一致，这个时候就要将浓缩路径中的feature map进行crop再和扩展路径中的feature map进行concatenate）。\n 2. **上采样的结果** 和**浓缩路径中的相应feature map的裁剪** 进行concatenate后，再跟上3x3的卷积。由于浓缩路径中卷积操作是没有padding的，因此feature map在卷积之后会越来越小，之后在扩展路径进行上采样无法恢复相应的分辨率，因此需要裁剪。\n 3. 最后一层使用1x1的卷积，将[通道数](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=3&q=%E9%80%9A%E9%81%93%E6%95%B0&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLpgJrpgZPmlbAiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjMsInpkX3Rva2VuIjpudWxsfQ.HZ64tgbyZ_PtLcBi1sqIZ9pGH9C-SjRb1QgkRzI7VUc&zhida_source=entity)map到类别数。\n\n\n## 训练\n## 1. 损失函数计算\n网络输出的是[pixel-wise](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=pixel-wise&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiJwaXhlbC13aXNlIiwiemhpZGFfc291cmNlIjoiZW50aXR5IiwiY29udGVudF9pZCI6NzMxMjg5OSwiY29udGVudF90eXBlIjoiQXJ0aWNsZSIsIm1hdGNoX29yZGVyIjoxLCJ6ZF90b2tlbiI6bnVsbH0.-IgpuJKIkfTjj2dfSllhcNCxkE3xRQ4DI8SsXN7O1v4&zhida_source=entity)的softmax。表达式如下：\n![](../images/006.jpg)\n其中， x 为[二维平面](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E4%BA%8C%E7%BB%B4%E5%B9%B3%E9%9D%A2&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLkuoznu7TlubPpnaIiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.xkSypgVyF5Q21I6Ice21kEBS_-UGLzfAyogxUJTgq6w&zhida_source=entity) Ω 上的像素位置， a_k(x) 表示网络最后输出层中pixel x 对应的第 k 个通道的值， K 是类别总数。 p_k(x) 表示像素 x 属于 k 类的概率。\n损失函数使用negative cross entropy。cross entropy的数学表达式如下：\n![](../images/007.jpg)\n其中 p_l(x) 表示 x 在真实label所在通道上的输出概率。需要特别注意的是cross entropy中还添加一个权重项 w(x) 。这是因为考虑到物体间的边界需要更多的关注，所对应的损失权重需要更大。\n## 2. 像素损失权重计算\n在损失函数计算中我们讲到对于[边界像素](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E8%BE%B9%E7%95%8C%E5%83%8F%E7%B4%A0&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLovrnnlYzlg4_ntKAiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.jKyMr2A8dwuRuNEj2ePCRzPqo1FjKe92h3tbiPDvHBI&zhida_source=entity)我们给的损失权重要更大，但怎么获取这个权重？我们得到一张图片的ground truth是一个二值的mask，本文首先采用[形态学](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E5%BD%A2%E6%80%81%E5%AD%A6&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLlvaLmgIHlraYiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.qvBqoIWDvrWUQHNHIkQOxt_pxBruKi1q-6Djc8ht2Kk&zhida_source=entity)方法去计算出物体的边界。然后通过以下的表达式去计算[权重图](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E6%9D%83%E9%87%8D%E5%9B%BE&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLmnYPph43lm74iLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.uJnnIGa-AWWr7yF41eVM5ERrn5YsJll1EJMH_5diNVg&zhida_source=entity)。\n![](../images/008.jpg)\n其中 w_c(x) 是类别权重，需要根据训练数据集中的各类别出现的频率来进行统计，类别出现的频率越高，应该给的权重越低，频率越低则给的权重越高（文章没有详细说是怎么计算的）。 d_1(x) 表示物体像素到最近cell的边界的距离， d_2(x) 表示物体像素到第二近的cell的边界的距离。在本文中，设置 w_0=10,\\sigma=5 。\n## 3. 图像增强\n用到了很多图像增强方法。其中，作者特别强调，在训练数据很少的情况下，任意的[弹性形变](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=2&q=%E5%BC%B9%E6%80%A7%E5%BD%A2%E5%8F%98&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLlvLnmgKflvaLlj5giLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjIsInpkX3Rva2VuIjpudWxsfQ.gDK8_SYQIcJRDGRuGUFgzVk4WM003LkHI7r9XzDNXHc&zhida_source=entity)对[网络训练](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E7%BD%91%E7%BB%9C%E8%AE%AD%E7%BB%83&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLnvZHnu5zorq3nu4MiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.luOYPBMpke2ZnP7GyzCYd9uU6mxKJlWY_FYovFF6lTU&zhida_source=entity)有非常好的帮助。\n编辑于 2018-06-21 13:33\n[计算机视觉](https://www.zhihu.com/topic/19590195)\n[机器学习](https://www.zhihu.com/topic/19559450)\n[深度学习（Deep Learning）](https://www.zhihu.com/topic/19813032)\n​赞同 28​​5 条评论​65 ​5 \n​分享\n​申请转载​\n​\n![](../images/body-7e064b35ba4350074989.jpeg)\n未登录用户\n \n\n5 条评论\n默认\n最新\n[![空都](../images/009.jpg)](https://www.zhihu.com/people/cb87265ac60b48ede1f881eba38338b1)\n[空都](https://www.zhihu.com/people/cb87265ac60b48ede1f881eba38338b1)\n感谢分享，您知道在训练中2. 像素损失权重计算，这一节有没有复现代码，我在对d1(x)、d2(x)进行计算的时候遇到了困难，我一开始的想法是：先计算距离距离最近的细胞即d1(x)，然后将归属于距离最近细胞的像素全设为背景像素；最后再计算距离最近的细胞壁（即第二近细胞壁），但是算法的复杂度太高，自己又没相当别的好的计算方式。\n2023-07-27\n​回复​喜欢\n[![BINGO Hong](../images/010.jpg)](https://www.zhihu.com/people/47af86ab4a98c497d14777b4cf343b2d)\n[BINGO Hong](https://www.zhihu.com/people/47af86ab4a98c497d14777b4cf343b2d)\n做overlaptile一方面是为了减少大分辨率图像的尺寸，另一方面是减少图像边缘分割时，图像边缘分割模糊。\n2018-06-24\n​回复​喜欢\n[![KOD C](../images/011.jpg)](https://www.zhihu.com/people/7395e6c291ca8a60d44d2ab447a63725)\n[KOD C](https://www.zhihu.com/people/7395e6c291ca8a60d44d2ab447a63725)\n您好，您的文章写得很棒。有一个问题想请教您。\n就是overlap-tile操作，论文中说的是对任意大的图像进行无缝分割。我的理解这个操作是在训练之前，对输入图片镜像操作来推断边缘区域的信息（388镜像操作后变成572），所以U-Net网络最后输出的是388图片，是跟原图一样大小的，这样实现了像素级别的分类。\n但是overlap-tile操作又对镜像操作后的图像中的每个小块（Fig2中左图蓝框），在对这些小框做了一些弹性形变、双线性插值的数据增强，放入网络中去训练。\n感觉有些乱，大佬能稍微解释一下么？ 感谢~\n2018-06-21\n​回复​喜欢\n[![stone](../images/012.jpg)](https://www.zhihu.com/people/35ce9d46f0df1f5d30681075645c590d)\n[stone](https://www.zhihu.com/people/35ce9d46f0df1f5d30681075645c590d)\n作者\n这里我也有点疑惑，我的理解是fig2中的蓝色框应该就是输入网络的图像，而不是你说的小块。因为原图可能分辨率非常大。\n2018-06-21\n​回复​喜欢\n展开其他 1 条回复​\n关于作者\n[![stone](../images/013.jpg)](https://www.zhihu.com/people/big-big-stone)\n[stone](https://www.zhihu.com/people/big-big-stone)\n收藏之前点个赞呗\n[ 回答 **30** ](https://www.zhihu.com/people/big-big-stone/answers)[ 文章 **15** ](https://www.zhihu.com/people/big-big-stone/posts)[ 关注者 **10,013** ](https://www.zhihu.com/people/big-big-stone/followers)\n​关注他​发私信\n大家都在搜\n换一换\n[江歌妈妈发长文尘埃终将落定704 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DynamicRouting：针对语义分割的动态路径选择网络 Learning Dynamic Routing for Semantic Segmentation作者团队：中科院&国科大&西安交大… 吴建明wujianming ](https://zhuanlan.zhihu.com/p/138893960) \n\n_想来知乎工作？请发送邮件到 jobs@zhihu.com_\n打开知乎App\n在「我的页」右上角打开扫一扫\n![](../images/body-0f9788d006ab0f4da762.png)\n其他扫码方式：微信\n下载知乎App\n无障碍模式\n验证码登录\n密码登录\n[开通机构号](https://zhuanlan.zhihu.com/org/signup)\n中国 +86\n获取短信验证码\n忘记密码\n登录/注册\n其他方式登录\n未注册手机验证后自动登录，注册即代表同意[《知乎协议》](https://www.zhihu.com/term/zhihu-terms)[《隐私保护指引》](https://www.zhihu.com/term/privacy)\n扫码下载知乎 App\n关闭二维码\n", "metadata": { "title": "语义分割之U-net - 知乎", "description": "更多语义分割文章，请看专栏：图像语义分割U-Net论文信息论文地址： U-Net: Convolutional Networks for Biomedical Image Segmentation发表时间：18 May 2015 创新点深度网络通常需要大量的数据进行训练，当样本…", "keywords": "计算机视觉,机器学习,深度学习（Deep Learning）", "author": null, "og:title": "语义分割之U-net", "og:url": "https://zhuanlan.zhihu.com/p/37804107", "og:description": "更多语义分割文章，请看专栏：图像语义分割U-Net论文信息论文地址： U-Net: Convolutional Networks for Biomedical Image Segmentation发表时间：18 May 2015 创新点深度网络通常需要大量的数据进行训练，当样本…", "og:image": "https://picx.zhimg.com/v2-bce050fb7f9d51abceef77aeb63aad40_720w.jpg?source=172ae18b", "og:type": "article", "og:site_name": "知乎专栏" }, "paywall": { "listed_paid": false, "detected": false, "marker": "", "public_only": false, "policy": "付费/会员内容只保留页面公开可见部分，不绕过付费墙" }, "crawl": { "success": true, "status_code": 200, "error": "" }, "code_blocks": [], "images": [ { "status": "http_403", "url": "https://zhuanlan.zhihu.com/p/37804107", "src": "https://zhuanlan.zhihu.com/p/37804107", "alt": "", "downloaded": false, "discovery": "saved_markdown", "retried_at": "2026-10-20T18:04:55Z" } ], "audio": [], "videos": [], "links": [ { "type": "internal", "href": "https://www.zhihu.com" }, { "type": "internal", "href": "https://www.zhihu.com/signin?next=%2Ffollow" }, { "type": "internal", "href": "https://www.zhihu.com/signin?next=%2F" }, { "type": "internal", "href": "https://www.zhihu.com/signin?next=%2Fhot" }, { "type": "internal", "href": 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更多语义分割文章，请看专栏：[图像语义分割](https://zhuanlan.zhihu.com/c_197474183)\n## U-Net\n## 论文信息\n论文地址：[U-Net: Convolutional Networks for Biomedical Image Segmentation](https://zhuanlan.zhihu.com/p/37804107/edit)\n发表时间：18 May 2015\n## 创新点\n深度网络通常需要大量的数据进行训练，当样本量较少的情况下，[深度网络](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=2&q=%E6%B7%B1%E5%BA%A6%E7%BD%91%E7%BB%9C&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLmt7HluqbnvZHnu5wiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjIsInpkX3Rva2VuIjpudWxsfQ.cNQq22OGBk9BANq-dyKgrzrOdABIeTkP7PKotTtS_mA&zhida_source=entity)可能表现没那么好。对于这个问题，本文提出了新的[网络架构](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E7%BD%91%E7%BB%9C%E6%9E%B6%E6%9E%84&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLnvZHnu5zmnrbmnoQiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.o_mSWjlg_g_3YtyR3AzbDrRfSAc74S-jpiLnNcTe8LE&zhida_source=entity)和图像增强策略。网络架构包括encoder和[decoder](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=decoder&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiJkZWNvZGVyIiwiemhpZGFfc291cmNlIjoiZW50aXR5IiwiY29udGVudF9pZCI6NzMxMjg5OSwiY29udGVudF90eXBlIjoiQXJ0aWNsZSIsIm1hdGNoX29yZGVyIjoxLCJ6ZF90b2tlbiI6bnVsbH0.hQlCZEc8dHa5XvjBb1wanjxtfnM6j99q7fGS8O0EwZw&zhida_source=entity)（论文中称为浓缩路径(contracting path)和扩展路径(expanding path)，实际上就是encoder和decoder），encoder可以有效地捕捉上下文信息，而decoder可以较好地预测位置信息。\n## 模型\n## 1. 模型设计思想\nU-net是基于[FCN](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=FCN&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiJGQ04iLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.On5AO9_vhtOMlsrCmiwsNd4M4tIjhvDV6FNaLJ-Ygo4&zhida_source=entity)网络的思想设计的，整个网络只有[卷积层](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E5%8D%B7%E7%A7%AF%E5%B1%82&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLljbfnp6_lsYIiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.o9yeEdW8iFD9oU6bRbIieoOLZHFsHgtq3kHfeFazaDE&zhida_source=entity)，而没有[全连接层](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E5%85%A8%E8%BF%9E%E6%8E%A5%E5%B1%82&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLlhajov57mjqXlsYIiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.YSzKILAVD6vH07DWi28BNcj3XMcUgpA8lw8jDoZSMmU&zhida_source=entity)。\n在FCN中：网络的浓缩路径，图像分辨率逐渐降低，上下文信息会逐渐增强。在扩展路径中，通过[上采样](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E4%B8%8A%E9%87%87%E6%A0%B7&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLkuIrph4fmoLciLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.x5T8LCqsnw-BzNj6hRe1bMRhwXVmhOTmpsYWjT9h7Zc&zhida_source=entity)的方式，让[特征图](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E7%89%B9%E5%BE%81%E5%9B%BE&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLnibnlvoHlm74iLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.f91_1Zl6sbvbOgDU7g1Uv3wJrzhbHqw3NKWAtDA31Go&zhida_source=entity)的分辨率逐渐增大。同时，为了结合低层feature map的强位置信息，将浓缩路径中的相应部分结合到扩展路径中。这种架构可以较好地进行位置定位。\n![](https://picx.zhimg.com/v2-ae022f07931a783b0d038b9335d4ee51_1440w.jpg)\nU-net做的修改有：\n 1. 在上采样部分，feature map的通道数非常大，作者认为这样可以将上下文信息传递到分辨率更高的层当中。这样做的一个结果就是它基本上和浓缩路径对称了，因此看上去像一个U形的结构。\n 2. 为了预测图像边界区域的像素点，采用[overlap-tile策略](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=overlap-tile%E7%AD%96%E7%95%A5&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiJvdmVybGFwLXRpbGXnrZbnlaUiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.ib6gX4EQmjA1dd1WxgUbikbs_hQHG8IiBg8wQ1FpKsk&zhida_source=entity)补全缺失的context。\n 3. 由于训练数据太少，采用大量弹性形变的方式增强数据。这可以让模型更好学习形变不变性。这种增强方式对于医学图像来说很重要。\n 4. 在[细胞分割](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E7%BB%86%E8%83%9E%E5%88%86%E5%89%B2&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLnu4bog57liIblibIiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.PHOo97dPhx7ZegI3uuVtyRQh2YqZs0pqUirQ0eOcbfM&zhida_source=entity)任务中的另一个挑战是，如何将同类别的相互接触的目标分开。本文提出了使用一种带权重的损失([weighted loss](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=weighted+loss&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiJ3ZWlnaHRlZCBsb3NzIiwiemhpZGFfc291cmNlIjoiZW50aXR5IiwiY29udGVudF9pZCI6NzMxMjg5OSwiY29udGVudF90eXBlIjoiQXJ0aWNsZSIsIm1hdGNoX29yZGVyIjoxLCJ6ZF90b2tlbiI6bnVsbH0.W3WipArjO8SSR-P04yYhF0qkLgWas9z4T0YBHn28oBQ&zhida_source=entity))。在[损失函数](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E6%8D%9F%E5%A4%B1%E5%87%BD%E6%95%B0&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLmjZ_lpLHlh73mlbAiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.u1yzS2xHe75Aw4fUGyS3d4o5_pgsK2ov4fxu5r66rq8&zhida_source=entity)中，分割相互接触的细胞像素获得了更大的权重。\n\n\n![](https://pic3.zhimg.com/v2-3d3ff211d354b1f97450e90b921dfbce_1440w.jpg)\n## 2. 网络结构\n网络结构包括浓缩路径和扩展路径。\n浓缩路径：\n 1. 注意图像输入是经过tile的。因此网络的输出是和图像的输入大小是不一样的。\n 2. 每经过两个3x3conv（没有padding）之后，会跟上一个2x2的max-pooling进行[下采样](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E4%B8%8B%E9%87%87%E6%A0%B7&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLkuIvph4fmoLciLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.GDgioToaOSmKGQ5M1FkSXK9_1Rxe6C7eXWYzHjKhQCw&zhida_source=entity)。\n\n\n扩展路径：\n 1. 使用2x2的[deconv](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=deconv&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiJkZWNvbnYiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.edl7eafFoT-zGJg0IG7ROO_Om9tFmXvJDbWJK_O3NE8&zhida_source=entity)来进行上采样，上采样的过程中，通道数减半。同时，将上采样的[feature map](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=3&q=feature+map&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiJmZWF0dXJlIG1hcCIsInpoaWRhX3NvdXJjZSI6ImVudGl0eSIsImNvbnRlbnRfaWQiOjczMTI4OTksImNvbnRlbnRfdHlwZSI6IkFydGljbGUiLCJtYXRjaF9vcmRlciI6MywiemRfdG9rZW4iOm51bGx9.TW4bILlT-j0BKl7-bDTX7Fx9vkdU21F1WMKXpvcKxqY&zhida_source=entity)和浓缩路径中相应的feature map进行concatenate（注意：由于浓缩路径中的conv都是没有做padding动作的，这会导致扩展路径中的feature map和浓缩路径中相应位置的feature map大小不一致，这个时候就要将浓缩路径中的feature map进行crop再和扩展路径中的feature map进行concatenate）。\n 2. **上采样的结果** 和**浓缩路径中的相应feature map的裁剪** 进行concatenate后，再跟上3x3的卷积。由于浓缩路径中卷积操作是没有padding的，因此feature map在卷积之后会越来越小，之后在扩展路径进行上采样无法恢复相应的分辨率，因此需要裁剪。\n 3. 最后一层使用1x1的卷积，将[通道数](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=3&q=%E9%80%9A%E9%81%93%E6%95%B0&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLpgJrpgZPmlbAiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjMsInpkX3Rva2VuIjpudWxsfQ.HZ64tgbyZ_PtLcBi1sqIZ9pGH9C-SjRb1QgkRzI7VUc&zhida_source=entity)map到类别数。\n\n\n## 训练\n## 1. 损失函数计算\n网络输出的是[pixel-wise](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=pixel-wise&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiJwaXhlbC13aXNlIiwiemhpZGFfc291cmNlIjoiZW50aXR5IiwiY29udGVudF9pZCI6NzMxMjg5OSwiY29udGVudF90eXBlIjoiQXJ0aWNsZSIsIm1hdGNoX29yZGVyIjoxLCJ6ZF90b2tlbiI6bnVsbH0.-IgpuJKIkfTjj2dfSllhcNCxkE3xRQ4DI8SsXN7O1v4&zhida_source=entity)的softmax。表达式如下：\n![](https://picx.zhimg.com/v2-e951d28f7c3fa6e9035630d8971916df_1440w.jpg)\n其中， x 为[二维平面](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E4%BA%8C%E7%BB%B4%E5%B9%B3%E9%9D%A2&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLkuoznu7TlubPpnaIiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.xkSypgVyF5Q21I6Ice21kEBS_-UGLzfAyogxUJTgq6w&zhida_source=entity) Ω 上的像素位置， a_k(x) 表示网络最后输出层中pixel x 对应的第 k 个通道的值， K 是类别总数。 p_k(x) 表示像素 x 属于 k 类的概率。\n损失函数使用negative cross entropy。cross entropy的数学表达式如下：\n![](https://picx.zhimg.com/v2-bb2bcbc1934d0062f4c6fd1f8fefb285_1440w.jpg)\n其中 p_l(x) 表示 x 在真实label所在通道上的输出概率。需要特别注意的是cross entropy中还添加一个权重项 w(x) 。这是因为考虑到物体间的边界需要更多的关注，所对应的损失权重需要更大。\n## 2. 像素损失权重计算\n在损失函数计算中我们讲到对于[边界像素](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E8%BE%B9%E7%95%8C%E5%83%8F%E7%B4%A0&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLovrnnlYzlg4_ntKAiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.jKyMr2A8dwuRuNEj2ePCRzPqo1FjKe92h3tbiPDvHBI&zhida_source=entity)我们给的损失权重要更大，但怎么获取这个权重？我们得到一张图片的ground truth是一个二值的mask，本文首先采用[形态学](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E5%BD%A2%E6%80%81%E5%AD%A6&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLlvaLmgIHlraYiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.qvBqoIWDvrWUQHNHIkQOxt_pxBruKi1q-6Djc8ht2Kk&zhida_source=entity)方法去计算出物体的边界。然后通过以下的表达式去计算[权重图](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E6%9D%83%E9%87%8D%E5%9B%BE&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLmnYPph43lm74iLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.uJnnIGa-AWWr7yF41eVM5ERrn5YsJll1EJMH_5diNVg&zhida_source=entity)。\n![](https://pica.zhimg.com/v2-2f5fdd6eb4c20645a2199f5484a558be_1440w.jpg)\n其中 w_c(x) 是类别权重，需要根据训练数据集中的各类别出现的频率来进行统计，类别出现的频率越高，应该给的权重越低，频率越低则给的权重越高（文章没有详细说是怎么计算的）。 d_1(x) 表示物体像素到最近cell的边界的距离， d_2(x) 表示物体像素到第二近的cell的边界的距离。在本文中，设置 w_0=10,\\sigma=5 。\n## 3. 图像增强\n用到了很多图像增强方法。其中，作者特别强调，在训练数据很少的情况下，任意的[弹性形变](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=2&q=%E5%BC%B9%E6%80%A7%E5%BD%A2%E5%8F%98&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLlvLnmgKflvaLlj5giLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjIsInpkX3Rva2VuIjpudWxsfQ.gDK8_SYQIcJRDGRuGUFgzVk4WM003LkHI7r9XzDNXHc&zhida_source=entity)对[网络训练](https://zhida.zhihu.com/search?content_id=7312899&content_type=Article&match_order=1&q=%E7%BD%91%E7%BB%9C%E8%AE%AD%E7%BB%83&zd_token=eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9.eyJpc3MiOiJ6aGlkYV9zZXJ2ZXIiLCJleHAiOjE3OTExMzk0NDAsInEiOiLnvZHnu5zorq3nu4MiLCJ6aGlkYV9zb3VyY2UiOiJlbnRpdHkiLCJjb250ZW50X2lkIjo3MzEyODk5LCJjb250ZW50X3R5cGUiOiJBcnRpY2xlIiwibWF0Y2hfb3JkZXIiOjEsInpkX3Rva2VuIjpudWxsfQ.luOYPBMpke2ZnP7GyzCYd9uU6mxKJlWY_FYovFF6lTU&zhida_source=entity)有非常好的帮助。\n编辑于 2018-06-21 13:33\n[计算机视觉](https://www.zhihu.com/topic/19590195)\n[机器学习](https://www.zhihu.com/topic/19559450)\n[深度学习（Deep Learning）](https://www.zhihu.com/topic/19813032)\n​赞同 28​​5 条评论​65 ​5 \n​分享\n​申请转载​\n​\n![](https://pic1.zhimg.com/v2-d41c2ceaed8f51999522f903672a521f_l.jpeg)\n未登录用户\n \n\n5 条评论\n默认\n最新\n[![空都](https://pic1.zhimg.com/v2-abed1a8c04700ba7d72b45195223e0ff_l.jpg?source=06d4cd63)](https://www.zhihu.com/people/cb87265ac60b48ede1f881eba38338b1)\n[空都](https://www.zhihu.com/people/cb87265ac60b48ede1f881eba38338b1)\n感谢分享，您知道在训练中2. 像素损失权重计算，这一节有没有复现代码，我在对d1(x)、d2(x)进行计算的时候遇到了困难，我一开始的想法是：先计算距离距离最近的细胞即d1(x)，然后将归属于距离最近细胞的像素全设为背景像素；最后再计算距离最近的细胞壁（即第二近细胞壁），但是算法的复杂度太高，自己又没相当别的好的计算方式。\n2023-07-27\n​回复​喜欢\n[![BINGO Hong](https://picx.zhimg.com/v2-b0e5f9e175807e0024b753b7c0ec2359_l.jpg?source=06d4cd63)](https://www.zhihu.com/people/47af86ab4a98c497d14777b4cf343b2d)\n[BINGO Hong](https://www.zhihu.com/people/47af86ab4a98c497d14777b4cf343b2d)\n做overlaptile一方面是为了减少大分辨率图像的尺寸，另一方面是减少图像边缘分割时，图像边缘分割模糊。\n2018-06-24\n​回复​喜欢\n[![KOD C](https://picx.zhimg.com/v2-4274e571c79459fb7814ceec98919dc2_l.jpg?source=06d4cd63)](https://www.zhihu.com/people/7395e6c291ca8a60d44d2ab447a63725)\n[KOD C](https://www.zhihu.com/people/7395e6c291ca8a60d44d2ab447a63725)\n您好，您的文章写得很棒。有一个问题想请教您。\n就是overlap-tile操作，论文中说的是对任意大的图像进行无缝分割。我的理解这个操作是在训练之前，对输入图片镜像操作来推断边缘区域的信息（388镜像操作后变成572），所以U-Net网络最后输出的是388图片，是跟原图一样大小的，这样实现了像素级别的分类。\n但是overlap-tile操作又对镜像操作后的图像中的每个小块（Fig2中左图蓝框），在对这些小框做了一些弹性形变、双线性插值的数据增强，放入网络中去训练。\n感觉有些乱，大佬能稍微解释一下么？ 感谢~\n2018-06-21\n​回复​喜欢\n[![stone](https://pic1.zhimg.com/36f310418_l.jpg?source=06d4cd63)](https://www.zhihu.com/people/35ce9d46f0df1f5d30681075645c590d)\n[stone](https://www.zhihu.com/people/35ce9d46f0df1f5d30681075645c590d)\n作者\n这里我也有点疑惑，我的理解是fig2中的蓝色框应该就是输入网络的图像，而不是你说的小块。因为原图可能分辨率非常大。\n2018-06-21\n​回复​喜欢\n展开其他 1 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