介绍

U-Net是15年出来的在显微组织切片细胞分割领域大获成功的一个CNN segmentation模型。它借鉴了当时新提出不久的FCN网络，进一步有效利用了各个尺度context feature map所具有的信息，充分使用了各种可行的
数据增强的手段，在生物细胞组织切片这种精度高、物体数目密集的图片数据集上获得了较好的效果。

关于FCN的具体情况，可参考区区的此篇博文：Semantic segmentation系列其一：FCN。

U-Net网络本质上就是一个FCN。但它也有些值得赞许的地方像通过在Conv中使用valid padding，使得feature map经过conv层时不断减少两个边缘像素；最终几经裁减并下采样的feature map获得了我们想要的mask
map的大小。它的具体网络结构请见下图。

U-Net网络架构

U-Net

或者U-Net中最值得一说的是它处理像生物组织切片此类数据的有效方式及所使用的有些特点的loss函数吧。

数据输入

笔者因为客户项目需求也增接触过某种类型的人体显微组织切片数据。项目需求是找到一种好的方案来定位出切片上的有问题细胞区域并给出初步判断，标明此切片的阴、阳性类别。
乍听上去并不难，像是一个典型的object detection或者复杂一点那就是semantic segmentation的问题。可它的数据却并非像我们平时玩坏了的Imagenet、Cifar10/100或者COCO/VOC那样‘正规’。。客户给我们的数据集
甚至标注都存在问题，要么有些图片标注不全（漏标），要么就是标注错误（错标）（可能是请老专家们费力盯着切片去标时钱没给够吧！）。每张图片更是有数百万个像素，单个图片文件大小有几个GB。

碰到这样的需求你会如何做呢？不过多讨论，先看下U-Net作者们的做法。可能会有些借鉴吧。

首先，它们将大的图片按照Tiling的方式切成许多个patch，然后再将patch作为网络的输入。因为Segmentation对图片之上物体的位置要求极其严格，因此使用Valid padding的方式对feature maps进行conv操作、处理。
这意味着我们需要让输入的patch有着更大的context，如此才能保证图片经过一层层conv的去border（因为valid padding的使用）最终也能保证其位置信息正确。

如下为U-Net在对输入图片进行overlapping patch处理的方式。

Overlapping_tiling处理策略

数据预处理

一般像这种生物类的切片数据集成本都较高（隐私、标注成本等），所以数据集规模都不会太大。为此需要多用些data augmentation的方法才能保证数据集对模型的充分拟合。
本篇中作者用的data augmentation方法有：shift/rotation（比如多些不同类型的角度旋转），进行些平滑过滤、变形等（被证明为在使用小的数据集时极其有效。）。

网络结构

从开篇图中亦可看出U-Net网络起的名字确实是名符其实。它共有两个Patch组成，一条为contracting path(left side)，它主要是典型的CNN特征提取网络（用于逐级精炼、提取特征）；另一条则为expansive path，用于使用
contracting path得到的不同尺度、级别的特征进一步上采样、变形、转换为高精度的mask map。

从里面隐约已经看出了后来的DSSD模型与FPN模型中使用的结构的影子。

模型训练

在训练时，我们通过在使用输入的label mask map与最终网络输出的结果mask map之间逐个元素进行cross-entropy求和来得到loss，并进行backward propagation计算。
如下为loss函数计算公式。

Loss_函数计算公式

有趣的是为了更好地学习出细胞间的细小分隔元素（以更好地表示细胞间的边缘），作者在loss函数计算时附加了一个反映元素级别位置的权重矩阵（w(x)，x为图片上的每一个像素)。

其中w(x)的值则是根据训练数据集中所知的segmentation map的类别情况及其上像素分布位置而定的。它的计算公式如下：

权重矩阵计算公式

乍看时感觉像是在使用先验的标注信息，有些像是作弊。可一思考它好像也符合机器学习的一贯做法，像Yolo v2中使用的对训练数据集中的所有ground truth box进行聚类以获得其prior box 合理width/height的做法不也是如此嘛。

实验结果

下面是它对细胞组织切片的处理结果，可以直观感觉到它的效果。

细胞组织切片分割效果

最后下表为它在2015ISBI细胞定位大赛中与其它模型比较的结果。

U-Net在图片分割标准数据集上与其它模型的结果比较

代码分析

下面是U-Net 的prototxt的构成。可见它是用的valid conv，同时在expand path中使用的上采样则是用了deconvolution。

name: 'phseg_v5'
force_backward: true
layers {                 top: 'data' top: 'label'  name: 'loaddata'       type: HDF5_DATA  hdf5_data_param { source: 'aug_deformed_phseg_v5.txt' batch_size: 1 } include: { phase: TRAIN }}

layers { bottom: 'data'              top: 'd0b'   name: 'conv_d0a-b'     type: CONVOLUTION  blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 64 pad: 0 kernel_size: 3 engine: CAFFE weight_filler { type: 'xavier' }} }
layers { bottom: 'd0b'               top: 'd0b'   name: 'relu_d0b'       type: RELU }
layers { bottom: 'd0b'               top: 'd0c'   name: 'conv_d0b-c'     type: CONVOLUTION  blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 64 pad: 0 kernel_size: 3 engine: CAFFE weight_filler { type: 'xavier' }} }
layers { bottom: 'd0c'               top: 'd0c'   name: 'relu_d0c'       type: RELU }

layers { bottom: 'd0c'               top: 'd1a'   name: 'pool_d0c-1a'    type: POOLING  pooling_param { pool: MAX kernel_size: 2 stride: 2 } }
layers { bottom: 'd1a'               top: 'd1b'   name: 'conv_d1a-b'     type: CONVOLUTION  blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 128 pad: 0 kernel_size: 3 engine: CAFFE weight_filler { type: 'xavier' }} }
layers { bottom: 'd1b'               top: 'd1b'   name: 'relu_d1b'       type: RELU }
layers { bottom: 'd1b'               top: 'd1c'   name: 'conv_d1b-c'     type: CONVOLUTION  blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 128 pad: 0 kernel_size: 3 engine: CAFFE weight_filler { type: 'xavier' }} }
layers { bottom: 'd1c'               top: 'd1c'   name: 'relu_d1c'       type: RELU }

layers { bottom: 'd1c'               top: 'd2a'   name: 'pool_d1c-2a'    type: POOLING  pooling_param { pool: MAX kernel_size: 2 stride: 2 } }
layers { bottom: 'd2a'               top: 'd2b'   name: 'conv_d2a-b'     type: CONVOLUTION  blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 256 pad: 0 kernel_size: 3 engine: CAFFE weight_filler { type: 'xavier' }} }
layers { bottom: 'd2b'               top: 'd2b'   name: 'relu_d2b'       type: RELU }
layers { bottom: 'd2b'               top: 'd2c'   name: 'conv_d2b-c'     type: CONVOLUTION  blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 256 pad: 0 kernel_size: 3 engine: CAFFE weight_filler { type: 'xavier' }} }
layers { bottom: 'd2c'               top: 'd2c'   name: 'relu_d2c'       type: RELU }

layers { bottom: 'd2c'               top: 'd3a'   name: 'pool_d2c-3a'    type: POOLING  pooling_param { pool: MAX kernel_size: 2 stride: 2 } }
layers { bottom: 'd3a'               top: 'd3b'   name: 'conv_d3a-b'     type: CONVOLUTION  blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 512 pad: 0 kernel_size: 3 engine: CAFFE weight_filler { type: 'xavier' }} }
layers { bottom: 'd3b'               top: 'd3b'   name: 'relu_d3b'       type: RELU }
layers { bottom: 'd3b'               top: 'd3c'   name: 'conv_d3b-c'     type: CONVOLUTION  blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 512 pad: 0 kernel_size: 3 engine: CAFFE weight_filler { type: 'xavier' }} }
layers { bottom: 'd3c'               top: 'd3c'   name: 'relu_d3c'       type: RELU }
layers { bottom: 'd3c'               top: 'd3c'   name: 'dropout_d3c'    type: DROPOUT dropout_param { dropout_ratio: 0.5 } include: { phase: TRAIN }}

layers { bottom: 'd3c'               top: 'd4a'   name: 'pool_d3c-4a'    type: POOLING  pooling_param { pool: MAX kernel_size: 2 stride: 2 } }
layers { bottom: 'd4a'               top: 'd4b'   name: 'conv_d4a-b'     type: CONVOLUTION  blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 1024 pad: 0 kernel_size: 3 engine: CAFFE weight_filler { type: 'xavier' }} }
layers { bottom: 'd4b'               top: 'd4b'   name: 'relu_d4b'       type: RELU }
layers { bottom: 'd4b'               top: 'd4c'   name: 'conv_d4b-c'     type: CONVOLUTION  blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 1024 pad: 0 kernel_size: 3 engine: CAFFE weight_filler { type: 'xavier' }} }
layers { bottom: 'd4c'               top: 'd4c'   name: 'relu_d4c'       type: RELU }
layers { bottom: 'd4c'               top: 'd4c'   name: 'dropout_d4c'    type: DROPOUT dropout_param { dropout_ratio: 0.5 } include: { phase: TRAIN }}

layers { bottom: 'd4c'               top: 'u3a'   name: 'upconv_d4c_u3a' type: DECONVOLUTION blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 512 pad: 0 kernel_size: 2 stride: 2 weight_filler { type: 'xavier' }} }
layers { bottom: 'u3a'               top: 'u3a'   name: 'relu_u3a'       type: RELU }
layers { bottom: 'd3c' bottom: 'u3a' top: 'd3cc'  name: 'crop_d3c-d3cc'  type: CROP }
layers { bottom: 'u3a' bottom: 'd3cc' top: 'u3b'  name: 'concat_d3cc_u3a-b'  type: CONCAT }
layers { bottom: 'u3b'               top: 'u3c'   name: 'conv_u3b-c'     type: CONVOLUTION  blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 512 pad: 0 kernel_size: 3 engine: CAFFE weight_filler { type: 'xavier' }} }
layers { bottom: 'u3c'               top: 'u3c'   name: 'relu_u3c'       type: RELU }
layers { bottom: 'u3c'               top: 'u3d'   name: 'conv_u3c-d'     type: CONVOLUTION  blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 512 pad: 0 kernel_size: 3 engine: CAFFE weight_filler { type: 'xavier' }} }
layers { bottom: 'u3d'               top: 'u3d'   name: 'relu_u3d'       type: RELU }

layers { bottom: 'u3d'               top: 'u2a'   name: 'upconv_u3d_u2a' type: DECONVOLUTION blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 256 pad: 0 kernel_size: 2 stride: 2 weight_filler { type: 'xavier' }} }
layers { bottom: 'u2a'               top: 'u2a'   name: 'relu_u2a'       type: RELU }
layers { bottom: 'd2c' bottom: 'u2a' top: 'd2cc'  name: 'crop_d2c-d2cc'  type: CROP }
layers { bottom: 'u2a' bottom: 'd2cc' top: 'u2b'   name: 'concat_d2cc_u2a-b'  type: CONCAT }
layers { bottom: 'u2b'               top: 'u2c'   name: 'conv_u2b-c'     type: CONVOLUTION  blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 256 pad: 0 kernel_size: 3 engine: CAFFE weight_filler { type: 'xavier' }} }
layers { bottom: 'u2c'               top: 'u2c'   name: 'relu_u2c'       type: RELU }
layers { bottom: 'u2c'               top: 'u2d'   name: 'conv_u2c-d'     type: CONVOLUTION  blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 256 pad: 0 kernel_size: 3 engine: CAFFE weight_filler { type: 'xavier' }} }
layers { bottom: 'u2d'               top: 'u2d'   name: 'relu_u2d'       type: RELU }

layers { bottom: 'u2d'               top: 'u1a'   name: 'upconv_u2d_u1a' type: DECONVOLUTION blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 128 pad: 0 kernel_size: 2 stride: 2 weight_filler { type: 'xavier' }} }
layers { bottom: 'u1a'               top: 'u1a'   name: 'relu_u1a'       type: RELU }
layers { bottom: 'd1c' bottom: 'u1a' top: 'd1cc'  name: 'crop_d1c-d1cc'  type: CROP }
layers { bottom: 'u1a' bottom: 'd1cc' top: 'u1b'   name: 'concat_d1cc_u1a-b'  type: CONCAT }
layers { bottom: 'u1b'               top: 'u1c'   name: 'conv_u1b-c'     type: CONVOLUTION  blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 128 pad: 0 kernel_size: 3 engine: CAFFE weight_filler { type: 'xavier' }} }
layers { bottom: 'u1c'               top: 'u1c'   name: 'relu_u1c'       type: RELU }
layers { bottom: 'u1c'               top: 'u1d'   name: 'conv_u1c-d'     type: CONVOLUTION  blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 128 pad: 0 kernel_size: 3 engine: CAFFE weight_filler { type: 'xavier' }} }
layers { bottom: 'u1d'               top: 'u1d'   name: 'relu_u1d'       type: RELU }

layers { bottom: 'u1d'               top: 'u0a'   name: 'upconv_u1d_u0a' type: DECONVOLUTION blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 128 pad: 0 kernel_size: 2 stride: 2 weight_filler { type: 'xavier' }} }
layers { bottom: 'u0a'               top: 'u0a'   name: 'relu_u0a'       type: RELU }
layers { bottom: 'd0c' bottom: 'u0a' top: 'd0cc'  name: 'crop_d0c-d0cc'  type: CROP }
layers { bottom: 'u0a' bottom: 'd0cc' top: 'u0b'   name: 'concat_d0cc_u0a-b'  type: CONCAT }
layers { bottom: 'u0b'               top: 'u0c'   name: 'conv_u0b-c'     type: CONVOLUTION  blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 64 pad: 0 kernel_size: 3 engine: CAFFE weight_filler { type: 'xavier' }} }
layers { bottom: 'u0c'               top: 'u0c'   name: 'relu_u0c'       type: RELU }
layers { bottom: 'u0c'               top: 'u0d'   name: 'conv_u0c-d'     type: CONVOLUTION  blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { num_output: 64 pad: 0 kernel_size: 3 engine: CAFFE weight_filler { type: 'xavier' }} }
layers { bottom: 'u0d'               top: 'u0d'   name: 'relu_u0d'       type: RELU }

layers { bottom: 'u0d'               top: 'score' name: 'conv_u0d-score' type: CONVOLUTION  blobs_lr: 1 blobs_lr: 2 weight_decay: 1 weight_decay: 0  convolution_param { engine: CAFFE num_output: 2 pad: 0 kernel_size: 1 weight_filler { type: 'xavier' }} }
layers { bottom: 'score' bottom: 'label' top: 'loss'  name: 'loss'   type: SOFTMAX_LOSS loss_param { ignore_label: 2 }include: { phase: TRAIN }}

参考文献

• U-Net: Convolutional Networks for Biomedical Image Segmentation, Olaf-Ronneberger, 2015
• https://lmb.informatik.uni-freiburg.de/people/ronneber/u-net/