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论文被引：12052(08/03/2020)
论文年份：2015

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U-Net: Convolutional Networks for Biomedical Image Segmentation

Abstract

There is large consent that successful training of deep networks requires many thousand annotated training samples. In this paper, we present a network and training strategy that relies on the strong use of data augmentation to use the available annotated samples more efficiently. The architecture consists of a contracting path to capture context and a symmetric expanding path that enables precise localization. We show that such a network can be trained end-to-end from very few images and outperforms the prior best method (a sliding-window convolutional network) on the ISBI challenge for segmentation of neuronal structures in electron microscopic stacks. Using the same network trained on transmitted light microscopy images (phase contrast and DIC) we won the ISBI cell tracking challenge 2015 in these categories by a large margin. Moreover, the network is fast. Segmentation of a 512x512 image takes less than a second on a recent GPU. The full implementation (based on Caffe) and the trained networks are available at http://lmb.informatik.uni-freiburg.de/people/ronneber/u-net.

人们普遍同意，成功地训练深度网络需要数千个带注释的训练样本。 在本文中，我们提出了一种网络和训练策略，该策略依赖于数据增强的强大使用来更有效地使用可用的带注释的样本。 该结构包括一个用于捕获上下文的收缩路径和一个能够实现精确定位的对称扩展路径。 我们展示了这样的网络可以从很少的图像进行端到端训练，并且在ISBI挑战方面优于现有的最佳方法（滑动窗口卷积网络），可以对电子显微镜堆栈中的神经元结构进行分割。 使用在透射光显微镜图像（相差和DIC）上训练过的同一网络，我们在这些类别中赢得了2015年ISBI细胞跟踪挑战赛的冠军。 而且，网络速度很快。 在最新的GPU上，对512x512图像进行分割所需的时间不到一秒钟。 完整的实现（基于Caffe）和经过训练的网络可在http://lmb.informatik.uni-freiburg.de/people/ronneber/u-net上获得。

1 Introduction

In the last two years, deep convolutional networks have outperformed the state of the art in many visual recognition tasks, e.g. [7,3]. While convolutional networks have already existed for a long time [8], their success was limited due to the size of the available training sets and the size of the considered networks. The breakthrough by Krizhevsky et al. [7] was due to supervised training of a large network with 8 layers and millions of parameters on the ImageNet dataset with 1 million training images. Since then, even larger and deeper networks have been trained [12].

在过去的两年中，深度卷积网络在许多视觉识别任务中的表现超越了现有技术，比如[7,3]。 尽管卷积网络已经存在很长时间[8]，但由于可用训练集的大小和所考虑网络的大小，卷积网络的成功受到限制。Krizhevsky等人[7]的突破是由于对具有8层的大型网络和具有100万个训练图像的ImageNet数据集上的数百万个参数进行了监督训练。从那时起，甚至更大更深的网络也得到了训练[12]。

The typical use of convolutional networks is on classification tasks, where the output to an image is a single class label. However, in many visual tasks, especially in biomedical image processing, the desired output should include localization, i.e., a class label is supposed to be assigned to each pixel. Moreover, thousands of training images are usually beyond reach in biomedical tasks. Hence, Ciresan et al. [1] trained a network in a sliding-window setup to predict the class label of each pixel by providing a local region (patch) around that pixel as input. First, this network can localize. Secondly, the training data in terms of patches is much larger than the number of training images. The resulting network won the EM segmentation challenge at ISBI 2012 by a large margin.

卷积网络的典型用途是用于分类任务，其中图像的输出是单个类别标签。 然而，在许多视觉任务中，特别是在生物医学图像处理中，期望的输出应包括定位，即应该将类别标签分配给每个像素。 此外，在生物医学任务中通常无法获得数千个训练图像。因此，Ciresan等[1]在滑动窗口设置中训练了一个网络，以通过提供围绕该像素的局部区域（补丁）来预测每个像素的类别标签。首先，该网络可以本地化。 其次，就补丁而言，训练数据远大于训练图像的数量。 最终的网络在ISBI 2012上大幅度赢得了EM细分挑战。

Obviously, the strategy in Ciresan et al. [1] has two drawbacks. First, it is quite slow because the network must be run separately for each patch, and there is a lot of redundancy due to overlapping patches. Secondly, there is a trade-off between localization accuracy and the use of context. Larger patches require more max-pooling layers that reduce the localization accuracy, while small patches allow the network to see only little context. More recent approaches [11,4] proposed a classifier output that takes into account the features from multiple layers. Good localization and the use of context are possible at the same time.

显然，Ciresan等人[1]的策略有两个缺点。 首先，它很慢，因为每个补丁程序（patch）都必须单独运行网络，而且由于补丁程序重叠（overlapping patches），因此存在很多冗余。 其次，在定位精度和上下文使用之间需要权衡。较大的补丁程序（patches）需要更多的最大池化层，这会降低定位精度，而较小的修补程序使网络只能看到很少的上下文。 最近的方法[11,4]提出了一种分类输出，该输出考虑了来自多层的特征。 良好的localization和上下文的使用是可能的。

In this paper, we build upon a more elegant architecture, the so-called “fully convolutional network” [9]. We modify and extend this architecture such that it works with very few training images and yields more precise segmentations; see Figure 1. The main idea in [9] is to supplement a usual contracting network by successive layers, where pooling operators are replaced by upsampling operators. Hence, these layers increase the resolution of the output. In order to localize, high resolution features from the contracting path are combined with the upsampled output. A successive convolution layer can then learn to assemble a more precise output based on this information.

在本文中，我们基于更优雅的结构，即所谓的“全卷积网络” [9]，我们修改并扩展了该结构，使其可以在很少的训练图像上工作并产生更精确的segmentations，请参见图1。[9]中的主要思想是在连续的层级上补充通常的合同网络（usual contracting network），其中池化运算由上采样运算代替。因此，这些层提高了输出的分辨率。 为了定位，将收缩路径（contracting path）中的高分辨率特征与上采样的输出结合在一起。 然后，连续的卷积层可以根据此信息学习组装更精确的输出。

图1. U-net架构（最低分辨率的32x32像素示例）。 每个蓝色框对应一个多通道特征图。 通道数显示在框的顶部。 x-y尺寸位于框的左下边缘。 白框代表复制的特征图。 箭头表示不同的操作。

One important modification in our architecture is that in the upsampling part we have also a large number of feature channels, which allow the network to propagate context information to higher resolution layers. As a consequence, the expansive path is more or less symmetric to the contracting path, and yields a u-shaped architecture. The network does not have any fully connected layers and only uses the valid part of each convolution, i.e., the segmentation map only contains the pixels, for which the full context is available in the input image. This strategy allows the seamless segmentation of arbitrarily large images by an overlap-tile strategy (see Figure 2). To predict the pixels in the border region of the image, the missing context is extrapolated by mirroring the input image. This tiling strategy is important to apply the network to large images, since otherwise the resolution would be limited by the GPU memory.

我们架构中的一个重要修改是在上采样部分，我们还有大量的特征通道，这些特征通道使网络可以将上下文信息传播到更高分辨率的层。 结果，扩展路径或多或少地相对于收缩路径对称，并且产生u形结构。 该网络没有全连接层，仅使用每个卷积的有效部分，即分割图仅包含像素，在输入图像中可获得完整的上下文。这种策略允许通过重叠拼贴策略对任意大图像进行无缝分割（参见图2）。 为了预测图像边界区域中的像素，可通过镜像输入图像来推断缺失的上下文。这种平铺策略对于将网络应用于大图像非常重要，因为否则分辨率会受到GPU内存的限制。

图2.任意大图像的无缝分割（此处为EM堆栈中神经元结构的分割）的重叠拼贴策略。 对黄色区域中的分割的预测需要蓝色区域内的图像数据作为输入。 丢失的输入数据通过镜像推断。

As for our tasks there is very little training data available, we use excessive data augmentation by applying elastic deformations to the available training images. This allows the network to learn invariance to such deformations, without the need to see these transformations in the annotated image corpus. This is particularly important in biomedical segmentation, since deformation used to be the most common variation in tissue and realistic deformations can be simulated efficiently. The value of data augmentation for learning invariance has been shown in Dosovitskiy et al. [2] in the scope of unsupervised feature learning.

至于我们的任务，几乎没有可用的训练数据，我们通过对可用的训练图像应用弹性变形（elastic deformations）来使用过多的数据增强。 这允许网络学习此类变形的不变性，而无需在带注释的图像语料库中查看这些转换。 这在生物医学分割中尤其重要，因为变形曾经是组织中最常见的变化，并且可以有效地模拟实际变形。 Dosovitskiy等人[2]已经证明了在无监督特征学习的范围内，数据增强对于学习不变性的价值。

Another challenge in many cell segmentation tasks is the separation of touching objects of the same class; see Figure 3. To this end, we propose the use of a weighted loss, where the separating background labels between touching cells obtain a large weight in the loss function.

许多细胞分割任务中的另一个挑战是分离同一类别的接触对象（touch
ing objects），参见图3。为此，我们建议使用加权损失（weighted loss），其中在接触细胞（touching cells）之间分开的背景标签在损失函数中获得较大的权重。

图3.用DIC（微分干涉对比）显微镜记录的玻璃上的HeLa细胞。（a）原始图像。（b）覆盖真实标签的分割。不同的颜色表示HeLa细胞的不同情况。（c）生成分割蒙版（白色：前景，黑色：背景）。（d）使用逐像素损失权重进行映射，以强制网络学习边界像素。

The resulting network is applicable to various biomedical segmentation problems. In this paper, we show results on the segmentation of neuronal structures in EM stacks (an ongoing competition started at ISBI 2012), where we outperformed the network of Ciresan et al. [1]. Furthermore, we show results for cell segmentation in light microscopy images from the ISBI cell tracking challenge 2015. Here we won with a large margin on the two most challenging 2D transmitted light datasets.

所得的网络适用于各种生物医学分割问题。 在本文中，我们显示了关于EM堆栈中神经元结构分割的结果（一场持续的竞争始于ISBI 2012），在此我们胜过了Ciresan等人[1]的网络。 此外，我们在2015年ISBI细胞追踪挑战赛的光学显微镜图像中显示了细胞分割的结果。在这里，我们在两个最具挑战性的2D透射光数据集上大获全胜。

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2 Network Architecture

The network architecture is illustrated in Figure 1. It consists of a contracting path (left side) and an expansive path (right side). The contracting path follows the typical architecture of a convolutional network. It consists of the repeated application of two 3x3 convolutions (unpadded convolutions), each followed by a rectified linear unit (ReLU) and a 2x2 max pooling operation with stride 2 for downsampling. At each downsampling step we double the number of feature channels. Every step in the expansive path consists of an upsampling of the feature map followed by a 2x2 convolution (“up-convolution”) that halves the number of feature channels, a concatenation with the correspondingly cropped feature map from the contracting path, and two 3x3 convolutions, each followed by a ReLU. The cropping is necessary due to the loss of border pixels in every convolution. At the final layer a 1x1 convolution is used to map each 64component feature vector to the desired number of classes. In total the network has 23 convolutional layers.

网络架构如图1所示。它由一个收缩路径（左侧）和一个扩展路径（右侧）组成。 收缩路径遵循卷积网络的典型架构。 它由两个3x3卷积（未填充卷积）的重复应用组成，每个卷积后跟一个矩形线性单位（ReLU）和一个2x2最大合并运算，步长为2用于下采样。 在每个降采样步骤中，我们将特征通道的数量增加一倍。 扩展路径中的每个步骤都包括对特征图进行上采样，然后是将特征通道数量减半的2x2卷积（“向上卷积”），与来自收缩路径的相应裁剪的特征图的串联以及两个3x3 卷积，每个后跟一个ReLU。 由于每次卷积中都会丢失边界像素，因此有必要进行裁剪（ cropping）。 在最终层，使用1x1卷积将每个64分量特征向量映射到所需的类数。 该网络总共有23个卷积层。

To allow a seamless tiling of the output segmentation map (see Figure 2), it is important to select the input tile size such that all 2x2 max-pooling operations are applied to a layer with an even x- and y-size.

为了无缝拼接输出分割图（请参见图2），重要的是选择输入图块大小，以便将所有2x2最大池化操作应用于x和y大小均等的层。

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3 Training

The input images and their corresponding segmentation maps are used to train the network with the stochastic gradient descent implementation of Caffe [6]. Due to the unpadded convolutions, the output image is smaller than the input by a constant border width. To minimize the overhead and make maximum use of the GPU memory, we favor large input tiles over a large batch size and hence reduce the batch to a single image. Accordingly we use a high momentum (0.99) such that a large number of the previously seen training samples determine the update in the current optimization step.

输入图像及其对应的分割图用于通过Caffe [6]的随机梯度下降（SGD）实现来训练网络。由于未填充（unpadded）卷积，因此输出图像比输入图像小一个恒定的边框宽度。 为了最大程度地减少开销并最大程度地利用GPU内存，我们倾向于在大批量时使用较大的输入图块，从而将批量减少为单个图像。 因此，我们使用高动量（momentum）（0.99），以使大量先前看到的训练样本确定当前优化步骤中的更新。

The energy function is computed by a pixel-wise soft-max over the final feature map combined with the cross entropy loss function. The soft-max is defined as $p_k(x) = exp(a_k(x))/ \sum^K_ {k'=1} exp(a_{k'}(x))$ where $a_k(x)$ denotes the activation in feature channel $k$ at the pixel position $x ∈ Ω$ with $Ω ⊂ Z^2$. $K$ is the number of classes and $p_k(x)$ is the approximated maximum-function. I.e. $p_k(x) ≈ 1$ for the $k$ that has the maximum activation $a_k(x)$ and $p_k(x) ≈ 0$ for all other $k$. The cross entropy then penalizes at each position the deviation of $p_{l(x)}(x)$ from 1 using

能量函数由最终特征图上的像素级soft-max与交叉熵损失函数组合而成。soft-max定义为 $p_k(x) = exp(a_k(x))/ \sum^K_ {k'=1} exp(a_{k'}(x))$ 其中 $a_k(x)$ 表示在特征通道 $k$ 中具有 $Ω ⊂ Z^2$ 的像素位置 $x ∈ Ω$ 处的激活。$K$ 是类的数量，$p_k(x)$ 是近似的最大函数。即对于具有最大激活$a_k(x)$ 的 $k$，$p_k(x) ≈ 1$，对于所有其他 $k$，$p_k(x) ≈ 0$。交叉熵然后惩罚每个位置上 $p_{l(x)}(x)$ 与1的偏差

where $l: Ω → {1, . . . , K}$ is the true label of each pixel and $w : Ω → R$ is a weight map that we introduced to give some pixels more importance in the training.

其中 $l: Ω → {1, . . . , K}$ 是每个像素的真实标签，$w : Ω → R$ 是一个权重图，我们引入它来使某些像素在训练中更加重要。

We pre-compute the weight map for each ground truth segmentation to compensate the different frequency of pixels from a certain class in the training data set, and to force the network to learn the small separation borders that we introduce between touching cells (See Figure 3c and d).

我们为每个真实标签的分割（ground truth segmentation）预先计算权重图，以补偿训练数据集中某个类别的像素的不同频率，并迫使网络学习我们在接触细胞（touching cells）之间引入的小的分隔边界（参见图3c和d）。

The separation border is computed using morphological operations. The weight map is then computed as

使用形态学运算来计算分离边界。 然后将权重图计算为：

where $w_c: Ω → R$ is the weight map to balance the class frequencies, $d_1: Ω → R$ denotes the distance to the border of the nearest cell and $d_2: Ω → R$ the distance to the border of the second nearest cell. In our experiments we set $w_0= 10$ and $σ ≈ 5$ pixels.

其中 $w_c: Ω → R$ 是平衡类频率的权重图，$d_1: Ω → R$ 表示到最近的细胞的边界的距离，而 $d_2: Ω → R$ 到第二个最近的细胞的边界的距离。在我们的实验中，我们设置 $w_0= 10$，$σ≈5$ 像素。

In deep networks with many convolutional layers and different paths through the network, a good initialization of the weights is extremely important. Otherwise, parts of the network might give excessive activations, while other parts never contribute. Ideally the initial weights should be adapted such that each feature map in the network has approximately unit variance. For a network with our architecture (alternating convolution and ReLU layers) this can be achieved by drawing the initial weights from a Gaussian distribution with a standard deviation of $\sqrt{2/N}$, where $N$ denotes the number of incoming nodes of one neuron [5]. E.g. for a $3\times3$ convolution and $64$ feature channels in the previous layer $N = 9 · 64 = 576$.

在具有许多卷积层和通过网络的不同路径的深层网络中，权重的良好初始化非常重要。 否则，网络的某些部分可能会进行过多的激活，而其他部分则永远不会起作用。 理想情况下，应调整初始权重，以使网络中的每个特征图都具有大约单位方差。 对于具有我们架构（交替卷积和ReLU层）的网络，可以通过从高斯分布中提取初始权重（标准差为 $\sqrt{2/N}$ ）来实现，其中 $N$ 表示一个神经元的传入节点数[5] 。 例如，对于上一层的 $3 \times3$ 卷积和 $64$ 个特征通道，$N = 9·64 = 576$。

3.1 Data Augmentation

Data augmentation is essential to teach the network the desired invariance and robustness properties, when only few training samples are available. In case of microscopical images we primarily need shift and rotation invariance as well as robustness to deformations and gray value variations. Especially random elastic deformations of the training samples seem to be the key concept to train a segmentation network with very few annotated images. We generate smooth deformations using random displacement vectors on a coarse 3 by 3 grid. The displacements are sampled from a Gaussian distribution with 10 pixels standard deviation. Per-pixel displacements are then computed using bicubic interpolation. Drop-out layers at the end of the contracting path perform further implicit data augmentation.

当只有少量训练样本可用时，数据增强对于向网络传授所需的不变性和鲁棒性至关重要。对于显微图像，我们首先需要平移和旋转不变性，以及对变形和灰度值变化的鲁棒性。 尤其是训练样本的随机弹性变形似乎是训练带有很少注释图像的分割网络的关键概念。我们使用在3 x 3粗网格上的随机位移矢量生成平滑变形。 从具有10个像素标准差的高斯分布中采样位移。 然后使用双三次插值法计算每个像素的位移。 收缩路径末端的退出层进一步执行隐式数据扩充。

4 Experiments

We demonstrate the application of the u-net to three different segmentation tasks. The first task is the segmentation of neuronal structures in electron microscopic recordings. An example of the data set and our obtained segmentation is displayed in Figure 2. We provide the full result as Supplementary Material. The data set is provided by the EM segmentation challenge [14] that was started at ISBI 2012 and is still open for new contributions. The training data is a set of 30 images (512x512 pixels) from serial section transmission electron microscopy of the Drosophila first instar larva ventral nerve cord (VNC). Each image comes with a corresponding fully annotated ground truth segmentation map for cells (white) and membranes (black). The test set is publicly available, but its segmentation maps are kept secret. An evaluation can be obtained by sending the predicted membrane probability map to the organizers. The evaluation is done by thresholding the map at 10 different levels and computation of the “warping error”, the “Rand error” and the “pixel error” [14].

我们演示了u-net在三个不同细分任务中的应用。 第一项任务是在电子显微镜记录中分割神经元结构。 图2显示了数据集和获得的细分的示例。我们提供完整结果作为补充材料。该数据集由EM细分挑战[14]提供，该挑战始于ISBI 2012，目前仍在接受新的贡献。 训练数据是一组来自果蝇第一龄幼虫腹侧腹侧神经索（VNC）的连续切片透射电镜的30张图像（512x512像素）。 每个图像都带有一个对应的完全注释的真实标签的分割图，用于细胞（白色）和膜（黑色）。 该测试集是公开可用的，但其分段图已保密。 可以通过将预测的膜概率图发送给组织者来获得评估。 通过在10个不同级别对地图进行阈值化和计算“warping error”，“ Rand error”和“pixel error” [14]，可以完成评估。

The u-net (averaged over 7 rotated versions of the input data) achieves without any further pre- or postprocessing a warping error of 0.0003529 (the new best score, see Table 1) and a rand-error of 0.0382.

u-net（输入数据的7个旋转版本的平均值）无需任何进一步的预处理或后处理即可实现0.0003529（新的最佳分数，请参见表1）的warping error和0.0382的rand error。

This is significantly better than the sliding-window convolutional network result by Ciresan et al. [1], whose best submission had a warping error of 0.000420 and a rand error of 0.0504. In terms of rand error the only better performing algorithms on this data set use highly data set specific post-processing methods1 applied to the probability map of Ciresan et al. [1].

这比Ciresan等人[1]的滑动窗口卷积网络结果好得多，其最佳提交的warping error为0.000420，rand error为0.0504。 就rand error而言，在此数据集上唯一表现更好的算法是使用适用于Ciresan等人概率图的高度数据集特定的后处理方法 [1]。

表1. EM细分挑战的排名[14]（2015年3月6日），按 warping error 排序。


Fig. 4. Result on the ISBI cell tracking challenge. (a) part of an input image of the “PhC-U373” data set. (b) Segmentation result (cyan mask) with manual ground truth (yellow border) © input image of the “DIC-HeLa” data set. (d) Segmentation result (random colored masks) with manual ground truth (yellow border).

图4. ISBI细胞追踪挑战的结果。 （a）“ PhC-U373”数据集的输入图像的一部分。 （b）具有手动地面真实性的分割结果（青色蒙版）（黄色边框）（c）“ DIC-HeLa”数据集的输入图像。 （d）具有人工标注（黄色边框）的分割结果（随机彩色蒙版）

表2. 2015年ISBI细胞跟踪挑战的分段结果（IOU）。

We also applied the u-net to a cell segmentation task in light microscopic images. This segmenation task is part of the ISBI cell tracking challenge 2014 and 2015 [10,13]. The first data set “PhC-U373”2 contains Glioblastoma-astrocytoma U373 cells on a polyacrylimide substrate recorded by phase contrast microscopy (see Figure 4a,b and Supp. Material). It contains 35 partially annotated training images. Here we achieve an average IOU (“intersection over union”) of 92%, which is significantly better than the second best algorithm with 83% (see Table 2). The second data set “DIC-HeLa”3 are HeLa cells on a flat glass recorded by differential interference contrast (DIC) microscopy (see Figure 3, Figure 4c,d and Supp. Material). It contains 20 partially annotated training images. Here we achieve an average IOU of 77.5% which is significantly better than the second best algorithm with 46%.

我们还将u-net应用于光学显微图像中的细胞分割任务。 该细分任务是ISBI电池跟踪挑战2014和2015的一部分[10,13]。 第一个数据集“PhC-U373”²通过相差显微镜（参见图4a，b和附加材料）在聚丙烯酰亚胺基底上包含胶质母细胞瘤-星形细胞瘤U373细胞（Glioblastoma-astrocytoma U373 cells）。它包含35个部分注释的训练图像。在这里，我们获得了平均值 IOU（联合上的“相交”）为92％，明显好于83％的次优算法（请参见表2）。 第二个数据集“ DIC-HeLa” ³是通过差动干涉对比（DIC）显微镜记录的at玻璃上的HeLa细胞（请参见图3，图4c，d和补充材料）。它包含20个部分注释的训练图像。 在这里，我们达到77.5％的平均IOU，明显好于46％的次优算法。

5 Conclusion

The u-net architecture achieves very good performance on very different biomedical segmentation applications. Thanks to data augmentation with elastic deformations, it only needs very few annotated images and has a very reasonable training time of only 10 hours on a NVidia Titan GPU (6 GB). We provide the full Caffe[6]-based implementation and the trained networks4. We are sure that the u-net architecture can be applied easily to many more tasks.

u-net结构在非常不同的生物医学细分应用程序中都具有非常好的性能。 由于具有弹性变形的数据增强，它仅需要很少的带注释的图像，并且在NVidia Titan GPU（6 GB）上只有10小时的非常合理的训练时间。 我们提供完整的基于Caffe [6]的实施方案和经过培训的网络4。 我们确信u-net架构可以轻松地应用于更多任务。

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U-Net Network Architecture

U-net体系结构如上所示。 它由收缩路径（ contraction path）和扩展路径（expansion path）组成。

Contraction path

• 连续进行两次 3×3 Cov 和 2×2 max pooling。 这可以帮助提取更多高级特征，并且可以减少特征图的大小。

Expansion path

• 连续执行 2×2 Up-conv 和两次 3×3 Conv 以恢复分割图的大小。 但是，上述过程虽然增加了“内容（what）”，但减少了“位置（where）”。 这意味着，我们可以获得高级特征，但同时也会丢失本地化信息。
• 因此，在每次向上转换之后，我们还可以连接具有相同级别的特征图（灰色箭头）。 这有助于提供从收缩路径到扩展路径的本地化信息。
• 最后，由于输出特征图仅具有 2 类（细胞和膜），因此 1×1Conv 可将特征图的大小从64映射到2。

U-net 网络详解

Keras 代码实现

def conv2d_block(input_tensor, n_filters, kernel_size = 3, batchnorm = True):"""Function to add 2 convolutional layers with the parameters passed to it"""# first layerx = Conv2D(filters = n_filters, kernel_size = (kernel_size, kernel_size),\kernel_initializer = 'he_normal', padding = 'same')(input_tensor)if batchnorm:x = BatchNormalization()(x)x = Activation('relu')(x)# second layerx = Conv2D(filters = n_filters, kernel_size = (kernel_size, kernel_size),\kernel_initializer = 'he_normal', padding = 'same')(input_tensor)if batchnorm:x = BatchNormalization()(x)x = Activation('relu')(x)return xdef get_unet(input_img, n_filters = 16, dropout = 0.1, batchnorm = True):# Contracting Pathc1 = conv2d_block(input_img, n_filters * 1, kernel_size = 3, batchnorm = batchnorm)p1 = MaxPooling2D((2, 2))(c1)p1 = Dropout(dropout)(p1)c2 = conv2d_block(p1, n_filters * 2, kernel_size = 3, batchnorm = batchnorm)p2 = MaxPooling2D((2, 2))(c2)p2 = Dropout(dropout)(p2)c3 = conv2d_block(p2, n_filters * 4, kernel_size = 3, batchnorm = batchnorm)p3 = MaxPooling2D((2, 2))(c3)p3 = Dropout(dropout)(p3)c4 = conv2d_block(p3, n_filters * 8, kernel_size = 3, batchnorm = batchnorm)p4 = MaxPooling2D((2, 2))(c4)p4 = Dropout(dropout)(p4)c5 = conv2d_block(p4, n_filters = n_filters * 16, kernel_size = 3, batchnorm = batchnorm)# Expansive Pathu6 = Conv2DTranspose(n_filters * 8, (3, 3), strides = (2, 2), padding = 'same')(c5)u6 = concatenate([u6, c4])u6 = Dropout(dropout)(u6)c6 = conv2d_block(u6, n_filters * 8, kernel_size = 3, batchnorm = batchnorm)u7 = Conv2DTranspose(n_filters * 4, (3, 3), strides = (2, 2), padding = 'same')(c6)u7 = concatenate([u7, c3])u7 = Dropout(dropout)(u7)c7 = conv2d_block(u7, n_filters * 4, kernel_size = 3, batchnorm = batchnorm)u8 = Conv2DTranspose(n_filters * 2, (3, 3), strides = (2, 2), padding = 'same')(c7)u8 = concatenate([u8, c2])u8 = Dropout(dropout)(u8)c8 = conv2d_block(u8, n_filters * 2, kernel_size = 3, batchnorm = batchnorm)u9 = Conv2DTranspose(n_filters * 1, (3, 3), strides = (2, 2), padding = 'same')(c8)u9 = concatenate([u9, c1])u9 = Dropout(dropout)(u9)c9 = conv2d_block(u9, n_filters * 1, kernel_size = 3, batchnorm = batchnorm)outputs = Conv2D(1, (1, 1), activation='sigmoid')(c9)model = Model(inputs=[input_img], outputs=[outputs])return model

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参考：
Understanding Semantic Segmentation with UNET
Review: U-Net (Biomedical Image Segmentation)