论文原文：点击此处
论文下载：点击此处
论文被引：14541
论文年份：2014
论文代码：点击此处

顾名思义，fully convolutional networks 就是全卷积网络，那么它与传统的神经网络架构有什么区别？

• 没有全连接层，只有卷积层，有时还有池化层组成；
• 输入图像，输出也是图像，而不是分类，因为输出层是卷积层。

看一下分类网络和FCN分割的对比。

这么做有什么优势？引用Quora上的一个回答1。

Input image size: If you don’t have any fully connected layer in your network, you can apply the network to images of virtually any size. Because only the fully connected layer expects inputs of a certain size, which is why in architectures like AlexNet, you must provide input images of a certain size (224x224).
Spatial information: Fully connected layer generally causes loss of spatial information - because its “fully connected”: all output neurons are connected to all input neurons. This kind of architecture can’t be used for segmentation, if you are working in a huge space of possibilities (e.g. unconstrained real images [1]). Although fully connected layers can still do segmentation if you are restricted to a relatively smaller space e.g. a handful of object categories with limited visual variation, such that the FC activations may act as a sufficient statistic for those images [2,3]. In the latter case, the FC activations are enough to encode both the object type and its spatial arrangement. Whether one or the other happens depends upon the capacity of the FC layer as well as the loss function.
Computational cost and representation power: There is also a distinction in terms of compute vs storage between convolutional layers and fully connected layers that I am a bit confused about. For instance, in AlexNet the convolutional layers comprised of 90% of the weights (~representational capacity) but contributed only to 10% of the computation; and the remaining (10% weights => less representation power, 90% computation) was eaten up by fully connected layers. Thus usually researchers are beginning to favor having a greater number of convolutional layers, tending towards fully convolutional networks for everything.

第二个回答2

Fully convolutional indicates that the neural network is composed of convolutional layers without any fully-connected layers or MLP usually found at the end of the network. A CNN with fully connected layers is just as end-to-end learnable as a fully convolutional one. The main difference is that the fully convolutional net is learning filters every where. Even the decision-making layers at the end of the network are filters.
A fully convolutional net tries to learn representations and make decisions based on local spatial input. Appending a fully connected layer enables the network to learn something using global information where the spatial arrangement of the input falls away and need not apply.

Fully Convolutional Networks for Semantic Segmentation

Abstract

Convolutional networks are powerful visual models that yield hierarchies of features. We show that convolutional networks by themselves, trained end-to-end, pixelstopixels, exceed the state-of-the-art in semantic segmentation.Our key insight is to build “fully convolutional” networks that take input of arbitrary size and produce correspondingly-sized output with efficient inference and learning. We define and detail the space of fully convolutional networks, explain their application to spatially dense prediction tasks, and draw connections to prior models. We adapt contemporary classification networks (AlexNet [22], the VGG net [34], and GoogLeNet [35]) into fully convolutional networks and transfer their learned representations by fine-tuning [5] to the segmentation task. We then define a skip architecture that combines semantic information from a deep, coarse layer with appearance information from a shallow, fine layer to produce accurate and detailed segmentations.Our fully convolutional network achieves state-of-the-art segmentation of PASCAL VOC (20% relative improvement to 62.2% mean IU on 2012), NYUDv2, and SIFT Flow, while inference takes less than one fifth of a second for a typical image.

卷积网络是强大的视觉模型，可产生要素层次结构。 我们证明，卷积网络本身（经过端到端训练的像素到像素）在语义分割方面超过了最新技术。我们的主要观点是建立“全卷积”的网络，该网络可以接受任意大小的输入，并通过有效的推理和学习产生相应大小的输出。 我们定义和详细说明了全卷积网络的空间，解释了它们在空间密集的预测任务中的应用，并绘制了与先前模型的对比关系图。 我们将当代分类网络（AlexNet [22]，VGG net [34]和GoogLeNet [35]）改编为全卷积网络，并通过微调[5]将其学习的表示传递给分割任务。 然后，我们定义一个跳过结构，该结构将来自较深的粗糙层的语义信息与来自较浅的精细层的外观信息相结合，以产生准确而详细的细分。我们的全卷积网络实现了PASCAL VOC（2012年相对改善，平均IU达到62.2％），NYUDv2和SIFT Flow的最新分割，而对于典型图像，推理所需的时间不到五分之一秒。

1. Introduction

Convolutional networks are driving advances in recognition. Convnets are not only improving for whole-image classification [19, 31, 32], but also making progress on local tasks with structured output. These include advances in bounding box object detection [29, 12, 17], part and keypoint prediction [39, 24], and local correspondence [24, 9].

卷积网络正在推动识别技术的进步。卷积不仅改善了全图像分类[22，34，35]，而且在具有结构化输出的定位任务上也取得了进展。 这些包括边界框对象检测[32、12、19]，部分和关键点预测[42、26]以及局部对应[26、10]方面的进步。

The natural next step in the progression from coarse to fine inference is to make a prediction at every pixel. Prior approaches have used convnets for semantic segmentation [27, 2, 8, 28, 16, 14, 11], in which each pixel is labeled with the class of its enclosing object or region, but with shortcomings that this work addresses.

从粗略推断到精细推断的下一步是对每个像素进行预测。 先前的方法已经使用卷积语义分割[30、3、9、31、17、15、11]，其中每个像素都用其封闭的对象或区域的类别标记，但是存在该工作要解决的缺点。

We show that a fully convolutional network (FCN), trained end-to-end, pixels-to-pixels on semantic segmentation exceeds the state-of-the-art without further machinery. To our knowledge, this is the first work to train FCNs end-to-end (1) for pixelwise prediction and (2) from supervised pre-training. Fully convolutional versions of existing networks predict dense outputs from arbitrary-sized inputs. Both learning and inference are performed whole-image-ata-time by dense feedforward computation and backpropagation. In-network upsampling layers enable pixelwise prediction and learning in nets with subsampled pooling.

我们显示，在语义分割上，经过端到端，像素到像素训练的全卷积网络（FCN）超过了最新技术，而无需其他机制。据我们所知，这是端到端训练FCN的第一项工作（1）用于像素预测，而（2）则来自监督式预训练。 现有网络的全卷积版本可以预测任意大小输入的密集输出。学习和推理都是通过密集的前馈计算和反向传播在整个图像时间进行的。网络内上采样层可通过子采样池在网络中实现像素级预测和学习。

This method is efficient, both asymptotically and absolutely, and precludes the need for the complications in other works. Patchwise training is common [27, 2, 8, 28, 11], but lacks the efficiency of fully convolutional training. Our approach does not make use of pre- and post-processing complications, including superpixels [8, 16], proposals [16, 14], or post-hoc refinement by random fields or local classifiers [8, 16]. Our model transfers recent success in classification [19, 31, 32] to dense prediction by reinterpreting classification nets as fully convolutional and fine-tuning from their learned representations. In contrast, previous works have applied small convnets without supervised pre-training [8, 28, 27].

这种方法在渐近性和绝对性上都是有效的，并且不需要其他工作中的复杂性。逐行训练是常见的[27、2、8、28、11]，但缺乏完全卷积训练的效率。我们的方法没有利用前后处理的复杂性，包括超像素[8，16]，建议[16，14]或通过随机字段或局部分类器进行的事后细化[8，16]。我们的模型通过将分类网络重新解释为全卷积并根据其学习表示进行微调，将最近在分类[19、31、32]中的成功转移到密集预测。相比之下，先前的工作在没有监督预训练的情况下应用了小型卷积网络[8，28，27]。

Semantic segmentation faces an inherent tension between semantics and location: global information resolves what while local information resolves where. Deep feature hierarchies jointly encode location and semantics in a localto-global pyramid. We define a novel “skip” architecture to combine deep, coarse, semantic information and shallow, fine, appearance information in Section 4.2 (see Figure 3).

语义分割面临着语义和位置之间的固有矛盾：全局信息解决了什么，而局部信息解决了什么。深度特征层次结构在局部到全局金字塔中共同编码位置和语义。我们在第4.2节中定义了一种新颖的“跳过”架构，以结合深度，粗略，语义信息和浅，精细，外观信息（参见图3）。

In the next section, we review related work on deep classification nets, FCNs, and recent approaches to semantic segmentation using convnets. The following sections explain FCN design and dense prediction tradeoffs, introduce our architecture with in-network upsampling and multilayer combinations, and describe our experimental framework. Finally, we demonstrate state-of-the-art results on PASCAL VOC 2011-2, NYUDv2, and SIFT Flow.

在下一部分中，我们将回顾有关深度分类网，FCN和使用卷积网络进行语义分割的最新方法的相关工作。 以下各节介绍了FCN设计和密集的预测权衡，介绍了具有网络内上采样和多层组合的结构，并描述了我们的实验框架。最后，我们演示了PASCAL VOC 2011-2，NYUDv2和SIFT Flow的最新结果。

---

2. Related work

Our approach draws on recent successes of deep nets for image classification [19, 31, 32] and transfer learning [4, 38]. Transfer was first demonstrated on various visual recognition tasks [4, 38], then on detection, and on both instance and semantic segmentation in hybrid proposal classifier models [12, 16, 14]. We now re-architect and finetune classification nets to direct, dense prediction of semantic segmentation. We chart the space of FCNs and situate prior models, both historical and recent, in this framework.

我们的方法借鉴了深层网络在图像分类[19，31，32]和迁移学习[4，38]方面的最新成功。首先在各种视觉识别任务上演示了迁移[4，38]，然后在混合提议分类器模型[12，16，14]中的检测以及实例和语义分割上进行了演示。现在，我们重新构造和微调分类网，以进行语义细分的直接，密集的预测。我们在此框架中绘制了FCN的空间并放置了历史模型和最新模型。

Fully convolutional networks. To our knowledge, the idea of extending a convnet to arbitrary-sized inputs first appeared in Matan et al. [25], which extended the classic LeNet [21] to recognize strings of digits. Because their net was limited to one-dimensional input strings, Matan et al. used Viterbi decoding to obtain their outputs. Wolf and Platt [37] expand convnet outputs to 2-dimensional maps of detection scores for the four corners of postal address blocks. Both of these historical works do inference and learning fully convolutionally for detection. Ning et al. [27] define a convnet for coarse multiclass segmentation of C. elegans tissues with fully convolutional inference.

全卷积网络。据我们所知，将卷积网络扩展到任意大小的输入的想法首先出现在Matan等人中[25]，它扩展了经典的LeNet [21]以识别数字字符串。因为它们的网络仅限于一维输入字符串，所以Matan等人使用Viterbi解码获得其输出。 Wolf和Platt [37]将convnet输出扩展为邮政地址块四个角的检测分数的二维图。这两个历史著作都进行推理和全卷积学习以进行检测。Ning 等[27]定义了一个卷积网络，用完全卷积推理对秀丽隐杆线虫组织进行粗分类。

Fully convolutional computation has also been exploited in the present era of many-layered nets. Sliding window detection by Sermanet et al. [29], semantic segmentation by Pinheiro and Collobert [28], and image restoration by Eigen et al. [5] do fully convolutional inference. Fully convolutional training is rare, but used effectively by Tompson et al. [35] to learn an end-to-end part detector and spatial model for pose estimation, although they do not exposit on or analyze this method.

在当今的多层网络中，也已经开发了全卷积计算。 Sermanet等人的滑动窗口检测。 [29]，由Pinheiro和Collobert [28]进行语义分割，以及由Eigen等人进行图像复原。 [5]做全卷积推理。全卷积训练是很少见的，但是被Tompson等人[35]有效地使用。 学习一个端到端的零件检测器和空间模型来进行姿态估计，尽管它们没有阐述或分析这种方法。

Alternatively, He et al. [17] discard the nonconvolutional portion of classification nets to make a feature extractor. They combine proposals and spatial pyramid pooling to yield a localized, fixed-length feature for classification. While fast and effective, this hybrid model cannot be learned end-to-end.

另外，He等[19]丢弃分类网的非卷积部分以制作特征提取器。 他们将提案和空间金字塔池相结合，以产生用于分类的局部固定长度特征。 虽然快速有效，但无法端对端学习这种混合模型。

Dense prediction with convnets. Several recent works have applied convnets to dense prediction problems, including semantic segmentation by Ning et al. [27], Farabet et al.[8], and Pinheiro and Collobert [28]; boundary prediction for electron microscopy by Ciresan et al. [2] and for natural images by a hybrid neural net/nearest neighbor model by Ganin and Lempitsky [11]; and image restoration and depth estimation by Eigen et al. [5, 6]. Common elements of these approaches include

卷积网络的密集预测。最近有几篇著作将卷积网络应用于密集预测问题，包括Ning等人[27]的语义分割，Farabet等[8]，以及Pinheiro和Collobert [28]； Ciresan等人的电子显微镜边界预测。 [2]和Ganin和Lempitsky [11]的混合神经网络/最近邻居模型的自然图像；以及Eigen等人的图像恢复和深度估计。 [5，6]。这些方法的共同要素包括：

• small models restricting capacity and receptive fields;
• patchwise training [27, 2, 8, 28, 11];
• post-processing by superpixel projection, random field regularization, filtering, or local classification [8, 2, 11];
• input shifting and output interlacing for dense output [28, 11] as introduced by OverFeat [29];
• multi-scale pyramid processing [8, 28, 11];
• saturating tanh nonlinearities [8, 5, 28]; and
• ensembles [2, 11],

whereas our method does without this machinery. However, we do study patchwise training 3.4 and “shift-and-stitch” dense output 3.2 from the perspective of FCNs. We also discuss in-network upsampling 3.3, of which the fully connected prediction by Eigen et al. [6] is a special case.

而我们的方法没有这种机制。但是，我们确实从FCN的角度研究了分批训练3.4和“移位和缝合”密集输出3.2。我们还将讨论网络中的上采样3.3，其中Eigen等人[6]的预测完全相关，是一个特例。

Unlike these existing methods, we adapt and extend deep classification architectures, using image classification as supervised pre-training, and fine-tune fully convolutionally to learn simply and efficiently from whole image inputs and whole image ground thruths.

与这些现有方法不同，我们采用图像分类作为监督的预训练来适应和扩展深度分类体系结构，并进行全面卷积微调，以从整个图像输入和整个图像地基中简单有效地学习。

Hariharan et al. [16] and Gupta et al. [14] likewise adapt deep classification nets to semantic segmentation, but do so in hybrid proposal-classifier models. These approaches fine-tune an R-CNN system [12] by sampling bounding boxes and/or region proposals for detection, semantic segmentation, and instance segmentation. Neither method is learned end-to-end.

Hariharan等[16]和Gupta等[14]同样使深度分类网适应语义分割，但在混合提议分类器模型中也是如此。 这些方法通过采样边界框和/或区域建议以进行检测，语义分割和实例分割来微调R-CNN网络[12]。这两种方法都不是端到端学习的。他们分别在PASCAL VOC和NYUDv2上实现了最新的分割结果，因此我们在第5节中直接将我们独立的端到端FCN与它们的语义分割结果进行比较。

They achieve state-of-the-art results on PASCAL VOC segmentation and NYUDv2 segmentation respectively, so we directly compare our standalone, end-to-end FCN to their semantic segmentation results in Section 5.

他们分别在PASCAL VOC分割和NYUDv2分割上获得了最新的结果，因此我们在第5节中直接将我们独立的端到端FCN与它们的语义分割结果进行比较。

---

3. Fully convolutional networks

Each layer of data in a convnet is a three-dimensional array of size h×w×d, where h and w are spatial dimensions, and d is the feature or channel dimension. The first layer is the image, with pixel size h×w, and d color channels.Locations in higher layers correspond to the locations in the image they are path-connected to, which are called their receptive fields.

卷积网络中的每一层数据都是尺寸为h×w×d的三维数组，其中h和w是空间维，而d是特征或通道维。 第一层是图像，像素大小为h×w，具有d个颜色通道。较高层中的位置对应于它们在路径上连接到的图像中的位置，称为它们的接收场（receptive fields）。

Convnets are built on translation invariance. Their basic components (convolution, pooling, and activation functions) operate on local input regions, and depend only on relative spatial coordinates. Writing xij for the data vector at location (i; j) in a particular layer, and yij for the following layer, these functions compute outputs yij by

卷积建立在翻译不变性上。它们的基本组件（卷积，池化和激活函数）在局部输入区域上运行，并且仅取决于相对空间坐标。将 $x_{ij}$ 写入特定层中位置 (i; j) 的数据矢量，并将 $y_{ij}$ 写入下一层，这些函数通过以下方式计算输出 $y_{ij}$

where k is called the kernel size, s is the stride or subsampling factor, and fks determines the layer type: a matrix multiplication for convolution or average pooling, a spatial max for max pooling, or an elementwise nonlinearity for an activation function, and so on for other types of layers.

其中 $k$ 称为核大小，$s$ 是跨度或二次采样因子，$f_{ks}$ 确定层类型：用于卷积或平均池化的矩阵乘法，用于最大池化的空间最大值，或用于激活函数的元素非线性，依此类推用于其他类型的层。

This functional form is maintained under composition, with kernel size and stride obeying the transformation rule

该函数形式保持组成不变，内核大小和步幅遵循转换规则

While a general deep net computes a general nonlinear function, a net with only layers of this form computes a nonlinear filter, which we call a deep filter or fully convolutional network. An FCN naturally operates on an input of any size, and produces an output of corresponding (possibly resampled) spatial dimensions.

一般的深层网络计算一般的非线性函数，而仅具有这种形式的层的网络将计算非线性滤波器，我们称其为深层滤波器或全卷积网络。 FCN自然可以在任何大小的输入上运行，并产生对应的（可能是重新采样的）空间尺寸的输出。

A real-valued loss function composed with an FCN defines a task. If the loss function is a sum over the spatial dimensions of the final layer, $l(x; θ) = Σ_{ij}·l'(x_{ij};θ)$, its gradient will be a sum over the gradients of each of its spatial components. Thus stochastic gradient descent on computed on whole images will be the same as stochastic gradient descent on $l'$, taking all of the final layer receptive fields as a minibatch.

由FCN组成的实值损失函数定义任务。 如果损失函数是最后一层空间维度上的总和，则$l(x; θ) = Σ_{ij}·l'(x_{ij};θ)$，其梯度将是其每个空间分量的梯度上的总和。 因此，将所有最终层接受场作为一个小批量，在整个图像上计算出的 $l$ 上的随机梯度下降将与 $l'$ 上的随机梯度下降相同。

When these receptive fields overlap significantly, both feedforward computation and backpropagation are much more efficient when computed layer-by-layer over an entire image instead of independently patch-by-patch.

当这些接收场显着重叠时，在整个图像上逐层计算而不是逐个补丁地进行时，前馈计算和反向传播都更加有效。

We next explain how to convert classification nets into fully convolutional nets that produce coarse output maps. For pixelwise prediction, we need to connect these coarse outputs back to the pixels. Section 3.2 describes a trick that OverFeat [29] introduced for this purpose. We gain insight into this trick by reinterpreting it as an equivalent network modification. As an efficient, effective alternative, we introduce deconvolution layers for upsampling in Section 3.3. In Section 3.4 we consider training by patchwise sampling, and give evidence in Section 4.3 that our whole image training is faster and equally effective.

接下来，我们将说明如何将分类网络转换为可生成粗糙输出图的全卷积网络。对于逐像素预测，我们需要将这些粗略输出连接回像素。 3.2节描述了OverFeat [29]为此目的引入的一个技巧。通过将其重新解释为等效的网络修改，我们可以深入了解此技巧。作为一种有效的替代方案，我们将在第3.3节中介绍反卷积层以进行上采样。在第3.4节中，我们考虑通过逐点采样进行训练，并在第4.3节中证明我们的整个图像训练更快且同样有效。

3.1. Adapting classifiers for dense prediction

Typical recognition nets, including LeNet [21], AlexNet [19], and its deeper successors [31, 32], ostensibly take fixed-sizedinputsandproducenonspatialoutputs. Thefully connected layers of these nets have fixed dimensions and throw away spatial coordinates. However, these fully connected layers can also be viewed as convolutions with kernels that cover their entire input regions. Doing so casts them into fully convolutional networks that take input of any size and output classification maps. This transformation is illustrated in Figure 2. (By contrast, nonconvolutional nets, such as the one by Le et al. [20], lack this capability.)

典型的识别网络，包括LeNet [21]，AlexNet [19]及其更深的后继者[31、32]，表面上采用固定大小的输入并产生非空间输出。这些网络的全连接层具有固定的尺寸并丢弃空间坐标。但是，这些全连接层也可以看作是覆盖整个输入区域的内核的卷积。这样做会将它们转换为全卷积网络，该网络可以接收任何大小的输入并输出分类图。这种转换如图2所示。（相比之下，非卷积网络（例如Le等人的文献[20]）缺乏这种能力。）

Figure 2. Transforming fully connected layers into convolution layers enables a classification net to output a heatmap. Adding layers and a spatial loss (as in Figure 1) produces an efficient machine for end-to-end dense learning.

图2.将全连接层转换为卷积层使分类网可以输出热图。增加层数和空间损失（如图1所示）将为端到端密集学习提供高效的机器。

Furthermore, while the resulting maps are equivalent to the evaluation of the original net on particular input patches, the computation is highly amortized over the overlapping regions of those patches. For example, while AlexNet takes 1.2 ms (on a typical GPU) to infer the classification scores of a 227×227 image, the fully convolutional net takes 22 ms to produce a 10×10 grid of outputs from a 500×500 image, which is more than 5 times faster than the naive approach1.

此外，虽然生成的映射等效于在特定输入色块上对原始网络的评估，但在这些色块的重叠区域上进行了高额摊销。 例如，虽然AlexNet需要1.2毫秒（在典型的GPU上）来推断227×227图像的分类得分，但全卷积网络却需要22毫秒才能从500×500图像中生成10×10的输出网格。 比单纯的方法快5倍以上。

The spatial output maps of these convolutionalized models make them a natural choice for dense problems like semantic segmentation. With ground truth available at every output cell, both the forward and backward passes are straightforward, and both take advantage of the inherent computational efficiency (and aggressive optimization) of convolution.

这些卷积模型的空间输出图使它们成为诸如语义分割之类的密集问题的自然选择。由于每个输出单元都有可用的基本事实，因此正向和反向传递都很简单，并且都利用了卷积的固有计算效率（和主动优化）。

The corresponding backward times for the AlexNet example are 2.4 ms for a single image and 37 ms for a fully convolutional 10 × 10 output map, resulting in a speedup similar to that of the forward pass. This dense backpropagation is illustrated in Figure 1.

对于AlexNet示例，相应的后退时间对于单个图像为2.4 ms，对于完全卷积的10×10输出映射为37 ms，从而导致加速效果类似于正向传递。这种密集的反向传播如图1所示。

While our reinterpretation of classification nets as fully convolutional yields output maps for inputs of any size, the output dimensions are typically reduced by subsampling. The classification nets subsample to keep filters small and computational requirements reasonable. This coarsens the output of a fully convolutional version of these nets, reducing it from the size of the input by a factor equal to the pixel stride of the receptive fields of the output units.

虽然我们将分类网重新解释为全卷积的输出图，但对于任何大小的输入而言，输出尺寸通常都会通过子采样来降低。分类网子采样可保持过滤器较小且计算要求合理。 这使这些网络的完全卷积形式的输出变得粗糙，从而将其从输入大小中减小到等于输出单元接收场的像素跨度的倍数。

3.2. Shift-and-stitch is filter rarefaction

Input shifting and output interlacing is a trick that yields dense predictions from coarse outputs without interpolation, introduced by OverFeat [29]. If the outputs are downsampled by a factor of $f$, the input is shifted (by left and top padding) $x$ pixels to the right and $y$ pixels down, once for every value of $(x, y) ∈ [0, . . . , f − 1] × [0, . . . , f − 1 ]$. These $f^2$ inputs are each run through the convnet, and the outputs are interlaced so that the predictions correspond to the pixels at the centers of their receptive fields.

输入移位和输出隔行扫描是一种技巧，它可以从粗略输出中获得密集预测而无需插值，这是由OverFeat [29]引入的。如果对输出进行下采样 $f$ 倍，则对于 $(x, y) ∈ [0, . . . , f − 1] × [0, . . . , f − 1 ]$ 的每个值，输入将向右移 $x$ 个像素，并向右移 $x$ 个像素，向下移 $y$ 个像素。这些 $f^2$ 输入每个都通过卷积网络，并且输出是隔行扫描的，因此预测对应于其接收场中心的像素。

Changing only the filters and layer strides of a convnet can produce the same output as this shift-and-stitch trick. Consider a layer (convolution or pooling) with input stride s, and a following convolution layer with filter weights $f_{ij}$ (eliding the feature dimensions, irrelevant here). Setting the lower layer’s input stride to 1 upsamples its output by a factor of s, just like shift-and-stitch. However, convolving the original filter with the upsampled output does not produce the same result as the trick, because the original filter only sees a reduced portion of its (now upsampled) input. To reproduce the trick, rarefy the filter by enlarging it as

仅更改卷积滤波器的滤镜和跨步可以产生与该移位和缝合技巧相同的输出。考虑具有输入步幅s的层（卷积或池化），以及下一个具有滤波器权重 $f_{ij}$ 的卷积层（忽略特征尺寸，在此不相关）。将下层的输入步幅设置为1，就像移位和缝制一样，将其输出上采样s倍。但是，将原始滤波器与上采样输出进行卷积不会产生与技巧相同的结果，因为原始滤波器只会看到其（现在是上采样）输入的减少部分。要重现该技巧，请将滤波器放大为

(with $i$ and $j$ zero-based). Reproducing the full net output of the trick involves repeating this filter enlargement layerby-layer until all subsampling is removed.

（其中 $i$ 和 $j$ 从零开始）。再现技巧的完整净输出涉及逐层重复此滤波器放大，直到删除所有子采样为止。

Simply decreasing subsampling within a net is a tradeoff: the filters see finer information, but have smaller receptive fields and take longer to compute. We have seen that the shift-and-stitch trick is another kind of tradeoff: the output is made denser without decreasing the receptive field sizes of the filters, but the filters are prohibited from accessing information at a finer scale than their original design.

简单地减少网络内的二次采样是一个折衷：滤波器看到的信息更好，但是接收场更小，计算所需的时间更长。我们已经看到，移位和绣制技巧是另一种折衷方案：在不减小过滤器的接收场大小的情况下，使输出更密集，但禁止过滤器以比其原始设计更精细的比例访问信息。

Decreasing subsampling within a net is a tradeoff: the filters see finer information, but have smaller receptive fields and take longer to compute. The shift-and-stitch trick is another kind of tradeoff: the output is denser without decreasing the receptive field sizes of the filters, but the filters are prohibited from accessing information at a finer scale than their original design.

减少网络内的二次采样是一个权衡：滤波器看到的信息更好，但接收场较小，计算所需的时间更长。 移位和缝合技巧是另一种折衷方案：输出更密集而不减小过滤器的接收场大小，但是与原始设计相比，滤波器被禁止以更精细的比例访问信息。

Although we have done preliminary experiments with shift-and-stitch, we do not use it in our model. We find learning through upsampling, as described in the next section, to be more effective and efficient, especially when combined with the skip layer fusion described later on.

尽管我们已经完成了平移和绣制的初步实验，但是我们并未在模型中使用它。我们发现通过下采样进行学习将变得更加有效，这将在下一节中介绍，特别是与稍后描述的跳过层融合结合使用时。

3.3. Upsampling is backwards strided convolution

Another way to connect coarse outputs to dense pixels is interpolation. For instance, simple bilinear interpolation computes each output $y_{ij}$ from the nearest four inputs by a linear map that depends only on the relative positions of the input and output cells.

将粗略输出连接到密集像素的另一种方法是插值。 例如，简单的双线性插值通过仅依赖于输入和输出像元的相对位置的线性映射从最近的四个输入计算每个输出 $y_{ij}$。

In a sense, upsampling with factor f is convolution with a fractional input stride of $1/f$. So long as $f$ is integral, a natural way to upsample is therefore backwards convolution (sometimes called deconvolution) with an output stride of $f$. Such an operation is trivial to implement, since it simply reverses the forward and backward passes of convolution.

从某种意义上说，因子为 $f$ 的向上采样是卷积，输入步幅为 $1/f$。 只要 $f$ 是整数，向上采样的自然方法就是以输出步幅 $f$ 向后进行卷积（有时称为反卷积）。 这样的操作很容易实现，因为它简单地反转了卷积的前进和后退。

Thus upsampling is performed in-network for end-to-end learning by backpropagation from the pixelwise loss.Note that the deconvolution filter in such a layer need not be fixed (e.g., to bilinear upsampling), but can be learned.A stack of deconvolution layers and activation functions can even learn a nonlinear upsampling.

因此，通过从像素方向的损失进行反向传播，在网络中执行上采样以进行端到端学习。注意，在这样的层中的去卷积滤波器不必是固定的（例如，固定为双线性上采样），而是可以学习的。一堆反卷积层和激活函数甚至可以学习非线性上采样。

In our experiments, we find that in-network upsampling is fast and effective for learning dense prediction. Our best segmentation architecture uses these layers to learn to upsample for refined prediction in Section 4.2.

在我们的实验中，我们发现网络内上采样对于学习密集预测是快速有效的。 我们最好的分割架构使用这些层来学习上采样，以进行第4.2节中的精确预测。

3.4. Patchwise training is loss sampling

In stochastic optimization, gradient computation is driven by the training distribution. Both patchwise training and fully convolutional training can be made to produce any distribution, although their relative computational efficiency depends on overlap and minibatch size. Whole image fully convolutional training is identical to patchwise training where each batch consists of all the receptive fields of the units below the loss for an image (or collection of images). While this is more efficient than uniform sampling of patches, it reduces the number of possible batches. However, random selection of patches within an image may be recovered simply. Restricting the loss to a randomly sampled subset of its spatial terms (or, equivalently applying a DropConnect mask [36] between the output and the loss) excludes patches from the gradient computation.

在随机优化中，梯度计算由训练分布驱动。 尽管它们的相对计算效率取决于重叠和最小批处理大小，但可以使补丁式（patchwise）训练和完全卷积训练两者都产生任何分布。完整图像的全卷积训练与逐块训练相同，在该训练中，每批都包含低于图像损失（或图像收集）的单位的所有接受场。虽然这比统一补丁采样更为有效，但它减少了可能的批数量。但是，可以简单地恢复图像内补丁的随机选择。将损失限制为其空间项的随机采样子集（或等效地在输出和损失之间应用DropConnect掩码[36]）可将色块排除在梯度计算之外。

If the kept patches still have significant overlap, fully convolutional computation will still speed up training. If gradients are accumulated over multiple backward passes, batches can include patches from several images.²

如果保留的色块仍具有明显的重叠，则完全卷积计算仍将加快训练速度。 如果梯度是在多个向后遍历上累积的，则批处理可以包含来自多个图像的补丁。²

Sampling in patchwise training can correct class imbalance [27, 8, 2] and mitigate the spatial correlation of dense patches [28, 16]. In fully convolutional training, class balance can also be achieved by weighting the loss, and loss sampling can be used to address spatial correlation.

逐块训练中的采样可以纠正类不平衡[27、8、2]，并减轻密集块的空间相关性[28、16]。在全卷积训练中，类平衡也可以通过加权损失来实现，并且损失采样可以用于解决空间相关性。

We explore training with sampling in Section 4.3, and do not find that it yields faster or better convergence for dense prediction. Whole image training is effective and efficient.

我们在第4.3节中探讨了采用采样的训练，但没有发现对于密集的预测它会产生更快或更佳的收敛。整个图像训练是有效和高效的。

4. Segmentation Architecture

We cast ILSVRC classifiers into FCNs and augment them for dense prediction with in-network upsampling and a pixelwise loss. We train for segmentation by fine-tuning.Next, we add skips between layers to fuse coarse, semantic and local, appearance information. This skip architecture is learned end-to-end to refine the semantics and spatial precision of the output.

我们将ILSVRC分类器转换为FCN，并通过网络内上采样和逐像素损失对它们进行增强以进行密集的预测。 我们通过微调训练分割。接下来，我们在各层之间添加跳过连接，以融合粗略的，语义的和局部的外观信息。 端到端学习了这种跳过架构，以改进输出的语义和空间精度。

For this investigation, we train and validate on the PASCAL VOC 2011 segmentation challenge [8]. We train with a per-pixel multinomial logistic loss and validate with the standard metric of mean pixel intersection over union, with the mean taken over all classes, including background. The training ignores pixels that are masked out (as ambiguous or difficult) in the ground truth.

对于此调查，我们训练并验证了PASCAL VOC 2011细分挑战[8]。 我们使用每像素多项式逻辑损失进行训练，并使用平均像素相交与并集的标准度量进行验证，并采用所有类别（包括背景）的均值。 训练会忽略在真实情况下被掩盖（模糊或困难）的像素。

Figure 3. Our DAG nets learn to combine coarse, high layer information with fine, low layer information. Pooling and prediction layers are shown as grids that reveal relative spatial coarseness, while intermediate layers are shown as vertical lines. First row (FCN-32s): Our singlestream net, described in Section 4.1, upsamples stride 32 predictions back to pixels in a single step. Second row (FCN-16s): Combining predictions from both the final layer and the pool4 layer, at stride 16, lets our net predict finer details, while retaining high-level semantic information. Third row (FCN-8s): Additional predictions from pool3, at stride 8, provide further precision.

图3.我们的DAG网络学习将粗糙的高层信息与精细的低层信息相结合。池化和预测层显示为显示相对空间粗糙度的网格，而中间层显示为垂直线。第一行（FCN-32s）：如第4.1节所述，我们的单流网络将一步一步将32个预测返回到像素。第二行（FCN-16）：在第16步结合来自最后一层和pool4层的预测，使我们的网络可以预测更精细的细节，同时保留高级语义信息。 第三行（FCN-8s）：在第8步中来自pool3的其他预测提供了更高的精度。

4.1. From classifier to dense FCN

We begin by convolutionalizing proven classification architectures as in Section 3. We consider the AlexNet³ architecture [22] that won ILSVRC12, as well as the VGG nets [34] and the GoogLeNet4 [35] which did exceptionally well in ILSVRC14. We pick the VGG 16-layer net5, which we found to be equivalent to the 19-layer net on this task. For GoogLeNet, we use only the final loss layer, and improve performance by discarding the final average pooling layer. We decapitate each net by discarding the final classifier layer, and convert all fully connected layers to convolutions. We append a 1×1 convolution with channel dimension 21 to predict scores for each of the PASCAL classes (including background) at each of the coarse output locations, followed by a deconvolution layer to bilinearly upsample the coarse outputs to pixel-dense outputs as described in Section 3.3. Table 1 compares the preliminary validation results along with the basic characteristics of each net. We report the best results achieved after convergence at a fixed learning rate (at least 175 epochs).

首先，如第3节所述，对经过验证的分类架构进行卷积。我们考虑赢得ILSVRC12的AlexNet³架构[22]，以及在ILSVRC14中表现出色的VGG网络[34]和GoogLeNet4 [35]。 我们选择了VGG 16层网络5，我们发现它相当于此任务上的19层网络。 对于GoogLeNet，我们仅使用最终的损失层，并通过丢弃最终的平均池化层来提高性能。 我们通过丢弃最终的分类器层来使每个网络断头，并将所有全连接层转换为卷积层。 我们将通道尺寸为21的1×1卷积附加到每个粗略输出位置处的每个PASCAL类（包括背景）的分数预测中，然后进行解卷积层将粗略输出双线性升采样为像素密集输出，如在第3.3节中所述。 表1比较了初步验证结果以及每个网络的基本特征。 我们报告了以固定的学习速度（至少175个epochs）收敛后获得的最佳结果。

Fine-tuning from classification to segmentation gave reasonable predictions for each net. Even the worst model achieved ~75% of state-of-the-art performance. The segmentation-equipped VGG net (FCN-VGG16) already appears to be state-of-the-art at 56.0 mean IU on val, compared to 52.6 on test [17]. Training on extra data raises FCN-VGG16 to 59.4 mean IU and FCN-AlexNet to 48.0 mean IU on a subset of val ⁷. Despite similar classification accuracy, our implementation of GoogLeNet did not match the VGG16 segmentation result.

从分类到细分的微调为每个网络提供了合理的预测。 即使是最差的型号，也可以达到约75％的最新性能。 配备分段功能的VGG网（FCN-VGG16）在val上的平均IU为56.0时已经是最新技术，而在测试时为52.6 [17]。 对额外数据的训练将val⁷的子集上的FCN-VGG16平均IU提高到59.4，将FCN-AlexNet的平均IU提高到48.0。 尽管分类精度相似，但我们的GoogLeNet实施与VGG16细分结果不匹配。

Table 1. We adapt and extend three classification convnets. We compare performance by mean intersection over union on the validation set of PASCAL VOC 2011 and by inference time (averaged over 20 trials for a 500×500 input on an NVIDIA Tesla K40c).We detail the architecture of the adapted nets with regard to dense prediction: number of parameter layers, receptive field size of output units, and the coarsest stride within the net. (These numbers give the best performance obtained at a fixed learning rate, not best performance possible.)

表1.我们适应并扩展了三个分类卷积。 我们通过PASCAL VOC 2011验证集上的平均交集与并集以及推理时间（在NVIDIA Tesla K40c上进行500×500输入的20多次试验平均）来比较性能。 预测：参数层数，输出单元的接收场大小以及网内最粗的步幅。（这些数字给出了以固定学习率获得的最佳性能，而不是最佳性能。）

4.2. Combining what and where

We define a new fully convolutional net (FCN) for segmentation that combines layers of the feature hierarchy and refines the spatial precision of the output. See Figure 3.

我们定义了一种用于分割的新的全卷积网（FCN），该网结合了要素层次结构的各个层并完善了输出的空间精度。 参见图3。

While fully convolutionalized classifiers can be finetuned to segmentation as shown in 4.1, and even score highly on the standard metric, their output is dissatisfyingly coarse (see Figure 4). The 32 pixel stride at the final prediction layer limits the scale of detail in the upsampled output.

尽管可以将完全卷积的分类器微调至如4.1所示的分段，甚至在标准度量上得分很高，但它们的输出却令人不满意地粗糙（请参见图4）。 最终预测层的32像素步幅限制了上采样输出中的细节比例。

We address this by adding skips [1] that combine the final prediction layer with lower layers with finer strides.This turns a line topology into a DAG, with edges that skip ahead from lower layers to higher ones (Figure 3). As they see fewer pixels, the finer scale predictions should need fewer layers, so it makes sense to make them from shallower net outputs. Combining fine layers and coarse layers lets the model make local predictions that respect global structure.By analogy to the jet of Koenderick and van Doorn [21], we call our nonlinear feature hierarchy the deep jet.

我们通过添加跳过连接[1]来解决此问题，这些跳过将最终预测层与较低层的步幅相结合。这会将线拓扑变成DAG，其边缘从较低的层向前跳到较高的层（图3）。当他们看到较少的像素时，更精细的比例预测应该需要较少的图层，因此从较浅的净输出中进行选择是有意义的。结合精细层和粗糙层，可以使模型做出尊重整体结构的局部预测。通过类似于Koenderick和van Doorn [21]的射流，我们将非线性特征层次称为深射流（deep jet）。

We first divide the output stride in half by predicting from a 16 pixel stride layer. We add a 1×1 convolution layer on top of pool4 to produce additional class predictions.We fuse this output with the predictions computed on top of conv7 (convolutionalized fc7) at stride 32 by adding a 2× upsampling layer and summing6 both predictions (see Figure 3). We initialize the 2× upsampling to bilinear interpolation, but allow the parameters to be learned as described in Section 3.3. Finally, the stride 16 predictions are upsampled back to the image. We call this net FCN-16s. FCN-16s is learned end-to-end, initialized with the parameters of the last, coarser net, which we now call FCN-32s. The new parameters acting on pool4 are zeroinitialized so that the net starts with unmodified predictions.The learning rate is decreased by a factor of 100.

我们首先根据16个像素的步幅层进行预测，将输出步幅分为两半。 我们在pool4的顶部添加一个1×1卷积层以产生附加的类别预测，并将此输出与在第32步的conv7（卷积化的fc7）顶部计算的预测相融合，方法是添加一个2×上采样层并对两个预测求和（参见图3）。 我们将2x上采样初始化为双线性插值，但允许按照第3.3节中的描述学习参数。 最后，将步幅16的预测上采样回图像。 我们称此为FCN-16s。 通过端到端学习FCN-16，并使用最后一个更粗糙的网络（现在称为FCN-32）的参数进行初始化。 作用于pool4的新参数被初始化为零，因此网络以未修改的预测开始。学习率降低了100倍。

Learning this skip net improves performance on the validation set by 3.0 mean IU to 62.4. Figure 4 shows improvement in the fine structure of the output. We compared this fusion with learning only from the pool4 layer, which resulted in poor performance, and simply decreasing the learning rate without adding the skip, which resulted in an insignificant performance improvement without improving the quality of the output.

学习此跳过连接网络可以将验证集的性能提高3.0个平均IU，达到62.4。 图4显示了输出精细结构的改进。 我们将这种融合与仅从pool4层进行的学习进行了比较，这导致性能较差，并且在不增加跳过连接的情况下简单地降低了学习速度，从而在不提高输出质量的情况下导致了微不足道的性能改进。

We continue in this fashion by fusing predictions from pool3 with a 2× upsampling of predictions fused from pool4 and conv7, building the net FCN-8s. We obtain a minor additional improvement to 62.7 mean IU, and find a slight improvement in the smoothness and detail of our output. At this point our fusion improvements have met diminishing returns, both with respect to the IU metric which emphasizes large-scale correctness, and also in terms of the improvement visible e.g. in Figure 4, so we do not continue fusing even lower layers.

我们以这种方式继续进行工作，将pool3的预测与pool4和conv7的预测进行2倍的上采样融合，构建净FCN-8。 我们将平均IU值略微提高了62.7 IU，并在输出的平滑度和细节上发现了轻微的改进。 在这一点上，我们的融合改进遇到了收益递减的问题，无论是在强调大规模正确性的IU度量方面，还是在可见的改进方面，例如 在图4中，因此我们不会继续融合更低的层。

Refinement by other means Decreasing the stride of pooling layers is the most straightforward way to obtain finer predictions. However, doing so is problematic for our VGG16-based net. Setting the pool5 stride to 1 requires our convolutionalized fc6 to have kernel size 14×14 to maintain its receptive field size. In addition to their computational cost, we had difficulty learning such large filters.We attempted to re-architect the layers above pool5 with smaller filters, but did not achieve comparable performance; one possible explanation is that the ILSVRC initialization of the upper layers is important.

通过其他手段进行优化减小池化层的步幅是获得更精细预测的最直接方法。 但是，这样做对于我们基于VGG16的网络是有问题的。 将pool5的跨度设置为1要求我们的卷积化的fc6具有14×14的内核大小，以维持其接收场大小。 除了计算量之外，我们还很难学习这么大的过滤器。我们试图用较小的过滤器重新构造pool5之上的层，但没有达到可比的性能； 一种可能的解释是高层的ILSVRC初始化很重要。

Another way to obtain finer predictions is to use the shiftandstitch trick described in Section 3.2. In limited experiments, we found the cost to improvement ratio from this method to be worse than layer fusion.

获得更好的预测的另一种方法是使用第3.2节中描述的shiftandstitch技巧。 在有限的实验中，我们发现此方法的成本改进率比层融合差。

Figure 4. Refining fully convolutional nets by fusing information from layers with different strides improves segmentation detail. The first three images show the output from our 32, 16, and 8 pixel stride nets (see Figure 3).

图4.通过融合来自具有不同跨度的图层的信息来完善全卷积网络，可以改善分割细节。前三个图像显示了我们32、16和8像素步幅网络的输出（请参见图3）。

Table 2. Comparison of skip FCNs on a subset of PASCAL VOC2011 validation7. Learning is end-to-end, except for FCN32s-fixed, where only the last layer is fine-tuned. Note that FCN32s is FCN-VGG16, renamed to highlight stride.

表2.在部分PASCAL VOC2011验证中跳过FCN的比较7。学习是端到端的，除了固定在FCN32s上，只有最后一层是微调的。请注意，FCN32是FCN-VGG16，已重命名以突出显示步幅。

4.3. Experimental framework

Optimization. We train by SGD with momentum. We use a minibatch size of 20 images and fixed learning rates of $10^{-3}, 10^{-4}, 5^{-5}$ for FCN-AlexNet, FCN-VGG16, and FCN-GoogLeNet, respectively, chosen by line search. We use momentum $0.9$, weight decay of $5^{-4}$ or $2^{-4}$, and doubled learning rate for biases, although we found training to be sensitive to the learning rate alone. We zero-initialize the class scoring layer, as random initialization yielded neither better performance nor faster convergence. Dropout was included where used in the original classifier nets.

优化。我们通过SGD进行有动量的训练。 对于FCN-AlexNet，FCN-VGG16和FCN-GoogLeNet，我们分别使用20张图像的小批量大小和 $10^{-3}, 10^{-4}, 5^{-5}$ 的固定学习率（按行选择） 搜索。 尽管我们发现训练仅对学习速率敏感，但我们使用的动量为 0.9，权重衰减为 $5^{-4}$ 或 $2^{-4}$，并将学习率提高了一倍。 我们将类计分层初始化为零，因为随机初始化既不会产生更好的性能，也不会带来更快的收敛。 在原始分类器网络中使用的地方包括了dropout。

Fine-tuning. We fine-tune all layers by backpropagation through the whole net. Fine-tuning the output classifier alone yields only 70% of the full finetuning performance as compared in Table 2. Training from scratch is not feasible considering the time required to learn the base classification nets. (Note that the VGG net is trained in stages, while we initialize from the full 16-layer version.) Fine-tuning takes three days on a single GPU for the coarse FCN-32s version, and about one day each to upgrade to the FCN-16s and FCN-8s versions.

微调。我们通过整个网络的反向传播对所有层进行微调。 与表2相比，仅对输出分类器进行微调只能产生全部微调性能的70％。考虑到学习基础分类网络所需的时间，从头开始训练是不可行的。（注意，VGG网络是分阶段训练的，而我们是从完整的16层版本开始进行初始化的。）对于粗略的FCN-32s版本，微调在单个GPU上花费三天，而在每个GPU上升级FCN-16s和FCN-8s版本大约需要一天。

Figure 5. Training on whole images is just as effective as sampling patches, but results in faster (wall time) convergence by making more efficient use of data. Left shows the effect of sampling on convergence rate for a fixed expected batch size, while right plots the same by relative wall time.

图5.对整个图像进行训练与采样补丁一样有效，但是通过更有效地利用数据可以加快（墙时间）收敛。 左图显示了对于固定的预期批次大小，采样对收敛速度的影响，而右图则通过相对壁时间绘制了相同的结果。

More Training Data The PASCAL VOC 2011 segmentation training set labels 1112 images. Hariharan et al. [16] collected labels for a larger set of 8498 PASCAL training images, which was used to train the previous state-of-theart system, SDS [17]. This training data improves the FCNVGG16 validation score7 by 3.4 points to 59.4 mean IU.

更多培训数据PASCAL VOC 2011细分培训设置了1112张图像标签。 Hariharan等。 [16]收集了更大的8498 PASCAL训练图像集的标签，这些图像用于训练以前的最新系统SDS [17]。 该训练数据将FCNVGG16验证得分7提高了3.4点，至59.4平均IU。

Patch Sampling As explained in Section 3.4, our full image training effectively batches each image into a regular grid of large, overlapping patches. By contrast, prior work randomly samples patches over a full dataset [30, 3, 9, 31, 11], potentially resulting in higher variance batches that may accelerate convergence [24]. We study this tradeoff by spatially sampling the loss in the manner described earlier, making an independent choice to ignore each final layer cell with some probability 1-p. To avoid changing the effective batch size, we simultaneously increase the number of images per batch by a factor 1/p. Note that due to the efficiency of convolution, this form of rejection sampling is still faster than patchwise training for large enough values of p (e.g., at least for p > 0.2 according to the numbers in Section 3.1). Figure 5 shows the effect of this form of sampling on convergence. We find that sampling does not have a significant effect on convergence rate compared to whole image training, but takes significantly more time due to the larger number of images that need to be considered per batch. We therefore choose unsampled, whole image training in our other experiments.

补丁采样如第3.4节所述，我们的完整图像训练将每个图像有效地批量成大块重叠补丁的规则网格。 相比之下，先前的工作在整个数据集上随机采样补丁[30、3、9、31、11]，可能会导致更高的方差批次，从而可能加速收敛[24]。 我们通过以前面描述的方式对损失进行空间采样来研究这种折衷，并做出独立选择，以某些概率“ 1-p”忽略每个最终层单元。 为了避免更改有效的批次大小，我们同时将每批次的图像数量增加了“ 1 / p”。 注意，由于卷积的效率，对于足够大的“ p”值（例如，至少根据第3.1节中的“ p> 0.2”而言），这种形式的拒绝采样仍比分片训练更快。 图5显示了这种形式的抽样对收敛的影响。 我们发现，与整个图像训练相比，采​​样对收敛速度没有显着影响，但是由于每批需要考虑的图像数量更多，因此花费的时间明显更多。 因此，我们在其他实验中选择未采样的整体图像训练。

Class Balancing Fully convolutional training can balance classes by weighting or sampling the loss. Although our labels are mildly unbalanced (about 3/4 are background), we find class balancing unnecessary.

类平衡完全卷积训练可以通过加权或采样损失来平衡类。尽管我们的标签略有不平衡（大约3 /4是背景），但我们发现类平衡是不必要的。

Dense Prediction The scores are upsampled to the input dimensions by deconvolution layers within the net. Final layer deconvolutional filters are fixed to bilinear interpolation, while intermediate upsampling layers are initialized to bilinear upsampling, and then learned.

密集预测通过网络中的反卷积层将分数上采样到输入维度。 最终层反卷积滤波器固定为双线性插值，而中间上采样层则初始化为双线性上采样，然后学习。

Augmentation We tried augmenting the training data by randomly mirroring and “jittering” the images by translating them up to 32 pixels (the coarsest scale of prediction) in each direction. This yielded no noticeable improvement.

增强我们尝试通过随机镜像和“抖动”图像​​来增强训练数据，方法是将图像在每个方向上最多转换为32个像素（最粗的预测比例）。 这没有产生明显的改善。

Implementation All models are trained and tested with Caffe [20] on a single NVIDIA Tesla K40c. Our models and code are publicly available at http://fcn.berkeleyvision.org.

实施所有模型都在单个NVIDIA Tesla K40c上使用Caffe [20]进行了培训和测试。 我们的模型和代码可在http://fcn.berkeleyvision.org上公开获得。

5. Results

We test our FCN on semantic segmentation and scene parsing, exploring PASCAL VOC, NYUDv2, and SIFT Flow. Although these tasks have historically distinguished between objects and regions, we treat both uniformly as pixel prediction. We evaluate our FCN skip architecture on each of these datasets, and then extend it to multi-modal input for NYUDv2 and multi-task prediction for the semantic and geometric labels of SIFT Flow.

我们在语义分割和场景解析方面测试了FCN，探索了PASCAL VOC，NYUDv2和SIFT Flow。尽管这些任务历来在对象和区域之间有所区别，但我们将两者均视为像素预测。我们在每个数据集上评估FCN跳过体系结构8，然后将其扩展到NYUDv2的多模式输入，以及SIFT Flow的语义和几何标签的多任务预测。

Metrics. We report four metrics from common semantic segmentation and scene parsing evaluations that are variations on pixel accuracy and region intersection over union (IU). Let $n_{ij}$ be the number of pixels of class $i$ predicted to belong to class $j$, where there are $n_{cl}$ different classes, and let $t_i = Σ_j·n_{ij}$ be the total number of pixels of class $i$. We compute:

度量。我们报告了来自常见语义分割和场景分析评估的四个度量，它们是像素精度和联合区域交集（IU）的变化。令 $n_{ij}$ 为类 $i$ 的预测像素数目属于类别 $j$，其中存在 $n_{cl}$ 个不同的类别，令 $t_i = Σ_j·n_{ij}$ 类别 $i$ 的像素总数。我们计算：

PASCAL VOC Table 3 gives the performance of our FCN-8s on the test sets of PASCAL VOC 2011 and 2012, and compares it to the previous state-of-the-art, SDS [16], and the well-known R-CNN [12]. We achieve the best results on mean IU9by a relative margin of 20%. Inference time is reduced 114× (convnet only, ignoring proposals and refinement) or 286× (overall).

表3给出了在PASCAL VOC 2011和2012测试的FCN-8的性能，并将其与之前的最新技术SDS[16]和著名的R-CNN进行了比较[12]。我们在平均IU9上达到了20％的相对裕度的最佳结果。推理时间减少了114倍（仅对convnet有效，忽略建议和改进）或总体的286倍。

Table 3. Our fully convolutional net gives a 20% relative improvement over the state-of-the-art on the PASCAL VOC 2011 and 2012 test sets, and reduces inference time.

表3.与PASCAL VOC 2011和2012测试集的最新技术相比，我们的全卷积网络提供了20％的相对改进，并减少了推理时间。

Table 4. Results on NYUDv2. RGBD is early-fusion of the RGB and depth channels at the input. HHA is the depth embedding of [14] as horizontal disparity, height above ground, and the angle of the local surface normal with the inferred gravity direction. RGB-HHA is the jointly trained late fusion model that sums RGB and HHA predictions.

表4. NYUDv2上的结果。 RGBD是输入端的RGB和深度通道的早期融合。 HHA是[14]的深度嵌入，它是水平差异，离地面的高度以及局部表面法线与推断重力方向的角度。 RGB-HHA是联合训练的后期融合模型，将RGB和HHA预测相加。

NYUDv2 [30] is an RGB-D dataset collected using the Microsoft Kinect. It has 1449 RGB-D images, with pixelwise labels that have been coalesced into a 40 class semantic segmentation task by Gupta et al. [13]. We report results on the standard split of 795 training images and 654 testing images. (Note: all model selection is performed on PASCAL 2011 val.) Table 4 gives the performance of our model in several variations. First we train our unmodified coarse model (FCN-32s) on RGB images. To add depth information, we train on a model upgraded to take four-channel RGB-D input (early fusion). This provides little benefit, perhaps due to the difficultly of propagating meaningful gradients all the way through the model. Following the success of Gupta et al. [14], we try the three-dimensional HHA encoding of depth, training nets on just this information, as well as a “late fusion” of RGB and HHA where the predictions from both nets are summed at the final layer, and the resulting two-stream net is learned end-to-end. Finally we upgrade this late fusion net to a 16-stride version.

NYUDv2 [30]是使用Microsoft Kinect收集的RGB-D数据集。 它具有1449个RGB-D图像，带有按像素划分的标签，由Gupta等人[13]合并为40类语义分割任务。 我们报告了795张训练图像和654张测试图像的标准分割结果。（注意：所有模型的选择均在PASCAL 2011 val上进行。）表4给出了几种模型的性能。 首先，我们在RGB图像上训练未修改的粗糙模型（FCN-32s）。 为了增加深度信息，我们训练了一个升级后的模型，以采用四通道RGB-D输入（早期融合），这几乎没有好处，这可能是由于难以在模型中一直传播有意义的梯度。 继Gupta等人[13]的成功之后，我们尝试对深度进行三维HHA编码，仅在此信息上训练网络，以及RGB和HHA的“后期融合”，其中来自两个网络的预测在最后一层相加，并得出结果 双流网络（two-stream net）是端到端学习的。 最后，我们将这个后期的融合网升级到16步的版本。

SIFT Flow is a dataset of 2,688 images with pixel labels for 33 semantic categories (“bridge”, “mountain”, “sun”), as well as three geometric categories (“horizontal”, “vertical”, and “sky”). An FCN can naturally learn a joint representation that simultaneously predicts both types of labels.We learn a two-headed version of FCN-16s with semantic and geometric prediction layers and losses. The learned model performs as well on both tasks as two independently trained models, while learning and inference are essentially as fast as each independent model by itself. The results in Table 5, computed on the standard split into 2,488 training and 200 test images,9 show state-of-the-art performance on both tasks.

SIFT Flow是一个包含2688个图像的数据集，带有33个语义类别（“桥”，“山”，“太阳”）以及三个几何类别（“水平”，“垂直”和“天空”）的像素标签。 FCN可以自然地学习可以同时预测两种标签类型的联合表示。我们学习了带有语义和几何预测层以及损失的FCN-16的两头版本。 学习的模型在两个任务上的表现都好于两个独立训练的模型，而学习和推理在本质上与每个独立模型一样快。表5中的结果按标准划分为2488个训练图像和200张测试图像9，显示出这两项任务的最新性能。

Table 5. Results on SIFT Flow⁹ with class segmentation (center) and geometric segmentation (right). Tighe [33] is a non-parametric transfer method. Tighe 1 is an exemplar SVM while 2 is SVM + MRF. Farabet is a multi-scale convnet trained on class-balanced samples (1) or natural frequency samples (2). Pinheiro is a multi-scale, recurrent convnet, denoted RCNN3 (o³). The metric for geometry is pixel accuracy.

表5. SIFT Flow ⁹ 的结果，包括类分割（中心）和几何分割（右）。 Tighe [33]是一种非参数传递方法。 Tighe 1是示例SVM，而2是SVM + MRF。 Farabet是在类平衡样本（1）或自然频率样本（2）上经过训练的多尺度卷积网络。 Pinheiro是一个多尺度的循环卷积网络，表示为RCNN3（o ³）。 几何指标是像素精度。

Figure 6. Fully convolutional segmentation nets produce stateofthe-art performance on PASCAL. The left column shows the output of our highest performing net, FCN-8s. The second shows the segmentations produced by the previous state-of-the-art system by Hariharan et al. [16]. Notice the fine structures recovered (first row), ability to separate closely interacting objects (second row), and robustness to occluders (third row). The fourth row shows a failure case: the net sees lifejackets in a boat as people.

图6.完全卷积分割网在PASCAL上表现出最先进的性能。 左列显示了性能最高的网络FCN-8的输出。 第二部分显示了Hariharan等人先前的最新系统所产生的分割结果。 [16]。 注意恢复的精细结构（第一行），分离紧密相互作用的对象的能力（第二行）以及对遮挡物的稳健性（第三行）。 第四行显示了一个失败案例：网络将船上的救生衣视为人。

6. Conclusion

Fully convolutional networks are a rich class of models, of which modern classification convnets are a special case. Recognizing this, extending these classification nets to segmentation, and improving the architecture with multi-resolution layer combinations dramatically improves the state-of-the-art, while simultaneously simplifying and speeding up learning and inference.

完全卷积网络是一类丰富的模型，现代分类卷积就是其中的特例。 认识到这一点，将这些分类网扩展到分段，并通过多分辨率图层组合改进体系结构，可以极大地改善现有技术，同时简化并加快学习和推理速度。

Acknowledgements This work was supported in part by DARPA’s MSEE and SMISC programs, NSF awards IIS1427425, IIS-1212798, IIS-1116411, and the NSF GRFP, Toyota, and the Berkeley Vision and Learning Center. We gratefully acknowledge NVIDIA for GPU donation. We thank Bharath Hariharan and Saurabh Gupta for their advice and dataset tools. We thank Sergio Guadarrama for reproducing GoogLeNet in Caffe. We thank Jitendra Malik for his helpful comments. Thanks to Wei Liu for pointing out an issue wth our SIFT Flow mean IU computation and an error in our frequency weighted mean IU formula.

A. Upper Bounds on IU

In this paper, we have achieved good performance on the mean IU segmentation metric even with coarse semantic prediction. To better understand this metric and the limits of this approach with respect to it, we compute approximate upper bounds on performance with prediction at various scales. We do this by downsampling ground truth images and then upsampling them again to simulate the best results obtainable with a particular downsampling factor. The following table gives the mean IU on a subset of PASCAL 2011 val for various downsampling factors.

在本文中，即使使用粗略的语义预测，我们在平均IU分割指标上也取得了良好的性能。 为了更好地理解该指标以及该方法相对于其的局限性，我们使用各种规模的预测来计算性能的近似上限。 为此，我们对带有真实标签的图像进行下采样，然后再次对其进行上采样，以模拟使用特定下采样因子可获得的最佳结果。 下表列出了各种下采样因子下PASCAL 2011 val子集的平均IU。

Pixel-perfect prediction is clearly not necessary to achieve mean IU well above state-of-the-art, and, conversely, mean IU is a not a good measure of fine-scale accuracy.

像素完美预测显然不需要达到远高于最新水平的平均IU，相反，平均IU并不是衡量小尺寸精度的好方法。

B. More Results

We further evaluate our FCN for semantic segmentation.
PASCAL-Context [26] provides whole scene annotations of PASCAL VOC 2010. While there are over 400 distinct classes, we follow the 59 class task defined by [26] that picks the most frequent classes. We train and evaluate on the training and val sets respectively. In Table 6, we compare to the joint object + stuff variation of Convolutional Feature Masking [3] which is the previous state-of-the-art on this task. FCN-8s scores 37.8 mean IU for a 20% relative improvement.

我们进一步评估FCN的语义分割。
PASCAL-Context [26]提供了PASCAL VOC 2010的整个场景注释。尽管有400多个不同的类，但我们遵循[26]定义的59类任务，该任务选择最频繁的类。 我们分别训练和评估训练集和评估集。 在表6中，我们将卷积特征蒙版[3]的联合对象+填充变量进行了比较，这是该任务的最新技术。 FCN-8s的平均IU得分为37.8，相对改善了20％。

Changelog

The arXiv version of this paper is kept up-to-date with corrections and additional relevant material. The following gives a brief history of changes.

本文的arXiv版本会进行更正和提供其他相关材料，以保持最新。 以下是更改的简要历史。

Table 6. Results on PASCAL-Context. CFM is the best result of [3] by convolutional feature masking and segment pursuit with the VGG net. O2P is the second order pooling method [1] as reported in the errata of [26]. The 59 class task includes the 59 most frequent classes while the 33 class task consists of an easier subset identified by [26].

表6. PASCAL上下文的结果。通过使用VGG网络进行卷积特征掩蔽和分段追踪，CFM是[3]的最佳结果。 O2P是二阶合并方法[1]，如勘误表[26]中所述。 59类任务包括59个最频繁的类，而33类任务则由[26]标识的一个较容易的子集组成。

v2 Add Appendix A giving upper bounds on mean IU and Appendix B with PASCAL-Context results. Correct PASCAL validation numbers (previously, some val images were included in train), SIFT Flow mean IU (which used an inappropriately strict metric), and an error in the frequency weighted mean IU formula. Add link to models and update timing numbers to reflect improved implementation (which is publicly available).

v2 添加附录A，以给出平均IU的上限，附录B为PASCAL-Context结果。 正确的PASCAL验证编号（以前在火车中包含一些val图像），SIFT流量平均IU（使用了不合适的严格度量）以及频率加权平均IU公式中的错误。 将链接添加到模型并更新时间编号以反映改进的实现（已公开）。

---