Abstract

创新点：用cnn做edge detection (HED)，端到端
解决两个问题：
1）holistic（整体的） image training and prediction;
2）multi-scale and multi-level feature learning;
特点：
1. 端到端：image-to-image
2. 基于FCN和VGG 改进
3. 通过多个side output输出不同scale的边缘，然后通过一个训练的权重融合函数得到最终的边缘输出。可以solve edge 和物体boundaries的ambiguity
工程主页：https://github.com/s9xie/hed

1 Introduction

典型的边缘检测工作：
I: early pioneering methods Sobel detector、Canny detector
II: information theory Statistical Edges [22], Pb [28], and gPb [1];
III:learning-based methods that remain reliant on features of human design, such as BEL [5], Multi-scale [30], Sketch Tokens [24], and Structured Edges [6]
IV:cnn N4-Fields [10], Deep- Contour [34], DeepEdge [2], and CSCNN [19].

We tackles two critical issues: (1) holistic image training and prediction, inspired by fully convolutional neural networks [26], for image-to-image classification (the system takes an image as input, and directly produces the edge map image as output); and (2) nested multi-scale feature learning, inspired by deeply-supervised nets [23], that performs deep layer supervision to “guide” early classification results.

2 Holistically-Nested Edge Detection

A recent wave of work using CNN for patch-based edge prediction [10, 34, 2, 19]基于三个方面：
（1）自动feature learning
（2）multi-scale response fusion
（3）possible engagement of different levels of visual perception
本文加了 deep supervision,基于全卷积网络（与输入尺寸无关）！

和 patch-based CNN edge detection methods相比，我们的方法一是速度快，二是性能好，主要体现在：
（1）FCN-like image-to-image training allows us to simultaneously train on a significantly larger amount of samples
（2）deep supervision in our model guides the learning of more transparent features
（3）interpolating the side outputs in the end-to-end learning encourages coherent contributions from each layer

2.1 Existing multiscale and multilevel NN

hierarchical learning
深度学习论文笔记之（一）HED边缘检测
由于multi-scale在不同情况下表示的含义可能不同，将其分为四类:

multi-stream learning[3,29],
The multiple (parallel) network streams have different parameter numbers and receptive field sizes, corresponding to multiple scales，输入是同时输进去，经过不同路的network之后，再连接到一个global out layer得到输出。
skip-net learning [26, 14, 2, 33, 10] ,
特点：只有一路network，从不同层提取信息连接到输出
1,2的共同特点是只有一个输出loss函数，并只能得到一个预测结果。
a single model running on multiple inputs , 就是不同尺寸的图片输入，One notable example is the tied-weight pyramid networks [8].。
training of independent networks. 训练多个不同的网络（深度不同且loss也不同）
，得到多个不同的输出，缺点显然是资源消耗太大。

下面介绍 Holistically-nested networks:由于已有的方法存在很大的冗余，本结构和deeply-supervised net[23] 很像，其中[23] shows that hidden layer supervision can improve both optimization and generalization for image classification tasks.

2.2 公式

训练阶段：

由于在ground-truth中，90%以上的像素点为非edge，因此极度不对称（biased）。针对这种biased sampling，文献[19] 引入cost-sensitive loss function,并增加额外的additional trade-off parameters。而HED中采用一种更简单的方法来保证正负样本的loss balance，即引入一个像素级的class-balancing weight β
则损失函数为class-balanced cross-entropy loss function：

为了利用side-output的预测结果，我们增加一层weighted-fusion layer
fusion layer 的损失函数为:

最终的目标函数为：

测试阶段：
给定图片X，我们从side-output layer和weighted-fusion layer同时获得边缘预测结果
最终的输出就是将这些结果进行一个聚合。

3 网络架构

3.1 Trimmed network for edge detection

基于VGG，做了以下改动：
1）将side output layer 与每个stage（理解为每一组卷积池化）的最后一层卷积层相连，也就是conv1 2, conv2 2, conv3 3, conv4 3, conv5 3.这些卷积层的感知野尺寸与对应的side-output layer完全相同。

2）去掉了VGG的最后一个stage,也就是最后一个池化和后面所有的全连接层。
这是因为全连接层太好耗资源（即使转换成conv也很费资源）
下面的表格是HED的网络配置

与FCN-网络对比：
直接替换FCN-8S中的loss为交叉熵的性能不好 ,FCN-2s network that adds additional links fromthe pool1 and pool2 layers.

什么是deep supervision呢？在这里指的是来自side-output 的结果
The “fusion-output without deep supervision” result is learned w.r.t Eqn. 3. The “fusion-output with deep supervision” result is learned w.r.t. to Eqn. 4

关于The role of deep supervision：
deep supervision terms (specifically, ℓside(W,w(m)):
每一层都看做是一个独立的network的输出（在不同的尺度上）
实验表明，仅仅用weighted-fusion supervision训练，在高层的side output上很多关键的边缘信息都丢失了。

4 实验

4.1 实现

基于Caffe,FCN[26]和DSN[23]的基础上，用VGG进行初始化。
调参：依据[6]在的评价策略
mini-batch size (10),
learning rate (1e-6),
loss-weight αm for each side-output layer (1),
momentum (0.9),
initialization of the nested filters (0),
initialization of the fusion layer weights (1/5),
weight decay (0.0002),
number of training iterations (10,000; divide learning rate by 10 after 5,000).

由于在每个side-output layer,我们将每个输出都resize到原始尺寸和ground truth对比，在高层输出，由于经过了较大的stride,此时只剩下一些大的边缘，而精细的边缘已经检测不出来了，而此时的ground truth仍然包含了很多精细的边缘（甚至有的是噪声），这导致了一个收敛困难的问题（在高层梯度爆炸）。因此作者只选取那些被至少三人标注为边缘的像素作为positive label
* Data augmentation*
rotate the images to 16 different angles and crop the largest rectangle in the rotated image; we also flip the image at each angle, leading to an augmented training set that is a factor of 32 larger than the unaugmented set. During testing we operate on an input image at its original size.
* In-network bilinear interpolation*
反卷积插值[26]的方式并没有明显的改善。

4.2 Dataset

Berkeley Segmentation Dataset and Benchmark (BSDS 500) [1]

参考文献：

[3] P. Buyssens, A. Elmoataz, and O. L´ezoray. Multiscale convolutional neural networks for vision–based classification of cells. In ACCV. 2013
[6] P. Doll´ar and C. L. Zitnick. Fast edge detection using structured forests. PAMI, 2015.
[23] C.-Y. Lee, S. Xie, P. Gallagher, Z. Zhang, and Z. Tu. Deeplysupervised nets. In AISTATS, 2015.
[26] J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In CVPR, 2015.

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深度学习论文笔记之（一）HED边缘检测