Histograms of Oriented Gradients for Human Detection

本文是论文笔记。

转载注明：http://blog.csdn.net/stdcoutzyx/article/details/40299383

Hog算子进行行人检测，是05年在CVPR上发表的经典文章。使用Hog算子提取特征，然后使用SVM来进行分类。

1. Definition

Hog Descriptor：locally normalized histogram of gradient orientation in dense overlapping grids, 即局部归一化梯度方向直方图。

2. Important Properties

1. Fine-scale gradients，较好尺度的梯度计算
2. Fine orientation binning，较好的方向分区
3. Relatively coarse spatial binning，相对粗粒度的空间分区
4. High-quality local contrast normalization in overlapping descriptor blocks，在重叠块中的高质量局部对比度归一化

3. Algorithms

Default detector properties：

• RGB colour space with no gamma correction.
• [-1,0,1] gradient filter with no smoothing.
• Linear gradient voting into 9 orientation bins in 0-180
• 16×16 pixel blocks of four 8×8 pixel cells.
• Gaussian spatial window with variance=8.
• L2-Hys(Lowe-style clipped L2 norm) block normalization.
• Block spacing stride of 8 pixels(hence 4-fold coverage of each cell).
• 64×128 detection window
• Linear SVM classifier

3.1 Process

基本概念：

• Cell：统计梯度直方图的最小单元，论文中为8×8。
• Blocks：做直方图归一化的单元，论文中为2×2个cell，即block大小为16×16.

Hog+SVM算法的过程分为如下几个步骤：

• 使用gamma变换对图片进行归一化。
• 计算每个像素点的梯度方向。
• 在Cell中对梯度方向进行统计，得到直方图。
• 在Block中对Cell的梯度直方图进行归一化，Block以窗口滑过每个Cell，Block可重叠。
• 将每个block的直方图串联起来，形成整幅图片的特征向量。
• 这里需要注意，每个Cell可能作为多个Block的子部分被归一化放到整幅图片的特征向量中。
• 使用Linear SVM算法对特征向量进行分类，得到最终模型。

3.2 Gamma / Colour Normalization

• Pixel representation: grayscale, RGB, LAB.
• Optionally with power law (gamma) equalization or log compression
• Best: LAB and RGB with square root gamma compression

3.3 Gradient Computation

Compare on schemes below:

• Various 1-D point derivatives
  • uncentred [-1,1]
  • centred [-1,0,1]
  • cubic-corrected [1,-8,0,8,-1]).
  • Those with Gaussian derivatives.
• 3×3 sobel masks.
• 2×2 diagonal ones (the most compact centred 2-D derivative masks)

Simplest scheme turns out to be the best. Uncentred [-1,0,1] without Gaussian smooth work best. Larger mask and smoothing damages the performance significantly.

For colour images, calculate separate gradients for each channel, take the one with largest norm as the pixel’s gradient vector.

3.4 Spatial / Orientation Binning

对每个Cell统计得到直方图，步骤如下：

• Calculate a weighted vote for each pixel based on the orientation of the gradient element centred on it.
  • Vote weight is function of the gradient magnitude at the pixel
    • Magnitude itself
    • Its square
    • Its square root
  • Magnitude itself gives the best result.
• Accumulated into orientation bins over local spatial regions that called cells
  • Orientation bins have two kinds:
    • 0-180: unsigned gradient
    • 0-360: signed gradient
  • Unsigned gradient is better, for human’s wide range of clothing and background colour make the the signs of contrasts uninformative.
    • Include the signs information maybe helpful in some other object recognition task like cars, motobikes.
  • Number of orientation bins get to the best at 9 using unsigned gradient.
  • To reduce aliasing, votes are interpolated bilinearly between the neighbouring bin centers in both orientation and position.

3.5 Normalization and Descriptor Blocks

• Gradient strengths vary over a wide range owing to local variations in illumination and fore-background contrast, so local contrast normalization is essential.
• Grouping cells into larger spatial blocks and contrast normalization each block separately.
  • An alternative center-surround style cell normalization scheme is also investigated.
    • 以某cell为中心，使用高斯为周围的cell加权，用该cell和周边cell得到一个总值，以此总值归一化。这样，在最终的结果中，一个cell的权重只出现一次。也因此效果下降。
• Overlapping of the blocks seems redundant but improves the performance significantly.
• 论文中使用了两种算子：R-HOG和C-HOG。
• Vertical cell (2×1) and horizontal cell (1×2) are also considered.
• It’s useful to down-weight pixels near the edges of the blocks by applying a Gaussian spatial window to each pixel before accumulating orientation votes into cells.

3.6 Block Normalization schemes

把多个Cell组合成一个Block后，就形成一个Block向量v，对于v，有如下几种方法做归一化：

• L2-norm
• L2-Hys
• L1-norm
• L1-sqrt

4. Experiment

共进行如下几组实验:

• Compare with previous algorithm
  • Generalized Haar Wavelets
  • PCA-Sift
  • Shape Contexts
• Effect of gradient scale
  • 在计算梯度时高斯平滑带来的效果测试
• Effect of orientation bins’ number
  • 考察角度分区带来的效果变化
• Effect of normalization method
  • 在block归一化时，考察不同归一化方法的效果
• Effect of overlap
  • 在block与cell进行组合时，不同的overlap带来的效果。此时cell的大小为8×8.
  • 注意：这里有一个参数stride，表示block每次滑动间隔的像素数。
• Block大小与Cell大小不同带来的效果变化
• 检测窗口大小不同带来的效果变化
• SVM参数带来的效果变化

检验指标：

• Miss Rate：错检率，所有判为有行人的sample中，被错判（没有行人被判为有行人）的样本比例。
• FPPW：False Positives Per Window，平均每个窗口的漏检率，漏检率为所有有行人的sample中，被判为没有行人的样本比例。平均到每个检测窗口

5. Hog算子深入理解

Hog算子最重要的思想是，在一副图像中，局部目标的appearance和shape能够被梯度或边缘的方向密度分布很好的描述。

Hog算子有很多优点：

• 由于其在图像的局部细胞单元上操作，所以对图像的几何（geometric）和光学（photometric）形变都能保持很好的不变形，因为这两种形变只会出现在更大的空间区域上。

• 实验表明，粗的空域抽样（coarse spatial sampling）、精细的方向抽样（fine orientation sampling）以及较强的局部光学归一化（strong local photometric normalization）等条件下，行人只要大体能够保持直立的姿势，容许有一些细微的肢体动作而不影响检测效果。

R-HOG跟SIFT描述器看起来很相似，但他们的不同之处是：R-HOG是在单一尺度下、密集的网格内、没有对方向排序的情况下被计算出来（are computed in dense grids at some single scale without orientation alignment）；而SIFT描述器是在多尺度下、稀疏的图像关键点上、对方向排序的情况下被计算出来（are computed at sparse, scale-invariant key image points and are rotated to align orientation）。补充一点，R-HOG是各区间被组合起来用于对空域信息进行编码（are used in conjunction to encode spatial form information），而SIFT的各描述器是单独使用的（are used singly）。

6. Reference

• [1]. Dalal N, Triggs B. Histograms of oriented gradients for human detection[C]//Computer Vision and Pattern Recognition, 2005. CVPR 2005. IEEE Computer Society Conference on. IEEE, 2005, 1: 886-893.

Histograms of Oriented Gradients for Human Detection