HOG(Histogram of Oriented Gradients)——方向梯度直方图，是一种表示图像特征量的方法，特征量是表示图像的状态等的向量集合。

在图像识别(图像是什么)和检测(物体在图像的哪个位置)中，我们需要：

从图像中获取特征量(特征提取)；

基于特征量识别和检测(识别和检测)；

由于深度学习通过卷积网络自动执行特征提取和识别，所以看不到HOG，但在深度学习变得流行之前，HOG经常被用作特征量表达。

获得HOG算法如下：

图像灰度化，然后在x方向和y方向上求出亮度的梯度：

x方向：

y方向：

从g_x和g_y确定梯度幅值和梯度方向：

梯度幅值：

梯度方向：

将梯度方向[0,180]进行9等分量化。也就是说，对于[0,20]量化为index 0，对于[20,40]量化为index 1......

将图像划分为N x N个区域(该区域称为cell)，并作出cell内上一步得到的index的直方图。

C x C个cell被称为一个block，对每个block内的cell的直方图通过下面的式子进行归一化。由于归一化过程中窗口一次移动一个cell来完成，因此一个cell会被归一化多次，通常ε=1。

以上，求出HOG特征值。

将得到的特征量可视化。为 cell 内的每个 index 的方向画一条线段，并且值越大，线段越白，

值越小，线段越黑。

import cv2

import numpy as np

import matplotlib.pyplot as plt

# get HOG

def HOG(img):

# Grayscale

def BGR2GRAY(img):

gray = 0.2126 * img[..., 2] + 0.7152 * img[..., 1] + 0.0722 * img[..., 0]

return gray

# Magnitude and gradient

def get_gradXY(gray):

H, W = gray.shape

# padding before grad

gray = np.pad(gray, (1, 1), 'edge')

# get grad x

gx = gray[1:H+1, 2:] - gray[1:H+1, :W]

# get grad y

gy = gray[2:, 1:W+1] - gray[:H, 1:W+1]

# replace 0 with

gx[gx == 0] = 1e-6

return gx, gy

# get magnitude and gradient

def get_MagGrad(gx, gy):

# get gradient maginitude

magnitude = np.sqrt(gx ** 2 + gy ** 2)

# get gradient angle

gradient = np.arctan(gy / gx)

gradient[gradient < 0] = np.pi / 2 + gradient[gradient < 0] + np.pi / 2

return magnitude, gradient

# Gradient quantization

def quantization(gradient):

# prepare quantization table

gradient_quantized = np.zeros_like(gradient, dtype=np.int)

# quantization base

d = np.pi / 9

# quantization

for i in range(9):

gradient_quantized[np.where((gradient >= d * i) & (gradient <= d * (i + 1)))] = i

return gradient_quantized

# get gradient histogram

def gradient_histogram(gradient_quantized, magnitude, N=8):

# get shape

H, W = magnitude.shape

# get cell num

cell_N_H = H // N

cell_N_W = W // N

histogram = np.zeros((cell_N_H, cell_N_W, 9), dtype=np.float32)

# each pixel

for y in range(cell_N_H):

for x in range(cell_N_W):

for j in range(N):

for i in range(N):

histogram[y, x, gradient_quantized[y * 4 + j, x * 4 + i]] += magnitude[y * 4 + j, x * 4 + i]

return histogram

# histogram normalization

def normalization(histogram, C=3, epsilon=1):

cell_N_H, cell_N_W, _ = histogram.shape

## each histogram

for y in range(cell_N_H):

for x in range(cell_N_W):

#for i in range(9):

histogram[y, x] /= np.sqrt(np.sum(histogram[max(y - 1, 0) : min(y + 2, cell_N_H),

max(x - 1, 0) : min(x + 2, cell_N_W)] ** 2) + epsilon)

return histogram

# 1. BGR -> Gray

gray = BGR2GRAY(img)

# 1. Gray -> Gradient x and y

gx, gy = get_gradXY(gray)

# 2. get gradient magnitude and angle

magnitude, gradient = get_MagGrad(gx, gy)

# 3. Quantization

gradient_quantized = quantization(gradient)

# 4. Gradient histogram

histogram = gradient_histogram(gradient_quantized, magnitude)

# 5. Histogram normalization

histogram = normalization(histogram)

return histogram

# draw HOG

def draw_HOG(img, histogram):

# Grayscale

def BGR2GRAY(img):

gray = 0.2126 * img[..., 2] + 0.7152 * img[..., 1] + 0.0722 * img[..., 0]

return gray

def draw(gray, histogram, N=8):

# get shape

H, W = gray.shape

cell_N_H, cell_N_W, _ = histogram.shape

## Draw

out = gray[1 : H + 1, 1 : W + 1].copy().astype(np.uint8)

for y in range(cell_N_H):

for x in range(cell_N_W):

cx = x * N + N // 2

cy = y * N + N // 2

x1 = cx + N // 2 - 1

y1 = cy

x2 = cx - N // 2 + 1

y2 = cy

h = histogram[y, x] / np.sum(histogram[y, x])

h /= h.max()

for c in range(9):

#angle = (20 * c + 10 - 90) / 180. * np.pi

# get angle

angle = (20 * c + 10) / 180. * np.pi

rx = int(np.sin(angle) * (x1 - cx) + np.cos(angle) * (y1 - cy) + cx)

ry = int(np.cos(angle) * (x1 - cx) - np.cos(angle) * (y1 - cy) + cy)

lx = int(np.sin(angle) * (x2 - cx) + np.cos(angle) * (y2 - cy) + cx)

ly = int(np.cos(angle) * (x2 - cx) - np.cos(angle) * (y2 - cy) + cy)

# color is HOG value

c = int(255. * h[c])

# draw line

cv2.line(out, (lx, ly), (rx, ry), (c, c, c), thickness=1)

return out

# get gray

gray = BGR2GRAY(img)

# draw HOG

out = draw(gray, histogram)

return out

# Read image

img = cv2.imread("../baby.png").astype(np.float32)

# get HOG

histogram = HOG(img)

# draw HOG

out = draw_HOG(img, histogram)

# Save result

cv2.imwrite("out.jpg", out)

cv2.imshow("result", out)

cv2.waitKey(0)

cv2.destroyAllWindows()