HOG简介

HOG全称：方向梯度直方图(Histogram of Oriented Gradient)，发表于2005年的CVPR，是一种图像特征提取算法，和SVM分类器结合应用于行人检测领域。HOG通过计算图像中每个像素的梯度的大小和方向，来获取图像的梯度特征，是一种特征描述子。

HOG特点

1.由于计算局部直方图和归一化，所以它对图像几何的和光学的形变都能保持很好的不变性；

2.细微的动作可以被忽略而不影响检测效果。

HOG计算步骤

1.对输入图像进行灰度化

2.利用gamma校正法对图像进行颜色空间归一化；

3.计算图像中每个像素的梯度大小和方向；

4.将图像划分cells，计算每个cell内的梯度直方图；

5.将每几个cell组成一个block，计算每个block内的梯度特征；

6.将图像中所有block的梯度特征组合起来就得到了图像的特征描述子；

7.将图像特征输入分类器进行分类。

HOG参数计算

计算流程

图像(image)->滑动图像块(block)->细胞单元(cells)

1.block个数计算

假设图像大小为128x128，block大小为16x16， block stride为8x8

则block个数 = ((128-16)/8+1) x ((128-16)/8 +1) = 15x15 = 225

2.每个block内的cell个数计算

假设cell size为8x8

则cell个数 = (16x16) / (8x8) = 4

3.每张图特征维度

假设直方图等级数 bins = 9

则每张图的特征维度 = 225 x 4 x 9 = 8100

HOG提取特征效果

原图：

HOG特征图：

HOG代码实现

1.基于python的scikit-image库提供了HOG特征提取的接口：

from skimage import feature as ft

features = ft.hog(image, # input image

orientations=ori, # number of bins

pixels_per_cell=ppc, # pixel per cell

cells_per_block=cpb, # cells per blcok

block_norm = 'L1', # block norm : str {‘L1’, ‘L1-sqrt’, ‘L2’, ‘L2-Hys’}

transform_sqrt = True, # power law compression (also known as gamma correction)

feature_vector=True, # flatten the final vectors

visualise=False) # return HOG map

应用示例：

from skimage.feature import hog

gray = rgb2gray(image) / 255.0

fd = hog(gray, orientations=12, block_norm='L1', pixels_per_cell=[10, 10], cells_per_block=[4, 4], visualize=False, transform_sqrt=True)

2.HOG代码实现

import cv2

import numpy as np

import math

import matplotlib.pyplot as plt

class Hog_descriptor():

def __init__(self, img, cell_size=16, bin_size=8):

self.img = img

self.img = np.sqrt(img / np.max(img))

self.img = img * 255

self.cell_size = cell_size

self.bin_size = bin_size

self.angle_unit = 360 / self.bin_size

def extract(self):

height, width = self.img.shape

# 计算图像的梯度大小和方向

gradient_magnitude, gradient_angle = self.global_gradient()

gradient_magnitude = abs(gradient_magnitude)

cell_gradient_vector = np.zeros((int(height / self.cell_size), int(width / self.cell_size), self.bin_size))

for i in range(cell_gradient_vector.shape[0]):

for j in range(cell_gradient_vector.shape[1]):

# cell内的梯度大小

cell_magnitude = gradient_magnitude[i * self.cell_size:(i + 1) * self.cell_size,

j * self.cell_size:(j + 1) * self.cell_size]

# cell内的梯度方向

cell_angle = gradient_angle[i * self.cell_size:(i + 1) * self.cell_size,

j * self.cell_size:(j + 1) * self.cell_size]

# 转化为梯度直方图格式

cell_gradient_vector[i][j] = self.cell_gradient(cell_magnitude, cell_angle)

# 绘制梯度直方图

hog_image = self.render_gradient(np.zeros([height, width]), cell_gradient_vector)

# block组合、归一化

hog_vector = []

for i in range(cell_gradient_vector.shape[0] - 1):

for j in range(cell_gradient_vector.shape[1] - 1):

block_vector = []

block_vector.extend(cell_gradient_vector[i][j])

block_vector.extend(cell_gradient_vector[i][j + 1])

block_vector.extend(cell_gradient_vector[i + 1][j])

block_vector.extend(cell_gradient_vector[i + 1][j + 1])

mag = lambda vector: math.sqrt(sum(i ** 2 for i in vector))

magnitude = mag(block_vector)

if magnitude != 0:

normalize = lambda block_vector, magnitude: [element / magnitude for element in block_vector]

block_vector = normalize(block_vector, magnitude)

hog_vector.append(block_vector)

return hog_vector, hog_image

def global_gradient(self):

gradient_values_x = cv2.Sobel(self.img, cv2.CV_64F, 1, 0, ksize=5)

gradient_values_y = cv2.Sobel(self.img, cv2.CV_64F, 0, 1, ksize=5)

gradient_magnitude = cv2.addWeighted(gradient_values_x, 0.5, gradient_values_y, 0.5, 0)

gradient_angle = cv2.phase(gradient_values_x, gradient_values_y, angleInDegrees=True)

return gradient_magnitude, gradient_angle

def cell_gradient(self, cell_magnitude, cell_angle):

orientation_centers = [0] * self.bin_size

for i in range(cell_magnitude.shape[0]):

for j in range(cell_magnitude.shape[1]):

gradient_strength = cell_magnitude[i][j]

gradient_angle = cell_angle[i][j]

min_angle, max_angle, mod = self.get_closest_bins(gradient_angle)

orientation_centers[min_angle] += (gradient_strength * (1 - (mod / self.angle_unit)))

orientation_centers[max_angle] += (gradient_strength * (mod / self.angle_unit))

return orientation_centers

def get_closest_bins(self, gradient_angle):

idx = int(gradient_angle / self.angle_unit)

mod = gradient_angle % self.angle_unit

return idx, (idx + 1) % self.bin_size, mod

def render_gradient(self, image, cell_gradient):

cell_width = self.cell_size / 2

max_mag = np.array(cell_gradient).max()

for x in range(cell_gradient.shape[0]):

for y in range(cell_gradient.shape[1]):

cell_grad = cell_gradient[x][y]

cell_grad /= max_mag

angle = 0

angle_gap = self.angle_unit

for magnitude in cell_grad:

angle_radian = math.radians(angle)

x1 = int(x * self.cell_size + magnitude * cell_width * math.cos(angle_radian))

y1 = int(y * self.cell_size + magnitude * cell_width * math.sin(angle_radian))

x2 = int(x * self.cell_size - magnitude * cell_width * math.cos(angle_radian))

y2 = int(y * self.cell_size - magnitude * cell_width * math.sin(angle_radian))

cv2.line(image, (y1, x1), (y2, x2), int(255 * math.sqrt(magnitude)))

angle += angle_gap

return image

img = cv2.imread('0.jpg', cv2.IMREAD_GRAYSCALE)

hog = Hog_descriptor(img, cell_size=8, bin_size=9)

vector, image = hog.extract()

# 输出图像的特征向量shape

print(np.array(vector).shape)

plt.imshow(image, cmap=plt.cm.gray)

plt.show()