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()

Hog图像特征提取算法,HOG

HOG特点

HOG计算步骤

HOG参数计算

HOG提取特征效果

HOG代码实现