使用积分图计算HOG特征
转自：http://smsoftdev-solutions.blogspot.com/2009/08/integral-histogram-for-fast-calculation.html
介绍使用积分图计算HOG特征特别好的一篇文章，条理非常清楚
Object Detection Using opencv I - Integral Histogram for fast Calculation of HOG Features
Histograms of Oriented Gradients or HOG features in combination with a support vector machine have been successfully used for object Detection (most popularly pedestrian detection).
An Integral Histogram representation can be used for fast calculation of
Histograms of Oriented Gradients over arbitrary rectangular regions of
the image. The idea of an integral histogram is analogous to that of an
integral image, used by viola and jones for fast calculation of haar
features for face detection. Mathematically,
where b represents the bin number of the histogram. This way the
calculation of hog over any arbitrary rectangle in the image requires
just 4*bins number of array references. For more details on integral
histogram representation, please refer,
Integral Histogram
The following demonstrates how such integral histogram can be calculated
from an image and used for the calculation of hog features using the
opencv computer vision library :
/*Function to calculate the integral histogram*/
IplImage** calculateIntegralHOG(IplImage* in)
{
/*Convert the input image to grayscale*/
IplImage* img_gray = cvCreateImage(cvGetSize(in), IPL_DEPTH_8U,1);
cvCvtColor(in, img_gray, CV_BGR2GRAY);
cvEqualizeHist(img_gray,img_gray);
/*
Calculate the derivates of the grayscale image in the x and y
directions using a sobel operator and obtain 2 gradient images for the x
and y directions*/
IplImage *xsobel, *ysobel;
xsobel = doSobel(img_gray, 1, 0, 3);
ysobel = doSobel(img_gray, 0, 1, 3);
cvReleaseImage(&img_gray);
/*
Create an array of 9 images (9 because I assume bin size 20 degrees and
unsigned gradient ( 180/20 = 9), one for each bin which will have
zeroes for all pixels, except for the pixels in the original image for
which the gradient values correspond to the particular bin. These will
be referred to as bin images. These bin images will be then used to
calculate the integral histogram, which will quicken the calculation of
HOG descriptors */
IplImage** bins = (IplImage**) malloc(9 * sizeof(IplImage*));
for (int i = 0; i < 9 ; i++) {
bins[i] = cvCreateImage(cvGetSize(in), IPL_DEPTH_32F,1);
cvSetZero(bins[i]);
}
/*
Create an array of 9 images ( note the dimensions of the image, the
cvIntegral() function requires the size to be that), to store the
integral images calculated from the above bin images. These 9 integral
images together constitute the integral histogram */
IplImage** integrals = (IplImage**) malloc(9 * sizeof(IplImage*)); for (int i = 0; i < 9 ; i++) {
integrals[i] = cvCreateImage(cvSize(in->width + 1, in->height + 1),
IPL_DEPTH_64F,1);
}
/* Calculate the bin images. The
magnitude and orientation of the gradient at each pixel is calculated
using the xsobel and ysobel images.{Magnitude = sqrt(sq(xsobel) +
sq(ysobel) ), gradient = itan (ysobel/xsobel) }. Then according to the
orientation of the gradient, the value of the corresponding pixel in the
corresponding image is set */
int x, y;
float temp_gradient, temp_magnitude;
for (y = 0; y <in->height; y++) {
/*
ptr1 and ptr2 point to beginning of the current row in the xsobel and
ysobel images respectively. ptrs[i] point to the beginning of the
current rows in the bin images */
float* ptr1 = (float*) (xsobel->imageData + y * (xsobel->widthStep));
float* ptr2 = (float*) (ysobel->imageData + y * (ysobel->widthStep));
float** ptrs = (float**) malloc(9 * sizeof(float*));
for (int i = 0; i < 9 ;i++){
ptrs[i] = (float*) (bins[i]->imageData + y * (bins[i]->widthStep));
}
/*For every pixel in a row gradient orientation and magnitude are calculated and corresponding values set for the bin images. */
for (x = 0; x <in->width; x++) {
/* if the xsobel
derivative is zero for a pixel, a small value is added to it, to avoid
division by zero. atan returns values in radians, which on being
converted to degrees, correspond to values between -90 and 90 degrees.
90 is added to each orientation, to shift the orientation values range
from {-90-90} to {0-180}. This is just a matter of convention. {-90-90}
values can also be used for the calculation. */
if (ptr1[x] == 0){
temp_gradient = ((atan(ptr2[x] / (ptr1[x] + 0.00001))) * (180/ PI)) + 90;
}
else{
temp_gradient = ((atan(ptr2[x] / ptr1[x])) * (180 / PI)) + 90;
}
temp_magnitude = sqrt((ptr1[x] * ptr1[x]) + (ptr2[x] * ptr2[x]));
/*The
bin image is selected according to the gradient values. The
corresponding pixel value is made equal to the gradient magnitude at
that pixel in the corresponding bin image */
if (temp_gradient <= 20) {
ptrs[0][x] = temp_magnitude;
}
else if (temp_gradient <= 40) {
ptrs[1][x] = temp_magnitude;
}
else if (temp_gradient <= 60) {
ptrs[2][x] = temp_magnitude;
}
else if (temp_gradient <= 80) {
ptrs[3][x] = temp_magnitude;
}
else if (temp_gradient <= 100) {
ptrs[4][x] = temp_magnitude;
}
else if (temp_gradient <= 120) {
ptrs[5][x] = temp_magnitude;
}
else if (temp_gradient <= 140) {
ptrs[6][x] = temp_magnitude;
}
else if (temp_gradient <= 160) {
ptrs[7][x] = temp_magnitude;
}
else {
ptrs[8][x] = temp_magnitude;
}
}
}
cvReleaseImage(&xsobel);
cvReleaseImage(&ysobel);
/*Integral images for each of the bin images are calculated*/
for (int i = 0; i <9 ; i++){
cvIntegral(bins[i], integrals[i]);
}
for (int i = 0; i <9 ; i++){
cvReleaseImage(&bins[i]);
}
/*The function returns an array of 9 images which consitute the integral histogram*/
return (integrals);
}
The following demonstrates how the integral histogram calculated using
the above function can be used to calculate the histogram of oriented
gradients for any rectangular region in the image:
/* The following
function takes as input the rectangular cell for which the histogram of
oriented gradients has to be calculated, a matrix hog_cell of dimensions
1x9 to store the bin values for the histogram, the integral histogram,
and the normalization scheme to be used. No normalization is done if normalization = -1 */
void calculateHOG_rect(CvRect cell, CvMat* hog_cell,
IplImage** integrals, int normalization) {
/* Calculate the bin values for each of the bin of the histogram one by one */
for (int i = 0; i < 9 ; i++){
float a =((double*)(integrals[i]->imageData + (cell.y)
* (integrals[i]->widthStep)))[cell.x];
float b = ((double*) (integrals[i]->imageData + (cell.y + cell.height)
* (integrals[i]->widthStep)))[cell.x + cell.width];
float c = ((double*) (integrals[i]->imageData + (cell.y)
* (integrals[i]->widthStep)))[cell.x + cell.width];
float d = ((double*) (integrals[i]->imageData + (cell.y + cell.height)
* (integrals[i]->widthStep)))[cell.x];
((float*) hog_cell->data.fl)[i] = (a + b) - (c + d);
}
/*Normalize the matrix*/
if (normalization != -1){
cvNormalize(hog_cell, hog_cell, 1, 0, normalization);
}
}
另外一篇同样很不错的文章：Integral histogram for fast HoG feature calculation
