Computing gradient orientation in c++ using opencv functions - opencv

Question

Can anyone help me out with this?
I am trying to calculate gradient orientation using the Sobel operator in OpenCV for gradient in x and y direction. I am using the atan2 function for computing the tangent in radians, which I later convert to degrees, but all the angles I am getting are between 0 and 90 degrees.
My expectation is to get angles between 0 and 360 degrees. The image I am using is grayscale. The code segment is here below.
Mat PeripheralArea;
Mat grad_x, grad_y; // this is the matrix for the gradients in x and y directions
int off_set_y = 0, off_set_x = 0;
int scale = 1, num_bins = 8, bin = 0;
int delta=-1 ;
int ddepth = CV_16S;
GaussianBlur(PeripheralArea, PeripheralArea, Size(3, 3), 0, 0, BORDER_DEFAULT);
Sobel(PeripheralArea, grad_y, ddepth, 0, 1,3,scale, delta, BORDER_DEFAULT);
Sobel(PeripheralArea, grad_x, ddepth, 1, 0,3, scale, delta, BORDER_DEFAULT);
for (int row_y1 = 0, row_y2 = 0; row_y1 < grad_y.rows / 5, row_y2 < grad_x.rows / 5; row_y1++, row_y2++) {
for (int col_x1 = 0, col_x2 = 0; col_x1 < grad_y.cols / 5, col_x2 < grad_x.cols / 5; col_x1++, col_x2++) {
gradient_direction_radians = (double) atan2((double) grad_y.at<uchar>(row_y1 + off_set_y, col_x1 + off_set_x), (double) grad_x.at<uchar>(row_y2 + off_set_y, col_x2 + off_set_x));
gradient_direction_degrees = (int) (180 * gradient_direction_radians / 3.1415);
gradient_direction_degrees = gradient_direction_degrees < 0
? gradient_direction_degrees+360
: gradient_direction_degrees;
}
}
Note the off_set_x and off_set_y variable are not part of the computation
but to offset to different square blocks for which I eventually want to
compute an histogram feature vector

Answer 1

You have specified that the destination depth of Sobel() is CV_16S.
Yet, when you access grad_x and grad_y, you use .at<uchar>(), implying that their elements are 8 bit unsigned quantities, when in fact they are 16 bit signed. You could use .at<short>() instead, but to me it looks like there a number of issues with your code, not the least of which is that there is an OpenCV function that does exactly what you want.
Use cv::phase(), and replace your for loops with
cv::Mat gradient_angle_degrees;
bool angleInDegrees = true;
cv::phase(grad_x, grad_y, gradient_angle_degrees, angleInDegrees);

Answer 2

I solved this need when I dived into doing some edge detection using C++.
For orientation of gradient I use artan2(), this standard API defines its +y and +x same as how we usually traverse a 2D image.
Plot it to show you my understanding.
///////////////////////////////
// Quadrants of image:
// 3(-dx,-dy) | 4(+dx,-dy) [-pi,0]
// ------------------------->+x
// 2(-dx,+dy) | 1(+dx,+dy) [0,pi]
// v
// +y
///////////////////////////////
// Definition of arctan2():
// -135(-dx,-dy) | -45(+dx,-dy)
// ------------------------->+x
// 135(-dx,+dy) | +45(+dx,+dy)
// v
// +y
///////////////////////////////
How I do for gradient:
bool gradient(double*& magnitude, double*& orientation, double* src, int width, int height, string file) {
if (src == NULL)
return false;
if (width <= 0 || height <= 0)
return false;
double gradient_x_correlation[3*3] = {-0.5, 0.0, 0.5,
-0.5, 0.0, 0.5,
-0.5, 0.0, 0.5};
double gradient_y_correlation[3*3] = {-0.5,-0.5,-0.5,
0.0, 0.0, 0.0,
0.5, 0.5, 0.5};
double *Gx = NULL;
double *Gy = NULL;
this->correlation(Gx, src, gradient_x_correlation, width, height, 3);
this->correlation(Gy, src, gradient_y_correlation, width, height, 3);
if (Gx == NULL || Gy == NULL)
return false;
//magnitude
magnitude = new double[sizeof(double)*width*height];
if (magnitude == NULL)
return false;
memset(magnitude, 0, sizeof(double)*width*height);
double gx = 0.0;
double gy = 0.0;
double gm = 0.0;
for (int j=0; j<height; j++) {
for (int i=0; i<width; i++) {
gx = pow(Gx[i+j*width],2);
gy = pow(Gy[i+j*width],2);
gm = sqrt(pow(Gx[i+j*width],2)+pow(Gy[i+j*width],2));
if (gm >= 255.0) {
return false;
}
magnitude[i+j*width] = gm;
}
}
//orientation
orientation = new double[sizeof(double)*width*height];
if (orientation == NULL)
return false;
memset(orientation, 0, sizeof(double)*width*height);
double ori = 0.0;
double dtmp = 0.0;
double ori_normalized = 0.0;
for (int j=0; j<height; j++) {
for (int i=0; i<width; i++) {
gx = (Gx[i+j*width]);
gy = (Gy[i+j*width]);
ori = atan2(Gy[i+j*width], Gx[i+j*width])/PI*(180.0); //[-pi,+pi]
if (gx >= 0 && gy >= 0) { //[Qudrant 1]:[0,90] to be [0,63]
if (ori < 0) {
printf("[Err1QUA]ori:%.1f\n", ori);
return false;
}
ori_normalized = (ori)*255.0/360.0;
if (ori != 0.0 && dtmp != ori) {
printf("[Qudrant 1]orientation: %.1f to be %.1f(%d)\n", ori, ori_normalized, (uint8_t)ori_normalized);
dtmp = ori;
}
}
else if (gx >= 0 && gy < 0) { //[Qudrant 4]:[270,360) equal to [-90, 0) to be [191,255]
if (ori > 0) {
printf("[Err4QUA]orientation:%.1f\n", ori);
return false;
}
ori_normalized = (360.0+ori)*255.0/360.0;
if (ori != 0.0 && dtmp != ori) {
printf("[Qudrant 4]orientation:%.1f to be %.1f(%d)\n", ori, ori_normalized, (uint8_t)ori_normalized);
dtmp = ori;
}
}
else if (gx < 0 && gy >= 0) { //[Qudrant 2]:(90,180] to be [64,127]
if (ori < 0) {
printf("[Err2QUA]orientation:%.1f\n", ori);
return false;
}
ori_normalized = (ori)*255.0/360.0;
if (ori != 0.0 && dtmp != ori) {
printf("[Qudrant 2]orientation: %.1f to be %.1f(%d)\n", ori, ori_normalized, (uint8_t)ori_normalized);
dtmp = ori;
}
}
else if (gx < 0 && gy < 0) { //[Qudrant 3]:(180,270) equal to (-180, -90) to be [128,190]
if (ori > 0) {
printf("[Err3QUA]orientation:%.1f\n", ori);
return false;
}
ori_normalized = (360.0+ori)*255.0/360.0;
if (ori != 0.0 && dtmp != ori) {
printf("[Qudrant 3]orientation:%.1f to be %.1f(%d)\n", ori, ori_normalized, (uint8_t)ori_normalized);
dtmp = ori;
}
}
else {
printf("[EXCEPTION]orientation:%.1f\n", ori);
return false;
}
orientation[i+j*width] = ori_normalized;
}
}
return true;
}
How I do for cross correlation:
bool correlation(double*& dst, double* src, double* kernel, int width, int height, int window) {
if (src == NULL || kernel == NULL)
return false;
if (width <= 0 || height <= 0 || width < window || height < window )
return false;
dst = new double[sizeof(double)*width*height];
if (dst == NULL)
return false;
memset(dst, 0, sizeof(double)*width*height);
int ii = 0;
int jj = 0;
int nn = 0;
int mm = 0;
double max = std::numeric_limits<double>::min();
double min = std::numeric_limits<double>::max();
double range = std::numeric_limits<double>::max();
for (int j=0; j<height; j++) {
for (int i=0; i<width; i++) {
for (int m=0; m<window; m++) {
for (int n=0; n<window; n++) {
ii = i+(n-window/2);
jj = j+(m-window/2);
nn = n;
mm = m;
if (ii >=0 && ii<width && jj>=0 && jj<height) {
dst[i+j*width] += src[ii+jj*width]*kernel[nn+mm*window];
}
else {
dst[i+j*width] += 0;
}
}
}
if (dst[i+j*width] > max)
max = dst[i+j*width];
else if (dst[i+j*width] < min)
min = dst[i+j*width];
}
}
//normalize double matrix to be an uint8_t matrix
range = max - min;
double norm = 0.0;
printf("correlated matrix max:%.1f, min:%.1f, range:%.1f\n", max, min, range);
for (int j=0; j<height; j++) {
for (int i=0; i<width; i++) {
norm = dst[i+j*width];
norm = 255.0*norm/range;
dst[i+j*width] = norm;
}
}
return true;
}
For me, I use an image like a hollow rectangle, you can download it on my sample.
The orientation of gradient of the hollow rectangle part of my sample image would move from 0 to 360 clockwise (Quadrant 1 to 2 to 3 to 4).
Here is my print which describes the trace of orientation:
[Qudrant 1]orientation: 45.0 to be 31.9(31)
[Qudrant 1]orientation: 90.0 to be 63.8(63)
[Qudrant 2]orientation: 135.0 to be 95.6(95)
[Qudrant 2]orientation: 180.0 to be 127.5(127)
[Qudrant 3]orientation:-135.0 to be 159.4(159)
[Qudrant 3]orientation:-116.6 to be 172.4(172)
[Qudrant 4]orientation:-90.0 to be 191.2(191)
[Qudrant 4]orientation:-63.4 to be 210.1(210)
[Qudrant 4]orientation:-45.0 to be 223.1(223)
You can see more source code about digital image processing on my GitHub :)