Plotting a Gradient Vector Field in OpenCV

Question

I want to compute the gradient of a gray-scale image (smoothed_plane in the code) and plot it as a vector field in OpenCV, superposed to an existing image.

I tried to apply a pair of Sobel operators (I also tried Scharr) to compute the two derivatives along x and y as described in OpenCV documentation, but when I try to plot, the vector field seems to be completely wrong. I would like to understand what is my mistake.

I put some code here to be more clear. Thanks in advance for your help.

//img is a gray-scale image
Mat abs_grad_x, abs_grad_y, grad;
Mat g_img;
int ddepth = CV_16S;
int scale = 1;
int delta = 0;    

cvtColor(img,g_img,CV_GRAY2BGR);


smoothed_plane = Mat::zeros(image_height,image_width,CV_8UC1);
gradient_field = Mat::zeros(image_height,image_width,CV_32FC2);

// Smooth the dominant plane by convolution with a Gaussian
GaussianBlur(dominant_plane,smoothed_plane,Size(51,51),image_height*image_width*0.5);

/// Morphological opening (remove small objects from the foreground)
erode(smoothed_plane, smoothed_plane, getStructuringElement(MORPH_ELLIPSE, Size(40+1,40+1)));
dilate(smoothed_plane, smoothed_plane, getStructuringElement(MORPH_ELLIPSE, Size(40, 40)));
/// Morphological closing (fill small holes in the foreground)
dilate(smoothed_plane, smoothed_plane, getStructuringElement(MORPH_ELLIPSE, Size(40, 40)));
erode(smoothed_plane, smoothed_plane, getStructuringElement(MORPH_ELLIPSE, Size(40, 40)));

imshow("Eroded plane",smoothed_plane);

/// Gradient X
Scharr( smoothed_plane, grad_x, ddepth, 1, 0, scale, delta, BORDER_DEFAULT );
convertScaleAbs( grad_x, abs_grad_x );

/// Gradient Y
Scharr( smoothed_plane, grad_y, ddepth, 0, 1, scale, delta, BORDER_DEFAULT );
convertScaleAbs( grad_y, abs_grad_y );

for (int i = 0 ; i < image_height ; i ++){
    for (int j = 0 ; j < image_width ; j ++){
        gradient_field.at<Point2f>(Point2f(j,i)) = Point2f(abs_grad_x.at<float>(Point2f(j,i)),abs_grad_y.at<float>(Point2f(j,i)));
    }
}

for (int i = 0 ; i < image_height ; i += flowResolution){
    for (int j = 0 ; j < image_width ; j+= flowResolution){
        Point2f p(j,i);
        Point2f p2(gradient_field.at<Point2f>(p)+p);
        arrowedLine(g_img,p,p2,Scalar(0,0,255),1.5,8,0,0.1);
    }
}//*/

imshow("Gradient Vector Field", g_img);

EDIT:

This is a pair of frames of my input/output results, as required

I tried to print out some values, and in some points I got very high or very low values. Thanks again

Answer 1

I solved my problem. The main mistake lied in the access method of the partial derivatives matrices, grad_x and grad_y. As described here, the method at.<>() returns a Scalar object, so to get access to the pixel intensity value one should use the .val[] field. This is how the code has to be changed:

Scharr(smoothed_plane,grad_x,ddepth,1,0,scale);
Scharr(smoothed_plane,grad_y,ddepth,0,1,scale);

for (int i = 0 ; i < image_height ; i ++){
    for (int j = 0 ; j < image_width ; j ++){
        Scalar xval = grad_x.at<float>(i,j);
        Scalar yval = grad_y.at<float>(i,j);
        gradient_field.at<Point2f>(i,j) = Point2f(xval.val[0],yval.val[0]);
    }
}

and this is the expected result: