Search code examples
javaimage-processinggraphicsedge-detectionsobel

Colored Canny edge detection calculation problems

I'm working on a school project for the graphics class. My task is detecting edges on a colored image, we received the suggestion to use the Canny edge detection algorithm.

I've decided to write the entire program by myself in Java, because it looks easy with the given formulas. I've created a window with Java Swing, I'm reading in the input image as an sRGB image, converting it to CIELab* (because thats part of the task). I have managed to apply the Sobel kernels (Cx,Cy) which determines the partial derivative. However I'm stuck with the direction formula, and coding it.

My first problem is, I don't know if I should calculate the directions in every separate color channel, or do it in one piece.

Here are the formulas for the calculations (first is the direction, I'm stuck with, and on the right size there is the magnitude which requires the direction -theta)

pic

Here is the source code for calculating the direction:

//Returns the gradients direction from Cx,Cy
public LabImg direction(LabImg Cx, LabImg Cy) {
    LabImg result = new LabImg(Cx.getWidth(),Cx.getHeight());
    for(int x = 0; x < result.getWidth(); x++) {
        for(int y = 0; y < result.getHeight(); y++) {
            float CxL = Cx.getPixel(x, y).getL();
            float Cxa = Cx.getPixel(x, y).getA();
            float Cxb = Cx.getPixel(x, y).getB();

            float CyL = Cy.getPixel(x, y).getL();
            float Cya = Cy.getPixel(x, y).getA();
            float Cyb = Cy.getPixel(x, y).getB();

            float dirL = (float) ((2*CxL*CyL)/((CxL*CxL)-(CyL*CyL)));
            float dira = (float) ((2*Cxa*Cya)/((Cxa*Cxa)-(Cya*Cya)));
            float dirb = (float) ((2*Cxb*Cyb)/((Cxb*Cxb)-(Cyb*Cyb)));

            //float dir = (2*CxL*CyL+Cxa*Cya+Cxb*Cyb)/((CxL*CxL+Cxa*Cxa+Cxb*Cxb)-(CyL*CyL+Cya*Cya+Cyb*Cyb));

            result.setLab(x, y, dirL, dira, dirb);
        }
    }
    return result;
}

LabImg is a data type, which contains the size of the image, a 2D array of pixel values, and a buffered image.

Solution

  • If you want to do color edge detection, then you will need to process each color channel separately. So, you will have to find gradient directions for the three color channels separately.

    Secondly, you can compute magnitude and directions as:

    magnitude = Math.sqrt(Xgrad*Xgrad + Ygrad*Ygrad)
theta = Math.atan2(Ygrad,Xgrad)