Edges and Corners

Activity 1: Directional Edge Detection

Edge detection in images is achieved by passing it through a high pass filter. Many edge operators like Roberts, Prewitt and Sobel have been proposed. In the spatial domain, edge detection is just a convolution, while in frequency domain, it involves multiplying the spectrums of the image and the edge operator. Here we consider the Prewitt operator.

In matlab, we can apply the edge operators using the imfilter or conv2 functions. Once edges in the X and Y direction are calculated, we can calculate the magnitude and angle of the edges as follows:

Iy = imfilter(double(img),  [-1 -1 -1; 0 0 0; 1 1 1]); 

Ix = imfilter(double(img), [-1 0 1; -1 0 1; -1 0 1]);

mag = sqrt(double(Ix.*Ix + Iy.*Iy));

ang = atan2(double(Ix), double(Iy));

Note that since Ix, Iy and mag are not real images, we must scale it between 0 and 1, before displaying. Hence the following function is used.

function normdisplay(img)

figure; i = img-min(img(:)); imshow(i/max(i(:)));

end

Now to find directional edges, we scan the ang matrix and retain only those edges which fall within a certain band.

function angleedges = directionaledge(mag, ang, th1, th2)

angleedges = zeros(size(ang));

for i = 1:size(ang,1)

    for j = 1:size(ang,2)

        if ang(i,j)>=th1 && ang(i,j)<=th2

            angleedges(i,j) = mag(i,j);

        end

    end

end

end

angleedges = directionaledge(mag, ang, 0.75, 0.8);  %find edges that are around 45 degrees

The following images show some directional edges in the image.

Activity 2: Harris Corner Detector

Corners are interest points in the images, because they usually occur at very discernible, unique parts of the image. In plain patches of images, if we move a small window around, then there is no change at all in any direction. If we are near an edge, then there is one direction along which there is no change (direction of the edge), but a large change in the direction perpendicular to it. Corners are however such points, which have large changes in any direction we move. This criteria can be used to identify corners.

The Harris Corner detector is summarized by the algorithm below: