The distance transform provides a metric or measure of the separation
of points in the image. The
bwdist function calculates
the distance between each pixel that is set to
and the nearest nonzero pixel for binary images.
bwdist function supports several distance
metrics, listed in the following table.
The Euclidean distance is the straight-line distance between two pixels.
The city block distance metric measures the path between the pixels based on a 4-connected neighborhood. Pixels whose edges touch are 1 unit apart; pixels diagonally touching are 2 units apart.
The chessboard distance metric measures the path between the pixels based on an 8-connected neighborhood. Pixels whose edges or corners touch are 1 unit apart.
The quasi-Euclidean metric measures the total Euclidean distance along a set of horizontal, vertical, and diagonal line segments.
This example creates a binary image containing two intersecting circular objects.
center1 = -10; center2 = -center1; dist = sqrt(2*(2*center1)^2); radius = dist/2 * 1.4; lims = [floor(center1-1.2*radius) ceil(center2+1.2*radius)]; [x,y] = meshgrid(lims(1):lims(2)); bw1 = sqrt((x-center1).^2 + (y-center1).^2) <= radius; bw2 = sqrt((x-center2).^2 + (y-center2).^2) <= radius; bw = bw1 | bw2; figure, imshow(bw), title('bw')
To compute the distance transform of the complement of the binary
image, use the
bwdist function. In the image of
the distance transform, note how the centers of the two circular areas
D = bwdist(~bw); figure, imshow(D,), title('Distance transform of ~bw')