MinFilter[image, r] finds the minimum in (2r+1)×(2r+1) blocks centered on each pixel.
At the edges of an image, MinFilter uses smaller neighborhoods.
MinFilter[image, {r1, r2}] uses neighborhoods with vertical range r1 and horizontal range r2.
For multichannel images, MinFilter[image, ...] replaces each pixel by a pixel in its neighborhood that has the minimum total intensity, averaged over all channels.
In MinFilter[data, ...], data can be an array of any rank.