Image pyramids are simply a collection of images obtained by downsampling an original image, so that each image is one-fourth the area of its predecessor. It is mainly used in image segmentation, since it can generate a very meaningful representation of the image in low resolution, so that a time consuming algorithm can run on it. This makes it easy for us to map this result back to a higher resolution image in the pyramid and makes it possible to refine the results there. Besides, an approximation to a Laplacian, by means of difference of Gaussians, can be generated. Note that a Laplacian image is the one that will show its edges.
In order to produce the downsample image, which we will call the layer i+1 in the Gaussian pyramid (Gi+1), we first convolve Gi with a Gaussian kernel, just like in Gaussian filtering, followed by removing every even numbered row and column. Then, we yield an image with one quarter of the area of the above layer. Averaging before downsampling is...
