The hierarchical structure of images

Using a Gaussian scale space, one can use the extra dimension, viz. scale, for investigation of "built-in" properties of the image in scale space. We show that one of such induced properties is the nesting of special iso-intensity manifolds, which yield an implicitly present hierarchy of the critical points and regions of their influence, in the original image. Its very nature allows one not only to segment the original image automatically, but also to apply "logical filters" to it, obtaining simplified images. We give an algorithm deriving this hierarchy and show its effectiveness on two different kinds of images, both with respect to segmentation and simplification.