Scale-space theory: A basic tool for analysing structures at different scales

An inherent property of objects in the world is that they only exist as meaningful entities over certain ranges of scale. If one aims at describing the structure of unknown real-world signals, then a multi-scale representation of data is of crucial importance. This chapter gives a tutorial review of a special type of multi-scale representation, linear scale-space representation, which has been developed by thecomputer vision community in order to handle image structures at di erent scales in a consistent manner. The basic idea is to embed the original signal into a oneparameter family of gradually smoothed signals, in which the ne scale details are successively suppressed. Under rather general conditions on the type of computations that are to performed at the rst stages of visual processing, in what can be termed the visual front end, it can be shown that the Gaussian kernel and its derivatives are singled out as the only possible smoothing kernels. The conditions that