REPEATEDLY SMOOTHING, DISCRETE SCALE-SPACE EVOLUTION AND DOMINANT POINT DETECTION

In this paper, the Fourier analysis is used to derive the properties o f an evolving curve. An arbitrary-kernel-repeatedly-smoothing (AKRS) e volution of a curve is then introduced. It is shown that when the repe ated number is large, the AKRS evolution of a curve is an approximatel y discrete implementation of the scale-based evolution of this curve i n the Euclidean space. As a special case, an exponential repeatedly sm oothing is proposed to implement the scale-based evolution. It is show n that in addition to its simple implementation and its desired approx imation to a Gaussian kernel, an exponential function is a function th at when it is selected as a repeatedly smoothing kernel, the motion (b oth magnitude and direction) of a point on a curve from the (i - 1)th to ith instant is equal to the curvature of the ith smoothed curve at this point. Finally, a perimeter-controlled-evolution method is propos ed to extract dominant points. It is shown experimentally that the pro posed method is robust to noise, object rotation and object changes in sizes. (C) 1996 Pattern Recognition Society. Published by Elsevier Sc ience Ltd.