Repeatedly smooting, discrete scale-space evolution and dominant point detection

摘要

In this paper, the Fourier analysis is used to derive the properties of an evolving curve. An arbitrary-kernel-repeatedly-smoothing (AKRS) evolution of a curve is then introduced. It is shown that when the repeated number is large, the AKRS evolution of a curve is an approximately discrete implementation of the scale-based evolution of this curve in the Euclidean space. As a special case, an exponential repeatedly smoothing is proposed to implement the scale-based evolution. It is shown that in addition to its simple implementation and its desired approximation to a Gaussian kernel, an exponential function is a function that when it is selected as a repeatedly smoothing kernel, the motion (both 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 proposed to extract dominant points. It is shown experimentally that the proposed method is robust to noise, object rotation and object changes in sizes.