2013年10月25日 · 曲线演化理论（Curve Evolution）是指仅利用曲线的单位法向量和曲率等几何测度来研究曲线随时间形变的理论。 其基本公式如下： (1) 其中， C (s,t) = (x (s,t),y (s,t))，为动态曲线， s 表示曲线的参变量， t 表示时间变量； T 表示单位切向量， N 表示向内单位法向量，α，β分别表示切向量和法向量的形变速度。 如果曲线演化过程中指关心曲线的形状和几何特征，这 (1) 可以表示为： (2) 若β = ak，其中 k 为曲率，则曲线演化过程中就会变的趋于光滑。 …

Curve evolution refers to the process of evolving curves over time based on properties such as mean curvature, resulting in transformations like shrinking and smoothing of the curves. AI generated definition based on: Handbook of Image and Video Processing (Second Edition), 2005

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The approach is axiomatic and formulated in terms of geometric invariance with respect to the position of the observer. This is translated into mathematical terms, and the author develops the approach of Olver, Sapiro and Tannenbaum, which classifies all curve evolution equations.

The simplest evolution problem is the evolution of curves in the plane by curvature °ow. Let ° 0 be a given smooth embedded convex closed plane curve, and let

2019年5月18日 · In this chapter, we discuss how curve or surface evolution can be formulated using partial differential equations, and discuss some applications in curve smoothing and image segmentation. We consider, in this section, curves that depend on time, which will be denoted by t, the curve parameter being denoted by u (or s for arc length).

Curve evolution overview We will consider “virtual time” within a single image – Given an initial curve, move it to line up with image features (i.e., edges) – Keep the curve reasonably smooth Notation: we will write a curve as C(p)=(x(p),y(p)), p∈[0,1] – …

In this paper, we will investigate a new curvature flow for closed convex plane curves which shortens the length of the evolving curve but expands the area it bounds and makes the curve more...

2016年1月1日 · A stochastic interpretation of curve-shortening flows is formulated, bringing together the theories of curve evolution and hydrodynamical limits, and thus impacts the growing use of joint methods from probability and PDEs in image processing and computer vision.

2007年5月30日 · Curve evolution forms the basis of active contour algorithms used for image segmentation. In many applications the curve under evolution needs to be restricted to the shape space given by...