We find the conditions under which attractor \(K({\mathcal {S}}')\) of a deformation \({\mathcal {S}}'\) contractible P-polygonal system {S}}\) in \(\mathbb {R}^2\) is dendrite. The most important one parameter matching condition at points where images vertices polygon P meet.

In this paper, we propose a new object classification technique based on polygonal approximation of the open profile of object. The vertices of polygonal approximation are formed by high curvature points of the profile and they are selected by Fourier transform of the object contour. A series of features are computed from the polygonal approximation and then the minimum distance classifier is u...

We provide conditional lower bounds on two problems on polygonal curves. First, we generalize a recent result on the (discrete) Fréchet distance to k curves. Specifically, we show that, assuming the Strong Exponential Time Hypothesis, the Fréchet distance between k polygonal curves in the plane with n edges cannot be computed in O(nk−ε) time, for any ε > 0. Our second construction shows that un...

We design a fast algorithm for computing the fundamental group of the complement to any knotted polygonal graph in 3-space. A polygonal graph consists of straight segments and is given by sequences of vertices along edge-paths. This polygonal model is motivated by protein backbones described in the Protein Data Bank by 3D positions of atoms. Our KGG algorithm simplifies a knotted graph and comp...

In this paper we propose to use invariant signatures of polygonal approximations of smooth curves for projective object recognition. Similar signatures have been proposed previously as simple and robust signatures. However, they were known to be sensitive to the curve sampling scheme and density, and worked well mainly for in-trinsically polygonal shapes. This paper proposes a re-sampling metho...