Shape Approximation Based on Higher-Degree Polynomials

Nikolay Dikusar,Gh Adam,M Hnatič,J Buša,D Podgainy

doi:10.1051/epjconf/201817301003

Nikolay Dikusar, Gh Adam + Show 3 more

Open Access

https://doi.org/10.1051/epjconf/201817301003

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Abstract

The planar shape (contour) of an object is a fundamental source of information in a pattern recognition problem. Obtaining the relevant information set rests on difficult procedures and is a key problem in pattern recognition. A method is proposed for the segmentation of contours with a complex geometrical form. It is based on a parametric piecewise approximation of 12th order spanned by a polynomial model defined by basic elements. Higher-order polynomial approximation allows to optimize the number of segments on the contour and to obtain analytically the dependence of the curvature for more exact calculation of informative signs that are invariant to geometrical transformations. The algorithm based on this method as well as specific examples are described in detail.

Highlights

Not the goal is the subject of decision, but the means to the goal . . . AristotelesThe planar shape of the object is a fundamental source of information in pattern recognition and in the information technologies as well
Instead of processing each point of the object, only its contour is processed. Analytical curves such as pieces of straight lines, circles and spirals arches, cubic splines, etc. are used more often in the approximation of contour lines (CL). In this case the efficiency of the CL approximation is decreased because a big number of short segments [1,2,3]
Results of Basic Element Method (BEM)-smoothing of a complex topology CL that was made in pencil by hand (Fig. 3)

Summary

Introduction

The planar shape (contour) of the object is a fundamental source of information in pattern recognition and in the information technologies as well. To recognize objects at complex image in real time, the processor’s performance should be approximately 108–1014 elementary operations per second. Instead of processing each point of the object, only its contour is processed. Analytical curves such as pieces of straight lines, circles and spirals arches, cubic splines, etc. The goal of this work is to increase the efficiency of the pattern recognition and image processing algorithms using high-degree polynomials for the approximation and smoothing of planar shapes In this case the efficiency of the CL approximation is decreased because a big number of short segments [1,2,3].

Objectives

Results

Conclusion