Length estimators for two dimensional and three dimensional images using relative direction chain code

Abstract

The normal practice of representing an image is in digitized form. Although digitization provides no knowledge about the continuous shape but by the assistance of discrete geometric estimators such as length estimators, it is possible to obtain the feature size. In digitization, two widely used chain code schemes for shape representation are Freeman and Bribiesca chain code. The Freeman chain code (FCC) is based on absolute direction while Bribiesca chain code is based on relative direction which makes it stable in shifting, turning, and mirroring movement of image. The main purpose of this study is to implement the relative direction chain code or so-called Bribiesca chain code in length estimator algorithms. This study can be divided into two main parts. The first part is to develop two-dimensional (2D) local and global length estimator based on Bribiesca vertex chain code (VCC). For local length estimator, all regular grids namely rectangular, hexagonal and triangular are applied. For global length estimator, only rectangular grid is considered. The second part is to develop threedimensional (3D) local length estimator based on Bribiesca Orthogonal Directional Change Chain Code (ODCCC). The process is divided into quantization of curve, chain code extraction, and development of length estimators. In quantization, different methods are implemented such as Grid Intersection Quantization, Grid Intersection- Enneagon Quantization, and Cube Quantization. There are four equations and one algorithm proposed for length estimation. The results of the proposed methods are promising such that the length estimators for 2D and 3D images become independent from starting point, and also the 2D global length estimator covers offline and online algorithm. Finally the comparison between the proposed and the established length estimators by FCC gives similar performance, however the resultant visualization of proposed algorithm works better.