2D Curve Modeling via the Method of Probabilistic Nodes Combination

Computer vision needs suitable methods of shape representation and contour reconstruction. One of them, invented by the author and called method of Hurwitz-Radon Matrices (MHR), can be used in representation and reconstruction of shapes of the objects in the plane. Proposed method is based on a family of Hurwitz-Radon (HR) matrices. The matrices are skew-symmetric and possess columns composed of orthogonal vectors. 2D shape is represented by the set of successive nodes. It is shown how to create the orthogonal and discrete OHR operator and how to use it in a process of shape representation and reconstruction. Then MHR method is generalized to Probabilistic Nodes Combination (PNC) method. This work clarifies the significance and novelty of the proposed method compared to existing methods. Previous published papers of the author were dealing with the method of Hurwitz-Radon Matrices (MHR method). Novelty of this monograph and proposed method consists in the fact that calculations are free from the family of Hurwitz-Radon Matrices. Problem statement of this paper is: how to reconstruct (interpolate) missing points of the curve and how to apply new method in computer calculations.

Autorentext

Dariusz Jacek Jakóbczak was born in Koszalin, Poland, on December 30, 1965. He graduated in mathematics (numerical methods and programming) from the University of Gdansk, Poland in 1990. He received the Ph.D. degree in 2007 in computer science from the Polish - Japanese Institute of Information Technology, Warsaw, Poland.