Discrete Average of Two-Dimensional Shapes

• Published in: Computer Analysis of Images and Patterns pp. 145 - 152
• Main Authors: Boukhriss, Isameddine, Miguet, Serge, Tougne, Laure
• Format: Book Chapter Conference Proceeding
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg 2005; Springer
• Series: Lecture Notes in Computer Science
• Subjects: Applied sciences; Artificial intelligence; Average Form; Average Shape; Computer science; control theory; systems; Exact sciences and technology; Inertia Moment; Maximal Elongation; Pattern recognition. Digital image processing. Computational geometry; Rigid Transformation; Two dimensional shape; Preservation; Image processing; Optimal algorithm; Variability; Global optimum; Geodesic structure; Topology; Distance transformation; Discrete geometry; Image analysis; Geodesic; Pattern analysis; Metamorphosis
• ISBN: 9783540289692; 3540289690
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/11556121_19

In this article we present an algorithm for computing discrete average of n two-dimensional shapes. Our previous work was limited to two shapes, we generalize it to an arbitrary number of objects with consideration of increasing inter-individual variability. The first step of our approach performs a rigid transformation that aligns the shapes as best as possible. The next step consists in searching the progressive metamorphosis of one object toward the other one, that iteratively adds or suppresses pixels. This process is then iterated between the last average shape obtained and the new object from the set according to weighting consideration. It considers the rank in which each shape is added and gives criteria of optimization in variability and global topology preservation. The basic operations are based on geodesic distance transformations and lead to an optimal (linear) algorithm.