1. Building Hierarchical Tree Representations Using Homological-Based Tools
- Author
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Fernando Diaz-del-Rio, Pedro Real, Pablo Sanchez-Cuevas, María José Moron-Fernández, Helena Molina-Abril, Universidad de Sevilla. Departamento de Arquitectura y Tecnología de Computadores, Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII), Universidad de Sevilla. TEP108 : Robotica y Tecnología de Computadores, Universidad de Sevilla. TIC245: Topological Pattern Analysis, Recognition and Learning, and Ministerio de Ciencia e Innovación (MICIN). España
- Subjects
Discrete mathematics ,Correctness ,Color image ,Homotopy ,Binary number ,Parallelism ,Alpha (programming language) ,Tree (descriptive set theory) ,Alpha-tree ,Hierarchical representation ,Adjacency list ,Representation (mathematics) ,Digital image ,Mathematics ,Homological spanning forest - Abstract
A new algorithm for computing the α-tree hierarchical repre sentation of a grey-scale digital image is presented here. The technique is based on an efficient simplified version of the Homological Spanning For est (HSF) for encoding homological and homotopy-based information of binary digital images. We create one Adjacency Tree (AdjT) for each intensity contrast in a fully parallel manner. These trees, which define a Contrast Adjacency Forest (CAdjF), are in turn transversely intercon nected by another couple of trees: the classical α-tree, and a new one complementing it, called here the α∗-tree. They convey the information of the contours and the flat regions of the original color image, plus the relations between them. Using both the α and α∗-trees, this new topolog ical representation prevents some classical drawbacks that appear when working with a single tree. An implementation in OCTAVE/MATLAB validates the correctness of our algorithm. Ministerio de Ciencia e Innovación PID2019-110455GB-I00 (Par-HoT)
- Published
- 2021