Characterizing Configurations of critical points through LBP Extended Abstract

In this abstract we extend ideas and results submitted to [3] in which a new codification of Local Binary Patterns (LBP) is given using combinatorial maps and a method for obtaining a representative LBP image is developed based on merging regions and Minimum Contrast Algorithm. The LBP code characterizes the topological category (max, min, slope, saddle) of the 2D gray level landscape around the center region. We extend the result studying how to merge non-singular slopes with one of its neighbors and how to extend the results to nonwell formed images/maps. Some ideas related to robust LBP and isolines are also given in last section. Keywords—ocal binary patterns, critical points, combinatorial mapsocal binary patterns, critical points, combinatorial mapsl I. LBP CODES AND COMBINATORIAL MAPS Given a grayscale digital image I , the local-binary-pattern codification of I , LBP (I) [8], [9] is a grayscale digital image (LBP codes) used to represent the texture element at each pixel in I . In this paper, for computing LBP codification, the 4 neighbors (on its top, bottom, right, left) of each pixel are considered for comparison. Where the center pixel’s gray value is smaller than the neighbor’s gray value, write 1. Otherwise, write 0. Example: 113 240 23 20 25 12 15 30 40 ⇒ 1 0 25 0 1 ⇒ 0101 ⇒ 9 A combinatorial map in two dimensions (shortly cal led 2−maps) [1], [7] consists of the triplet G = (D, σ, α), where D is a set called the set of darts and σ, α are two permutations defined on D such that α is an involution: ∀d ∈ D α(d) = d. The composition σα is denoted by φ. Each dart d ∈ D defines a region by the orbit1 of φ: φ∗(d) = {φ(d), φ(d), . . . , φ(d) = d}. The vertices of the region are given by the set σ∗(d). Two regions φ(d1) and φ(d2) 6= φ(d1) are direct neighbors if their orbits have a non-empty intersection: