Parallel connected-Component-Labeling based on homotopy trees

Abstract

Taking advantage of the topological and isotopic properties of binary digital images, we present here a new algorithm for connected component labeling (CLL). A local-to-global treatment of the topological information within the image, allows us to develop an inherent parallel approach. The time complexity order for an image of m × n pixels, under the assumption that a processing element exists for each pixel, is near O (log(m + n )) . Additionally, our method computes both the foreground and background CCL, and allows a straightforward computation of topological features like Adjacency Trees. Experiments show that our method obtains better performance metrics than other approaches. Our work aims at generating a new class of labeling algorithms: those centered in fully parallel approaches based on computational topology, thus allowing a perfect concurrent execution in multiple threads and preventing the use of critical sections and atomic instructions.

On the Topological Disparity Characterization of Square-Pixel Binary Image Data by a Labeled Bipartite Graph

“…This computation is based on the algorithm CCLT (Connected Component Labelling Tree) for labelling connected components published in [15]. An example of this (non-unique) CCLT representation is shown in Fig.…”

“…Within each sub-tree, the root (called attractor) appears when an edge "touches" two different colors. This simplified representation implies a more efficient parallel topological computation [14,15]. From now on, the CCLT will be the underlying topological encoding for all the digital image structures used in this paper.…”

“…In this paper, the problems of classification of 2D images in terms of degree of topological disparity or well-composedness and adjacency tree representations are both dealt with here. We use a complete parallel approach based on the HSF framework [14,15], allowing an efficient computation of all the needed structures and measures.…”

Building Hierarchical Tree Representations Using Homological-Based Tools

“…2. This simplified representation implies a more efficient topological computation [10,11] and, from now on, it will be the underlying topological encoding for all the digital image structures used in this paper. The method presented here is based on building the adjacency trees (AdjT ) of a set of q + 2 contrast images of dimension (2m + 1) × (2n + 1) I c ,{c = −1, 0, 1, .…”

A Topologically Consistent Color Digital Image Representation by a Single Tree

“…We call this representation the Contour Region incidence Tree (CRIT for short). CRITs promise to be simple, easy to manipulate and fast to compute in an almost fully parallel manner, due to the fact that the method is based on the HSF (Homological Spanning Forest) framework for topological parallel computing of 2D digital objects [7][8][9].…”