Parallel connected-Component-Labeling based on homotopy trees

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 x 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. (C) 2019 Elsevier B.V. All rights reserved.