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Mathematical Problems in Engineering
Volume 2018, Article ID 5714638, 17 pages
Research Article

A Parallel Algorithm for the Counting of Ellipses Present in Conglomerates Using GPU

1Facultad de Matemáticas, Universidad Autónoma de Yucatán, Mérida, YUC, Mexico
2Centro de Investigación en Matemáticas, Conacyt, Mérida, YUC, Mexico

Correspondence should be addressed to José López-Martínez; xm.ydau.oerroc@zepol.esoj

Received 7 November 2017; Revised 2 February 2018; Accepted 8 March 2018; Published 18 April 2018

Academic Editor: Benjamin Ivorra

Copyright © 2018 Reyes Yam-Uicab et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Detecting and counting elliptical objects are an interesting problem in digital image processing. There are real-world applications of this problem in various disciplines. Solving this problem is harder when there is occlusion among the elliptical objects, since in general these objects are considered as part of the bigger object (conglomerate). The solution to this problem focusses on the detection and segmentation of the precise number of occluded elliptical objects, while omitting all noninteresting objects. There are a variety of computational approximations that focus on this problem; however, such approximations are not accurate when there is occlusion. This paper presents an algorithm designed to solve this problem, specifically, to detect, segment, and count elliptical objects of a specific size when these are in occlusion with other objects within the conglomerate. Our algorithm deals with a time-consuming combinatorial process. To optimize the execution time of our algorithm, we implemented a parallel GPU version with CUDA-C, which experimentally improved the detection of occluded objects, as well as lowering processing times compared to the sequential version of the method. Comparative test results with another method featured in literature showed improved detection of objects in occlusion when using the proposed parallel method.