Enhanced Parallel Generation of Tree Structures for the Recognition of 3D Images

• Published in: Pattern Recognition pp. 292 - 301
• Main Authors: Real, P., Molina-Abril, H., Díaz-del-Río, F., Blanco-Trejo, S., Onchis, D.
• Format: Book Chapter
• Language: English
• Published: Cham Springer International Publishing 2019
• Series: Lecture Notes in Computer Science
• Subjects: 3D digital images; Abstract cell complex; Crack transport; Homological Spanning Forest; Parallel computing
• ISBN: 9783030210762; 3030210766
• ISSN: 0302-9743; 1611-3349
• DOI: 10.1007/978-3-030-21077-9_27

Segmentations of a digital object based on a connectivity criterion at n-xel or sub-n-xel level are useful tools in image topological analysis and recognition. Working with cell complex analogous of digital objects, an example of this kind of segmentation is that obtained from the combinatorial representation so called Homological Spanning Forest (HSF, for short) which, informally, classifies the cells of the complex as belonging to regions containing the maximal number of cells sharing the same homological (algebraic homology with coefficient in a field) information. We design here a parallel method for computing a HSF (using homology with coefficients in $$\mathbb {Z}/2\mathbb {Z}$$ ) of a 3D digital object. If this object is included in a 3D image of $$m_1\times m_2 \times m_3$$ voxels, its theoretical time complexity order is near $$O(log(m_1+m_2+m_3))$$ , under the assumption that a processing element is available for each voxel. A prototype implementation validating our results has been written and several synthetic, random and medical tridimensional images have been used for testing. The experiments allow us to assert that the number of iterations in which the homological information is found varies only to a small extent from the theoretical computational time.