A Parallel Implementation for Computing the Region-Adjacency-Tree of a Segmentation of a 2D Digital Image

A design and implementation of a parallel algorithm for computing the Region-Adjacency Tree of a given segmentation of a 2D digital image is given. The technique is based on a suitable distributed use of the algorithm for computing a Homological Spanning Forest (HSF) structure for each connected region of the segmentation and a classical geometric algorithm for determining inclusion between regions. The results show that this technique scales very well when executed in a multicore processor.Ministerio de Ciencia e Innovación TEC2012-37868-C04-02Universidad de Sevilla 2014/75

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

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 Z/2Z) of a 3D digital object. If this object is included in a 3D image of m1 × m2 × m3 voxels, its theoretical time complexity order is near O(log(m1 + m2 + m3)), 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.Ministerio de Economía y Competitividad MTM2016-81030-

Labeling Color 2D Digital Images in Theoretical Near Logarithmic Time

A design of a parallel algorithm for labeling color flat zones (precisely, 4-connected components) of a gray-level or color 2D digital image is given. The technique is based in the construction of a particular Homological Spanning Forest (HSF) structure for encoding topological information of any image.HSFis a pair of rooted trees connecting the image elements at inter-pixel level without redundancy. In order to achieve a correct color zone labeling, our proposal here is to correctly building a sub- HSF structure for each image connected component, modifying an initial HSF of the whole image. For validating the correctness of our algorithm, an implementation in OCTAVE/MATLAB is written and its results are checked. Several kinds of images are tested to compute the number of iterations in which the theoretical computing time differs from the logarithm of the width plus the height of an image. Finally, real images are to be computed faster than random images using our approach.Ministerio de Economía y Competitividad TEC2016-77785-PMinisterio de Economía y Competitividad MTM2016-81030-

Membrane Computing for Real Medical Image Segmentation

In this paper, membrane-based computing image segmentation, both region-based and edge-based, is proposed for medical images that involve two types of neighborhood relations between pixels. These neighborhood relations—namely, 4-adjacency and 8-adjacency of a membrane computing approach—construct a family of tissue-like P systems for segmenting actual 2D medical images in a constant number of steps; the two types of adjacency were compared using different hardware platforms. The process involves the generation of membrane-based segmentation rules for 2D medical images. The rules are written in the P-Lingua format and appended to the input image for visualization. The findings show that the neighborhood relations between pixels of 8-adjacency give better results compared with the 4-adjacency neighborhood relations, because the 8-adjacency considers the eight pixels around the center pixel, which reduces the required communication rules to obtain the final segmentation results. The experimental results proved that the proposed approach has superior results in terms of the number of computational steps and processing time. To the best of our knowledge, this is the first time an evaluation procedure is conducted to evaluate the efficiency of real image segmentations using membrane computing

Tissue-like P system for Segmentation of 2D Hexagonal Images

Membrane computing, which is a new computational model inspired by the structure and functioning of biological cells and by the way the cells are organized in tissues. MC has been adopted in many real world applications including image segmentation. In contrast to the traditional square grid for representing and sampling digital images, hexagonal grid is an alternative efficient mechanism which can better represents and visualizes the curved objects. In this paper, a tissue-like P system with region-based and edge-based segmentation is used to segment two dimensional hexagonal images, wherein P-Lingua programming language is used to implement and validate the proposed system. The achieved experimental results clearly demonstrated the effectiveness of using hexagonal connectivity to segment two dimensional images in a less number of rules and computational steps. Moreover, the results reveal that this approach has the potential of segmenting large images in few number of steps

Building Hierarchical Tree Representations Using Homological-Based Tools

A new algorithm for computing the α-tree hierarchical repre sentation of a grey-scale digital image is presented here. The technique is based on an efficient simplified version of the Homological Spanning For est (HSF) for encoding homological and homotopy-based information of binary digital images. We create one Adjacency Tree (AdjT) for each intensity contrast in a fully parallel manner. These trees, which define a Contrast Adjacency Forest (CAdjF), are in turn transversely intercon nected by another couple of trees: the classical α-tree, and a new one complementing it, called here the α∗-tree. They convey the information of the contours and the flat regions of the original color image, plus the relations between them. Using both the α and α∗-trees, this new topolog ical representation prevents some classical drawbacks that appear when working with a single tree. An implementation in OCTAVE/MATLAB validates the correctness of our algorithm.Ministerio de Ciencia e Innovación PID2019-110455GB-I00 (Par-HoT

Tissue-like p system for region-based and edge-based image segmentations

Membrane Computing (MC), a relatively recent branch of natural computing is an emerging field in molecular computing. MC aims at abstracting models, called membrane systems or P systems, which mimic the function and structure of a biological cell. Many studies have utilized MC in various applications such as image segmentation. Due to the high computational cost of conventional segmentation techniques, bio-inspired models including MC may be applicable to tackle this limitation. In this study, tissue-like P systems, a variant of MC, with sophisticated communication rules were developed to improve regionbased and edge-based segmentation algorithms for manual and automatic segmenting of 2D artificial and real images. Manual segmentation was applied for artificial images, whereas, the automatic segmentation was applied for artificial and real medical images. The manual segmentation of 2D artificial images was achieved using four, six and eight adjacency pixel connectivity relationships, whereas, the automatic segmentation of 2D artificial and real medical images were achieved using four and eight adjacency pixel connectivity relationships. Two methods were used to realize the automatic edge-based and region-based segmentations. The first method is for 2D artificial images using P-lingua linked to Java Netbeans using the P-linguaCore4 Java Library. The second method is for the 2D real and real medical images using C# linked to P-linguaCore4 Java library. The results of the second method demonstrated the ability of the system to automatically segment 2D real and real medical images with arbitrary sizes and different image formats. The experimental results statistically proved that the methods markedly outpaced the state-of-the-art methods of 2D real image segmentation using the same data set. Furthermore, the methods showed better segmentation accuracy and ability to deal with images of different sizes and types. Extra efficient results such as reducing the number of rules and computational steps were achieved for 2D hexagonal artificial images based on Tissue-like P systems. The main contributions of this study are automatic loading and codifying of the input image as well as automatic visualization of output images after segmentation. Furthermore, six and eight adjacency pixel connectivity relationships should be considered for reducing computational steps, number of rules used and processing time in molecular computing

Image Segmentation Inspired by Cellular Models using hardware programming

Several features of image segmentation make it suitable for bio–inspired techniques. It can be parallelized, locally solved and the input data can be easily encoded using representations inspired by nature. In this paper, we present a new hardware system that follows the Membrane Computing approach, and performs edge–based segmentation, noise removal and thresholding of digital images