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-

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-

Parallel Image Processing Using a Pure Topological Framework

Image processing is a fundamental operation in many real time applications, where lots of parallelism can be extracted. Segmenting the image into different connected components is the most known operations, but there are many others like extracting the region adjacency graph (RAG) of these regions, or searching for features points, being invariant to rotations, scales, brilliant changes, etc. Most of these algorithms part from the basis of Tracing-type approaches or scan/raster methods. This fact necessarily implies a data dependence between the processing of one pixel and the previous one, which prevents using a pure parallel approach. In terms of time complexity, this means that linear order O(N) (N being the number of pixels) cannot be cut down. In this paper, we describe a novel approach based on the building of a pure Topological framework, which allows to implement fully parallel algorithms. Concerning topological analysis, a first stage is computed in parallel for every pixel, thus conveying the local neighboring conditions. Then, they are extended in a second parallel stage to the necessary global relations (e.g. to join all the pixels of a connected component). This combinatorial optimization process can be seen as the compression of the whole image to just one pixel. Using this final representation, every region can be related with the rest, which yields to pure topological construction of other image operations. Besides, complex data structures can be avoided: all the processing can be done using matrixes (with the same indexation as the original image) and element-wise operations. The time complexity order of our topological approach for a m×n pixel image is near O(log(m+n)), under the assumption that a processing element exists for each pixel. Results for a multicore processor show very good scalability until the memory bandwidth bottleneck is reached, both for bigger images and for much optimized implementations. The inherent parallelism of our approach points to the direction that even better results will be obtained in other less classical computing architectures.1Ministerio de Economía y Competitividad (España) TEC2012-37868-C04-02AEI/FEDER (UE) MTM2016-81030-PVPPI of the University of Sevill

Pigment Melanin: Pattern for Iris Recognition

Recognition of iris based on Visible Light (VL) imaging is a difficult problem because of the light reflection from the cornea. Nonetheless, pigment melanin provides a rich feature source in VL, unavailable in Near-Infrared (NIR) imaging. This is due to biological spectroscopy of eumelanin, a chemical not stimulated in NIR. In this case, a plausible solution to observe such patterns may be provided by an adaptive procedure using a variational technique on the image histogram. To describe the patterns, a shape analysis method is used to derive feature-code for each subject. An important question is how much the melanin patterns, extracted from VL, are independent of iris texture in NIR. With this question in mind, the present investigation proposes fusion of features extracted from NIR and VL to boost the recognition performance. We have collected our own database (UTIRIS) consisting of both NIR and VL images of 158 eyes of 79 individuals. This investigation demonstrates that the proposed algorithm is highly sensitive to the patterns of cromophores and improves the iris recognition rate.Comment: To be Published on Special Issue on Biometrics, IEEE Transaction on Instruments and Measurements, Volume 59, Issue number 4, April 201

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

Given an nD digital image I based on cubical n-xel, to fully characterize the degree of internal topological dissimilarity existing in I when using different adjacency relations (mainly, comparing 2n or 2n −1 adjacency relations) is a relevant issue in current problems of digital image processing relative to shape detection or identification. In this paper, we design and implement a new self-dual representation for a binary 2D image I, called {4, 8}-region adjacency forest of I ({4, 8}-RAF, for short), that allows a thorough analysis of the differences between the topology of the 4-regions and that of the 8-regions of I. This model can be straightforwardly obtained from the classical region adjacency tree of I and its binary complement image Ic, by a suitable region label identification. With these two labeled rooted trees, it is possible: (a) to compute Euler number of the set of foreground (resp. background) pixels with regard to 4-adjacency or 8-adjacency; (b) to identify new local and global measures and descriptors of topological dissimilarity not only for one image but also between two or more images. The parallelization of the algorithms to extract and manipulate these structures is complete, thus producing efficient and unsophisticated codes with a theoretical computing time near the logarithm of the width plus the height of an image. Some toy examples serve to explain the representation and some experiments with gray real images shows the influence of the topological dissimilarity when detecting feature regions, like those returned by the MSER (maximally stable extremal regions) method.Ministerio de Economía, Industria y Competitividad PID2019-110455GB-I00 (Par-HoT)Junta de Andalucía US-138107

P systems and computational algebraic topology

Membrane Computing is a paradigm inspired from biological cellular communication. Membrane computing devices are called P systems. In this paper we calculate some algebraic-topological information of 2D and 3D images in a general and parallel manner using P systems. First, we present a new way to obtain the homology groups of 2D digital images in time logarithmic with respect to the input data involving an improvement with respect to the algorithms development by S. Peltier et al. Second, we obtain an edge-segmentation of 2D and 3D digital images in constant time with respect to the input data

Using membrane computing for obtaining homology groups of binary 2D digital images

Membrane Computing is a new paradigm inspired from cellular communication. Until now, P systems have been used in research areas like modeling chemical process, several ecosystems, etc. In this paper, we apply P systems to Computational Topology within the context of the Digital Image. We work with a variant of P systems called tissue-like P systems to calculate in a general maximally parallel manner the homology groups of 2D images. In fact, homology computation for binary pixel-based 2D digital images can be reduced to connected component labeling of white and black regions. Finally, we use a software called Tissue Simulator to show with some examples how these systems wor

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

Nopea mittakaava- ja valaistusinvariantti metodi alueiden luokitteluun

This work describes how to find 3D objects in 2D images. The images may contain various illumination conditions and backgrounds. Furthermore the distance and the rotation of the camera with respect to the object can be arbitrary. The method described in this work provides a way to reduce computation time of the 3D object localization problem by searching only from the regions of the image that include a combination of the most common colors of the object. The accuracy and speed of the implementation is tested on images taken under various illuminations and backgrounds.Tämä työ kuvailee miten kolmiulotteisia esineitä voi löytää kaksiulotteisista kuvista. Kuvat voivat sisältää vaihtelevia valaistusolosuhteita ja taustoja. Lisäksi kameran etäisyys ja avaruuskulma suhteessa esineeseen on mielivaltainen. Tässä työssä esitetty menetelmä antaa tavan vähentää kolmiulotteisen esineen löytämisen laskenta-aikaa etsimällä ainoastaan niistä kohdista, joissa on yhdistelmä esineen yleisimpiä värejä. Menetelmän tarkkuus ja nopeus on testattu kuvilla, jotka on otettu erilaisilla valaistuksilla ja taustoilla