A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

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-

An efficient recursive shortest spanning tree algorithm using linking properties

Published versio

Histopathological image analysis : a review

Over the past decade, dramatic increases in computational power and improvement in image analysis algorithms have allowed the development of powerful computer-assisted analytical approaches to radiological data. With the recent advent of whole slide digital scanners, tissue histopathology slides can now be digitized and stored in digital image form. Consequently, digitized tissue histopathology has now become amenable to the application of computerized image analysis and machine learning techniques. Analogous to the role of computer-assisted diagnosis (CAD) algorithms in medical imaging to complement the opinion of a radiologist, CAD algorithms have begun to be developed for disease detection, diagnosis, and prognosis prediction to complement the opinion of the pathologist. In this paper, we review the recent state of the art CAD technology for digitized histopathology. This paper also briefly describes the development and application of novel image analysis technology for a few specific histopathology related problems being pursued in the United States and Europe

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-

Brain Tumor Segmentation Based on Minimum Spanning Tree

In this paper, we propose a minimum spanning tree-based method for segmenting brain tumors. The proposed method performs interactive segmentation based on the minimum spanning tree without tuning parameters. The steps involve preprocessing, making a graph, constructing a minimum spanning tree, and a newly implemented way of interactively segmenting the region of interest. In the preprocessing step, a Gaussian filter is applied to 2D images to remove the noise. Then, the pixel neighbor graph is weighted by intensity differences and the corresponding minimum spanning tree is constructed. The image is loaded in an interactive window for segmenting the tumor. The region of interest and the background are selected by clicking to split the minimum spanning tree into two trees. One of these trees represents the region of interest and the other represents the background. Finally, the segmentation given by the two trees is visualized. The proposed method was tested by segmenting two different 2D brain T1-weighted magnetic resonance image data sets. The comparison between our results and the gold standard segmentation confirmed the validity of the minimum spanning tree approach. The proposed method is simple to implement and the results indicate that it is accurate and efficient.publishedVersio

Accurate video object tracking using a region-based particle filter

Usually, in particle filters applied to video tracking, a simple geometrical shape, typically an ellipse, is used in order to bound the object being tracked. Although it is a good tracker, it tends to a bad object representation, as most of the world objects are not simple geometrical shapes. A better way to represent the object is by using a region-based approach, such as the Region Based Particle Filter (RBPF). This method exploits a hierarchical region based representation associated with images to tackle both problems at the same time: tracking and video object segmentation. By means of RBPF the object segmentation is resolved with high accuracy, but new problems arise. The object representation is now based on image partitions instead of pixels. This means that the amount of possible combinations has now decreased, which is computationally good, but an error on the regions taken for the object representation leads to a higher estimation error than methods working at pixel level. On the other hand, if the level of regions detail in the partition is high, the estimation of the object turns to be very noisy, making it hard to accurately propagate the object segmentation. In this thesis we present new tools to the existing RBPF. These tools are focused on increasing the RBPF performance by means of guiding the particles towards a good solution while maintaining a particle filter approach. The concept of hierarchical flow is presented and exploited, a Bayesian estimation is used in order to assign probabilities of being object or background to each region, and the reduction, in an intelligent way, of the solution space , to increase the RBPF robustness while reducing computational effort. Also changes on the already proposed co-clustering in the RBPF approach are proposed. Finally, we present results on the recently presented DAVIS database. This database comprises 50 High Definition video sequences representing several challenging situations. By using this dataset, we compare the RBPF with other state-ofthe- art methods