Mathematical Morphology - Theory and Applications

Open Access Published by De Gruyter Open Access

Volume 1 Issue 1

January 2016

Issue of Mathematical Morphology - Theory and Applications

Contents
Journal Overview

Open Access March 4, 2016

Effcient and Effective Automated Digital Hair Removal from Dermoscopy Images

Joost Koehoorn, André Sobiecki, Paulo Rauber, Andrei Jalba, Alexandru Telea

More Download PDF

Abstract

We propose a method for digital hair removal from dermoscopic images, based on a threshold-set model. For every threshold, we adapt a recent gap-detection algorithm to find hairs, and merge results in a single mask image.We find hairs in this mask by combining morphological filters and medial descriptors.We derive robust parameter values for our method from over 300 skin images.We detail a GPU implementation of our method and show how it compares favorably with five existing hair removal methods, in terms of removing both long and stubble hair of various colors, contrasts, and curvature. We also discuss qualitative and quantitative validations of the produced hair-free images, and show how our method effectively addresses the task of automatic skin-tumor segmentation for hair-occluded images.

Open Access March 10, 2016

Generalized Morphology using Sponges

Jasper J. van de Gronde, Jos B. T. M. Roerdink

More Download PDF

Abstract

Mathematical morphology has traditionally been grounded in lattice theory. For non-scalar data lattices often prove too restrictive, however. In this paper we present a more general alternative, sponges, that still allows useful definitions of various properties and concepts from morphological theory. It turns out that some of the existing work on “pseudo-morphology” for non-scalar data can in fact be considered “proper” mathematical morphology in this new framework, while other work cannot, and that this correlates with how useful/intuitive some of the resulting operators are.

Open Access March 18, 2016

N-ary Mathematical Morphology

Emmanuel Chevallier, Augustin Chevallier, Jesús Angulo

More Download PDF

Abstract

Mathematical morphology on binary images can be fully described by set theory. However, it is not sufficient to formulate mathematical morphology for grey scale images. This type of images requires the introduction of the notion of partial order of grey levels, together with the definition of sup and inf operators. More generally, mathematical morphology is now described within the context of the lattice theory. For a few decades, attempts are made to use mathematical morphology on multivariate images, such as color images, mainly based on the notion of vector order. However, none of these attempts has given fully satisfying results. Instead of aiming directly at the multivariate case we propose first an extension of binary mathematical morphology to an intermediary situation: images composed of a finite number of independent unordered labels. We propose then an second extension to a continuous case.

Open Access March 18, 2016

Improved Part-Based Segmentation of Voxel Shapes by Skeleton Cut Spaces

Cong Feng, Andrei C. Jalba, Alexandru C. Telea

More Download PDF

Abstract

We present a refined method for part-based segmentation of voxel shapes by constructing partitioning cuts from every voxel of the shape’s medial surface. Our cuts have several desirable properties – smoothness, tightness, and orientation with respect to the shape’s local symmetry axis, making it a good segmentation tool.We analyze the space of all cuts created for a given shape and detect cuts which are good segment borders. We present a detailed analysis of the parameter space of our method, which yields good preset values for all its parameters. Our method is robust to noise, pose invariant, independent on the shape geometry and genus, and is simple to implement.We demonstrate our method for both automatic and interactive segmentation on a wide selection of 3D shapes.

Open Access March 18, 2016

Defining and computing Hausdorff distances between distributions on the real line and on the circle: link between optimal transport and morphological dilations

Isabelle Bloch, Jamal Atif

More Download PDF

Abstract

Comparing probability or possibility distributions is important in many fields of information processing under uncertainty. In this paper we address the question of defining and computing Hausdorff distances between distributions in a general sense. We propose several dilations of distributions, and exhibit some links between Lévy-Prokhorov distances and dilation-based distances. In particular, mathematical morphology provides an elegant way to deal with periodic distributions. The case of possibility distributions is addressed using fuzzy mathematical morphology. As an illustration, the proposed approaches are applied to the comparison of spatial relations between objects in an image or a video sequence, when these relations are represented as distributions.

Open Access March 30, 2016

Statistical attribute filtering to detect faint extended astronomical sources

Paul Teeninga, Ugo Moschini, Scott C. Trager, Michael H.F. Wilkinson

More Download PDF

Abstract

In astronomy, sky surveys contain a large number of light-emitting sources, often with intensities close to the noise level. Automatic extraction of astronomical objects is therefore needed. SExtractor is a widely used program for automated source extraction and cataloguing, but it is not optimal with faint extended sources. Using SExtractor as a reference, the paper describes an improvement of a previous method proposed by the authors. It is a Max-Tree-based method for extraction of faint extended sources without using a stronger image smoothing. The Max-Tree structure is a hierarchical representation of an image, in which attributes can be computed in every node. Object detection is performed on the nodes of the tree and it relies on the distribution of a statistic calculated using the power attribute, compared to the expected distribution in case of noise. Statistical tests are presented, a comparison with the object extraction of SExtractor is shown and results are discussed.

Open Access April 14, 2016

Cluster Based Vector Attribute Filtering

Fred N. Kiwanuka, Michael H.F. Wilkinson

More Download PDF

Abstract

Morphological attribute filters operate on images based on properties or attributes of connected components. Until recently, attribute filtering was based on a single global threshold on a scalar property to remove or retain objects. A single threshold struggles in case no single property or attribute value has a suitable, usually multi-modal, distribution. Vector-attribute filtering allows better description of characteristic features for 2D images. In this paper, we apply vector-attribute filtering to 3D and incorporate unsupervised pattern recognition, where connected components are classified based on the similarity of feature vectors. Using a single attribute allows multi-thresholding for attribute filters where more than two classes of structures of interest can be selected. In vector-attribute filters automatic clustering avoids the need for either setting very many attribute thresholds, or finding suitable class prototypes in 3D and setting a dissimilarity threshold. Explorative visualization reduces to visualizing and selecting relevant clusters. We show that the performance of these new filters is better than those of regular attribute filters in enhancement of objects in medical images.

Open Access April 19, 2016

Quantile Filtering of Colour Images via Symmetric Matrices

Martin Welk, Andreas Kleefeld, Michael Breuß

More Download PDF

Abstract

Quantile filters, or rank-order filters, are local image filters which assign quantiles of intensities of the input image within neighbourhoods as output image values. Combining a multivariate quantile definition developed in matrix-valued morphology with a recently introduced mapping between the RGB colour space and the space of symmetric 2 × 2 matrices, we state a class of colour image quantile filters, along with a class of morphological gradient filters derived from these.We consider variants of these filters based on three matrix norms – the nuclear, Frobenius, and spectral norm – and study their differences. We investigate the properties of the quantile and gradient filters and their links to dilation and erosion operators. Using amoeba structuring elements,we devise image-adaptive versions of our quantile and gradient filters. Experiments are presented to demonstrate the favourable properties of the filters, and compare them to existing approaches in colour morphology.

Open Access April 27, 2016

Tracking sub-atomic particles through the Attribute Space

M. Babai, N. Kalantar-Nayestanaki, J. G. Messchendorp, M. H. F. Wilkinson

More Download PDF

Abstract

In this paper, we present the results of an application of attribute space morphological filters for tracking sub-atomic particles in magnetic fields. For this purpose, we have applied the concept of attribute space and connectivity to the binary images produced by charged particles passing through the tracking detector for the future experiment PANDA. This detector could be considered as an undirected graph with irregular neighbourhood relations. For this project, we rely only on the detector geometry. In addition, we have extended the graph to estimate the z-coordinates of the particle paths. The result is an O(n2), proof of concept algorithm with a total error of approximately 0.17; this value depends on track multiplicity and particle type and its parameters. The results look promising; however, more work needs to be done to make this algorithm applicable for the real-life case.

Open Access May 5, 2016

Efficient Computation of Greyscale Path Openings

Herman Schubert, Jasper J. van de Gronde, Jos B. T. M. Roerdink

More Download PDF

Abstract

Path openings are morphological operators that are used to preserve long, thin, and curved structures in images. They have the ability to adapt to local image structures,which allows them to detect lines that are not perfectly straight. They are applicable in extracting cracks, roads, and similar structures. Although path openings are very efficient to implement for binary images, the greyscale case is more problematic. This study provides an analysis of the main existing greyscale algorithm, and shows that although its time complexity can be quadratic in the number of pixels, this is optimal in terms of the output (if the full opening transform is created). Also, it is shown that under many circumstances the worst-case running time is much less than quadratic. Finally, a new algorithm is provided,which has the same time complexity, but is simpler, faster in practice and more amenable to parallelization

Open Access May 16, 2016

Local 2D Pattern Spectra as Connected Region Descriptors

Petra Bosilj, Michael H. F. Wilkinson, Ewa Kijak, Sébastien Lefèvre

More Download PDF

Abstract

We validate the usage of augmented 2D shape-size pattern spectra, calculated on arbitrary connected regions. The evaluation is performed on MSER regions and competitive performance with SIFT descriptors achieved in a simple retrieval system, by combining the local pattern spectra with normalized central moments. An additional advantage of the proposed descriptors is their size: being half the size of SIFT, they can handle larger databases in a time-efficient manner. We focus in this paper on presenting the challenges faced when transitioning from global pattern spectra to the local ones. An exhaustive study on the parameters and the properties of the newly constructed descriptor is offered, as well as performance results from preliminary experiments, validating the usage of the descriptor. We also consider possible improvements to the quality and computation efficiency of the proposed local descriptors.

Open Access December 30, 2016

Morphological probabilistic hierarchies for texture segmentation

Dominique Jeulin

More Download PDF

Abstract

A general methodology is introduced for texture segmentation in binary, scalar, or multispectral images. Textural information is obtained from morphological operations on images. Starting from a fine partition of the image in regions, hierarchical segmentations are designed in a probabilistic framework by means of probabilistic distances conveying the textural or morphological information, and of random markers accounting for the morphological content of the regions and of their spatial arrangement. The probabilistic hierarchies are built from binary or multiple fusion of regions.

About this journal

THE JOURNAL IS CLOSED FOR SUBMISSIONS

Mathematical Morphology - Theory and Applications (MMTA) was an Open Access electronic journal publishing either purely theoretical advances, or new ways of applying mathematical morphology to real-world problems.
MMTA was a forum open to other related mathematical image processing approaches as discrete geometry, topological imaging and scale-space models.

The journal was published in Open Access model and is archived in Portico.

All authors retain copyright, unless – due to their local circumstances – their work is not copyrighted. The copyrights are governed by the Creative-Commons license.

The journal was edited by Nicolas Passat (Université de Reims Champagne-Ardenne, France) and Hugues Talbot (Universite Paris-Saclay, France)