Pedro Bibiloni

A survey on curvilinear object segmentation in multiple applications

Curvilinear object segmentation is a paramount step for many applications ranging from medical to aerial image processing. In particular, vessel segmentation in retinal images, detection of spiculated lesions in mammograms or extraction of airways in CT scans provide essential information to experts to evaluate, diagnose and propose a treatment. The significance of these applications has conducted important efforts to propose curvilinear object segmentation algorithms based on the most different techniques. The main objective of this review is to clearly present the similarities and differences between curvilinear structures in different applications and the different techniques used to segment them more effectively. To do so, we propose a general definition of curvilinear structures that encompasses the distinct models considered in the literature. In addition, we analyse and classify the mathematical techniques used to segment the curvilinear structures found across all considered applications, studying their strengths and weaknesses. In particular, we present the most relevant benchmarks related to curvilinear object segmentation as well as the best algorithms according to several performance measures. By doing so, it is acquired a wider point of view to extend the results from some fields to others, and to understand under which conditions some methodologies should be favoured over the rest of them. HighlightsWe study what curvilinear objects are found across different imagery techniques.We study and classify which algorithms have been used to segment them.We present multiple performance measures of such segmentation algorithms.We discuss which approaches are better to segment which curvilinear structures.

Soft color morphology

Morphological operators have been used extensively when dealing with binary or grayscale images, but there is no general-purpose approach for multivariate images that meets the expectactions of practitioners under diferent circumstances. Although several approaches have been proposed, state-of-the-art applications tend to process channels independently, obviating interchannel correlation. In this work, we introduce a new definition of erosion and dilation that can handle images with any number of channels, study their theoretical properties and analyse its behaviour. It is based on the Fuzzy Mathematical Morphology, from which it inherits essential theoretical properties. Our operators consider the first channel to evaluate a pixels importance, but handles all channels to generate coherent outputs. It successfully processes natural images in the L∗a∗b∗ space and can also avoid the creation of new chromatic values, specially important for hyperspectral imagery. We provide, thus, a general and well-founded framework to process color images with morphological operators.

Mayor-Torrens t-norms in the Fuzzy Mathematical Morphology and Their Applications

Fuzzy mathematical morphology has been extensively used in many different applications such as edge detection, noise reduction and shape and pattern recognition. The fundamentals of this morphology are based on an appropriate selection of the operators involved, namely the conjunction and implication. In this work we investigate the use of the Mayor-Torrens family of t-norms, from both theoretical and practical point of view. The results suggest that competitive results can be obtained by using the t-norms of this family.

Retinal Vessel Detection Based on Fuzzy Morphological Line Enhancement

The paradigm of Fuzzy Morphology extends the concept of binary morphology to handle grayscale images. Fuzzy Morphology provides meaningful, local and simple operations that, when properly combined, form powerful transformations. We use this approach to segment out vessels in eye-fundus images, which can be used to diagnose medical conditions such as diabetic retinopathy. To automatically estimate the presence of such conditions, distinguishing vessels from other artifacts becomes a necessary initial step. To address the problem of segmenting curvilinear-like objects such as vessels, our methodology consists on applying the same structuring element rotated several times. We construct a vessel segmentation method and compare it with current state-of-the-art alternatives, showing the potential of our approach.

Skin Hair Removal in Dermoscopic Images Using Soft Color Morphology

Dermoscopic images are useful tools towards the diagnosis and classification of skin lesions. One of the first steps to automatically study them is the reduction of noise, which includes bubbles caused by the immersion fluid and skin hair. In this work we provide an effective hair removal algorithm for dermoscopic imagery employing soft color morphology operators able to cope with color images. Our hair removal filter is essentially composed of a morphological curvilinear object detector and a morphological-based inpainting algorithm. Our work is aimed at fulfilling two goals. First, to provide a successful yet efficient hair removal algorithm using the soft color morphology operators. Second, to compare it with other state-of-the-art algorithms and exhibit the good results of our approach, which maintains lesion’s features.

Vote Validatability in Mix-Net-Based eVoting

One way to build secure electronic voting systems is to use Mix-Nets, which break any correlation between voters and their votes. One of the characteristics of Mix-Net-based eVoting is that ballots are usually decrypted individually and, as a consequence, invalid votes can be detected during the tallying of the election. In particular, this means that the ballot does not need to contain a proof of the vote being valid. However, allowing for invalid votes to be detected only during the tallying of the election can have bad consequences on the reputation of the election. First, casting a ballot for an invalid vote might be considered as an attack against the eVoting system by non-technical people, who might expect that the system does not accept such ballots. Besides, it would be impossible to track the attacker due to the anonymity provided by the Mix-Net. Second, if a ballot for an invalid vote is produced by a software bug, it might be only detected after the election period has finished. In particular, voters would not be able to cast a valid vote again. In this work we formalize the concept of having a system that detects invalid votes during the election period. In addition, we give a general construction of an eVoting system satisfying such property and an efficient concrete instantiation based on well-studied assumptions.

Fuzzy Hit-or-Miss Transform Using Uninorms

The Hit-or-Miss transform (HMT) is a morphological operator which has been successfully used to identify shapes and patterns satisfying certain geometric restrictions in an image. Recently, a novel HMT operator, called the fuzzy morphological HMT, was introduced within the framework of the fuzzy mathematical morphology based on fuzzy conjunctions and fuzzy implication functions. Taking into account that the particular case of considering a t-norm as fuzzy conjunction and its residual implication as fuzzy implication functions has proved its potential in several applications, in this paper, the case when residual implications derived from uninorms and a general fuzzy conjunction, possibly a t-norm or the same uninorm, is deeply analysed. In particular, some theoretical results related to properties desirable for the applications are proved. Finally, some experimental results are presented showing the potential of this choice of operator to detect shapes and patterns in images.

Soft Color Morphology: A Fuzzy Approach for Multivariate Images

Mathematical morphology is a framework composed by a set of well-known image processing techniques, widely used for binary and grayscale images, but less commonly used to process color or multivariate images. In this paper, we generalize fuzzy mathematical morphology to process multivariate images in such a way that overcomes the problem of defining an appropriate order among colors. We introduce the soft color erosion and the soft color dilation, which are the foundations of the rest of operators. Besides studying their theoretical properties, we analyze their behavior and compare them with the corresponding morphological operators from other frameworks that deal with color images. The soft color morphology outstands when handling images in the CIEL

General-purpose curvilinear object detection with fuzzy mathematical morphology

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