Manuel González-Hidalgo

On the Choice of the Pair Conjunction–Implication Into the Fuzzy Morphological Edge Detector

In this paper, the fuzzy morphological gradients from the fuzzy mathematical morphologies based on t-norms and conjunctive uninorms are deeply analyzed in order to establish which pair of conjunction and fuzzy implications are optimal, in accordance with their performance in edge detection applications. A novel three-step algorithm based on the fuzzy morphology is proposed. The comparison is performed by means of the so-called Pratts figure of merit. In addition, a statistical analysis is carried out to study the relationship between the different configurations and to establish a classification of the conjunctions and implications considered. Both the objective measure and the statistical analysis conclude that the pairs nilpotent minimum t-norm and the Kleene-Dienes implication, and the idempotent uninorm obtained with the classical negation as a generator and its residual implication, are the best configurations in this approach, because they also obtain competitive results with respect to other approaches.

A fuzzy mathematical morphology based on discrete t-norms: fundamentals and applications to image processing

In this paper, a new approach to fuzzy mathematical morphology based on discrete t-norms is studied. The discrete t-norms that have to be used in order to preserve the most usual algebraical and morphological properties, such as monotonicity, idempotence, scaling invariance, among others, are fully determined. In addition, the properties related to B-open and B-closed objects and the generalized idempotence are also studied. In fact, all properties satisfied by the approach based on continuous nilpotent t-norms hold in the discrete case. This is quite important since in practice we only work with discrete objects. In addition, it is proved that more discrete t-norms satisfying all the properties are available in this approach than in the continuous case, which reduces to the Łukasiewicz t-norm. This morphology based on discrete t-norms can be considered embedded in more general frameworks, such as L-fuzzy sets or quantale modules, but all these frameworks have been studied only from a theoretical point of view. Our main contribution is the practical application of this discrete approach to image processing. Experimental results on edge detection, noise removal and top-hat transformations for some discrete t-norms and their comparison with the corresponding ones obtained by the umbra approach and the continuous Łukasiewicz t-norm are included showing that this theory can be suitable to be used in a wide range of applications on image processing. In particular, a new edge detector based on the morphological gradient, non-maxima suppression and a hysteresis method is presented.

Edge-Images Using a Uninorm-Based Fuzzy Mathematical Morphology: Opening and Closing

In this paper a fuzzy mathematical morphology based on fuzzy logical operators is proposed and the Generalized Idempotence (GI) property for fuzzy opening and fuzzy closing operators is studied. It is proved that GI holds in fuzzy mathematical morphology when the selected fuzzy logical operators are left-continuous uninorms (including left-continuous t-norms) and their corresponding residual implications, generalizing known results on continuous t-norms. Two classes of left-continuous uninorms are emphasized as the only ones for which duality between fuzzy opening and fuzzy closing holds. Implementation results for these two kinds of left-continuous uninorms are included. They are compared with the classical umbra approach and the fuzzy approach using t-norms, proving that they are specially adequate for edge detection.

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.

Red Blood Cell Cluster Separation From Digital Images for Use in Sickle Cell Disease

The study of cell morphology is an important aspect of the diagnosis of some diseases, such as sickle cell disease, because red blood cell deformation is caused by these diseases. Due to the elongated shape of the erythrocyte, ellipse adjustment and concave point detection are applied widely to images of peripheral blood samples, including during the detection of cells that are partially occluded in the clusters generated by the sample preparation process. In the present study, we propose a method for the analysis of the shape of erythrocytes in peripheral blood smear samples of sickle cell disease, which uses ellipse adjustments and a new algorithm for detecting notable points. Furthermore, we apply a set of constraints that allow the elimination of significant image preprocessing steps proposed in previous studies. We used three types of images to validate our method: artificial images, which were automatically generated in a random manner using a computer code; real images from peripheral blood smear sample images that contained normal and elongated erythrocytes; and synthetic images generated from real isolated cells. Using the proposed method, the efficiency of detecting the two types of objects in the three image types exceeded 99.00%, 98.00%, and 99.35%, respectively. These efficiency levels were superior to the results obtained with previously proposed methods using the same database, which is available at http://erythrocytesidb.uib.es/. This method can be extended to clusters of several cells and it requires no user inputs.

A Fuzzy Filter for High-Density Salt and Pepper Noise Removal

In this paper, a novel filter for high-density salt and pepper noise removal based on the fuzzy mathematical morphology using t-norms is proposed. This filter involves two phases, namely, a detection step of the corrupted pixels and the restoration of the image using a specialized regularization method using fuzzy open-close and close-open sequences. The experimental results show that the proposed algorithm outperforms other nonlinear filtering methods both from the visual point of view and the values of some objective performance measures for images corrupted up to 90% of noise.

High-density impulse noise removal using fuzzy mathematical morphology

This paper proposes a filtering method for highdensity impulse noise removal based on the fuzzy mathematical morphology using t-norms. The method is a two phased method. In the first phase, an impulse noise detector based on the fuzzy tophat transforms is used to identify pixels which are likely to be contaminated by noise. In the second phase, the image is restored using a specialized regularization method using fuzzy open-close or fuzzy close-open sequences applied only to those selected contaminated pixels and applying then a block smart erase algorithm. Experimental results show that the proposed algorithm presents a better performance in terms of edge preservation and noise suppression than other nonlinear filtering methods, including the presented in [1], in which this method is based on.

Discrete t-norms in a fuzzy mathematical morphology: Algebraic properties and experimental results

In this paper, a new approach to fuzzy mathematical morphology based on discrete t-norms is studied. It is proved that the most usual algebraic and morphological properties are preserved, such as, duality, monotonicity, interaction with union and intersection, invariance under translating and scaling, local knowledge property, extensitivity, idempotence, and many others. In fact, all properties satisfied by the approach based on nilpotent t-norms hold in the discrete case. This is quite important since in practice we only work with discrete objects. Experimental results for some discrete t-norms are included. They are compared with classical morphological algorithms based on the Łukasiewicz t-norm and the umbra approach, and with the fuzzy approach based on idempotent uninorms, proving that they are suitable to be used in edge detection.

Noisy Image Edge Detection Using an Uninorm Fuzzy Morphological Gradient

Medical images edge detection is one of the most important pre-processing steps in medical image segmentation and 3D reconstruction. In this paper, an edge detection algorithm using an uninorm-based fuzzy morphology is proposed. It is shown that this algorithm is robust when it is applied to different types of noisy images. It improves the results of other well-known algorithms including classical algorithms of edge detection, as well as fuzzy-morphology based ones using the {\L}ukasiewicz t-norm and umbra approach. It detects detailed edge features and thin edges of medical images corrupted by impulse or gaussian noise. Moreover, some different objective measures have been used to evaluate the filtered results obtaining for our approach better values than for other approaches.

Interactive Constrained Deformations of NURBS Surfaces: N-SCODEF

In this paper we propose a generalized SCODEF deformation method in order to deform NURBS surface. The deformation method propose a wide class of deformation functions applied to a set of select-user constraints and a wide range of influence zones, expanding the used one for the original SCODEF method. Also, we propose the use of several norms and distances in order to define and compute the deformation function and the constraint influence zone, ensuring a wide range of deformed shapes.