Fuzzy Mathematical Morphology Research Articles

Processing of microCT implant-bone systems images using Fuzzy Mathematical Morphology

The relationship between a metallic implant and the existing bone in a surgical permanent prosthesis is of great importance since the fixation and osseointegration of the system leads to the failure or success of the surgery. Micro Computed Tomography is a technique that helps to visualize the structure of the bone. In this study, the microCT is used to analyze implant-bone systems images. However, one of the problems presented in the reconstruction of these images is the effect of the iron based implants, with a halo or fluorescence scattering distorting the micro CT image and leading to bad 3D reconstructions. In this work we introduce an automatic method for eliminate the effect of AISI 316L iron materials in the implant-bone system based on the application of Compensatory Fuzzy Mathematical Morphology for future investigate about the structural and mechanical properties of bone and cancellous materials.

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

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.

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 Pratt's 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.

Fuzzy mathematical morphology using triangular operators and its application to images

Fuzzy mathematical morphology using triangular operators and its application to images

A fuzzy morphological hit-or-miss transform for grey-level images: A new approach

The translation of the hit-or-miss transform (HMT) for grey-level images from the HMT for binary images is not simple. Initially established as a powerful tool for morphological binary image processing, some generalizations for grey-level images have been proposed in the literature. The difficulty lies in the definition of the complement of a given grey-level image. In this paper, after performing a detailed review of the different approaches proposed in the literature, including those based on fuzzy logic, we propose the definition of the hit-or-miss transform for grey-level images in the framework of the fuzzy mathematical morphology based on fuzzy conjunctions and implications under the duality with respect to a fuzzy negation approach. Some theoretical properties of this operator are studied when a general fuzzy conjunction is considered. In particular, we prove that this fuzzy morphological HMT reduces to the binary one when it is applied to binary images. After that, we focus on the fuzzy morphological HMT derived from t-norms and we introduce the concept of “part of an image” which will guide the study of the desirable properties of our operator and the interpretability of the obtained results. Some preliminary experimental results provide evidence of the potential of this tool to be feasible in design algorithms for detecting patterns. Moreover, some comparisons with other hit-or-miss transforms proposed in the literature are performed.

Improving learning rule for fuzzy associative memory with combination of content and association

FAM is an associative memory that uses operators of fuzzy logic and mathematical morphology (MM). FAMs possess important advantages including noise tolerance, unlimited storage, and one pass convergence. An important property, deciding FAM performance, is the ability to capture content of each pattern, and association of patterns. Existing FAMs capture either content or association of patterns well, but not both of them. They are designed to handle either erosive or dilative noise in distorted inputs but not both. Therefore, they cannot recall distorted input patterns very well when both erosive and dilative noises are present. In this paper, we propose a new FAM called content-association associative memory (ACAM) that stores both content and association of patterns. The weight matrix is formed with the weighted sum of output pattern and the difference between input and output patterns. Our ACAM can handle inputs with both erosive and dilative noises better than existing models.

PERFORMANCE ANALYSIS OF FUZZY MATHEMATICAL MORPHOLOGY OPERATORS ON NOISY MRI

Despite a large amount of publications on Fuzzy Mathematical Morphology, little effort was done on systematic evaluation of the performance of this technique. The goal of this work is to compare the robustness against noise of Fuzzy and non Fuzzy Morphological operators when applied to noisy images. Magnetic Resonance Images (MRI) of the brain are a kind of images containing some characteristics that make fuzzy operators an interesting choice, because of their intrinsic noise and imprecision. The robustness was evaluated as the degree in which the results of the operators are not affected by artificial noise in the images. In the analysis we compared different implementation of Fuzzy Mathematical Morphology, and observed that in most of the cases they show higher robustness against noise than the classical morphological operators.

Image Restoration Based on Morphological Operations

Image processing including noise suppression, feature extraction, edge detection, image segmentation, shape recognition, texture analysis, image restoration and reconstruction, image compression etc uses mathematical morphology which is a method of nonlinear filters. It is modulated from traditional morphology to order morphology, soft mathematical morphology and fuzzy soft mathematical morphology. This paper is covers 6 morphological operations which are implemented in the matlab program, including erosion, dilation, opening, closing, boundary extraction and region filling.

IDENTIFICATION OF EXUDATES USING FUZZY MATHEMATICAL MORPHOLOGY

Diabetic Retinopathy is the damage to the retina ca used by complication and the most common cause of blindness in Thailand. Retinal image is essential f or expert ophthalmologists to diagnose diseases. Several of method can achieve good performance on retinal feature are clearly visible. Unfortunately, the color retinal image in Thailand are low-resolution images. The existing method cannot identified lowresolution image. Therefore, this study is part of a larger effort to develop a new method for identification of exudates in low-resolution retina l image. In this study a fuzzy mathematical morphol ogy based on fuzzy logical operator and mathematical mo rphology method is presented. The color retinal image are segmented by using fuzzy logical operator following key preprocessing step, i.e., color normalization, contrast enhancement, noise removal and color space selection. Afterward, a segmentatio n using mathematical morphology method was applied in this step. This enables its difference in our methods compared to other approach and the methods can achieve good performance even on lowresolution retinal images. Respect to the experimental results, the results ob tained with fuzzy mathematical morphology better than the ones obtained with the fuzzy logical operator only method.

Fuzzy mathematical morphology for biological image segmentation

Due to the imaging devices, real-world images such as biological images may have poor contrast and be corrupted by noise, so that regions in the images present soft edges and their segmentation turns out to be quite difficult. Fuzzy mathematical morphology can be successfully applied to segment biological images having such characteristics of vagueness and imprecision. In this work we introduce an approach based on fuzzy mathematical morphology to segment images of human oocytes in order to extract the oocyte region from the entire image. The approach applies fuzzy morphological operators to detect soft edges in the oocyte images, followed by morphological reconstruction operators to isolate the oocyte region. The main concepts from fuzzy mathematical morphology are briefly introduced and the results of applying fuzzy morphological operators are reported in low-contrast images of human oocytes.

Application of the L-fuzzy concept analysis in the morphological image and signal processing

In this work we are going to set up a new relationship between the L-fuzzy Concept Analysis and the Fuzzy Mathematical Morphology. Specifically we prove that the problem of finding fuzzy images or signals that remain invariant under a fuzzy morphological opening or under a fuzzy morphological closing, is equal to the problem of finding the L-fuzzy concepts of some L-fuzzy context. Moreover, since the Formal Concept Analysis and the Mathematical Morphology are the particular cases of the fuzzy ones, the showed result has also an interpretation for binary images or signals.

Dynamic laser speckle and fuzzy mathematical morphology applied to studies of chemotaxis towards hydrocarbons

The movement of the microorganisms towards a higher concentration of the chemical attractant is called positive chemotaxis and is involved in the efficiency of chemical degradation. Several studies are focused in this field related to genomics, and towards demonstrating chemotactic responses by bacteria, but there is little information related to the activity and morphology of their response. In this work, we use a recently reported dynamic speckle laser method, to process images and to distinguish motile surface patterns per area of colonisation by applying image processing techniques called fuzzy mathematical morphology (FMM). The images of bacterial colonies are usually surfaced, with vague edges and non-homogeneous grey levels. Hence, conventional image processing methods for shape analysis cannot be applied in these cases. In this paper, we propose the application FMM to solve this problem. The approach given was effective to segment, detect and also to describe colonisation patterns.

Analysing some R-Implications and its application in fuzzy mathematical morphology

The fuzzy mathematical morphology extends the binary morphological operators to gray-scale and coloured images using concepts of fuzzy logic. To define the morphological operators of fuzzy erosion and dilatation it is used the implications and conjunctions respectively. This work presents an analysis of some R-implications to verify if the pairs of implications and T-norms (conjunctions) were adjunctions. It was used a fuzzy application developed in the Matlab for implementation and tests with the respectively results.

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 ?ukasiewicz 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 ?ukasiewicz 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.

Fuzzy Mathematical Morphology Toolbox and Graphical Interface

The task of solving problems using Digital Image Processing requires of the choice of the correct methodology for the issues to be tackled, and a sound selection of parameters for each algorithm to be used. Fuzzy Mathematical Morphology is one of the existing techniques for image processing, being already applied with success on several problems of medical images analysis. However, the selection and use of its operators requires of the continual observation of the results, over a varied range of parameters, for the selection of the optimal ones. Toward that goal, in this work we develop a library of Fuzzy Mathematical Morphology operators, plus a flexible graphical interface, which is of great help in the selection of the optimal parameters and the implementation of Fuzzy operators, with the addition of several classical Image Processing operators. We describe the properties of the library and analyze the simplicity of the graphical interface.

DIGITAL MAMMOGRAM ENHANCEMENT USING KAPUR MEASURE OF ENTROPY AND MATHEMATICAL MORPHOLOGY

Mammography is the most reliable, effective, low cost and highly sensitive method for early detection of breast cancer. Mammogram analysis usually refers to the processing of mammograms with the goal of finding abnormality presented in the mammogram. Mammogram enhancement is one of the most critical tasks in automatic mammogram image analysis. Main purpose of mammogram enhancement is to enhance the contrast of details and subtle features while suppressing the background heavily. In this paper, a hybrid approach is proposed to enhance the contrast of microcalcifications while suppressing the background heavily, using fuzzy logic and mathematical morphology. First, mammogram is fuzzified using Gaussian fuzzy membership function whose bandwidth is computed using Kapur measure of entropy. After this, mathematical morphology is applied on fuzzified mammogram. Mathematical morphology provides tools for the extraction of microcalcifications even if the microcalcifications are located on a nonuniform background. Main advantage of Kapur measure of entropy over Shannon entropy is that Kapur measure of entropy has α and β parameters that can be used as adjustable values. These parameters can play an important role as tuning parameters in the image processing chain for the same class of images. Experiments have been conducted on images of mini-Mammogram Image Analysis Society (MIAS) database (UK). Experiment results of the proposed approach are compared with histogram equalization (HE), contrast limited adaptive histogram equalization (CLAHE) and fuzzy histogram hyperbolization (FHH) which are well-established image enhancement techniques. In order to validate the results, several different kinds of standard test images (fatty, fatty-glandular and dense-glandular) of mini-MIAS database are considered. Objective image quality assessment parameters: Target-to-background contrast enhancement measurement based on standard deviation (TBCSD), target-to-background contrast enhancement measurement based on entropy (TBCE), contrast improvement index (CII), peak signal-to-noise ratio (PSNR) and average signal-to-noise ratio (ASNR) are used to evaluate the performance of proposed approach. The experimental results show that the proposed approach performs well. This study can be a part of developing a computer-aided diagnosis (CAD) system for early detection of breast cancer.

Characterization of bio-dynamic speckles through classical and fuzzy mathematical morphology tools

In this paper we characterize dynamic speckle signals, obtaining selective information through the differentiation of morphological patterns of the temporal history of each pixel, using the morphological granulometric function. This method is applied to the analysis of images of apples and corn seeds. Studies on the first ones were focused on the activity on their surface, related to healthy and damaged areas, while for seeds on the viability of the embryo and endosperm. Subsequently, the analysis was repeated using fuzzy mathematical morphology techniques, comparing the results obtained by both methods.

Detecção de exsudatos em imagens de retina por técnicas de morfologia matemática e agrupamento nebuloso

Diabetic retinopathy (DR) is one of the major complications of diabetes mellitus and, furthermore it causes severe damage to the retina and consequently to the vision. DR may lead to blindness and therefore it is important to prevent it or early detect and treat it. The diagnosis of DR is performed by visual analysis of retinal images being exudates (fat deposits) the main patterns traced by a specialist doctor. It is noteworthy that early diagnosis, through regular monitoring when coupled with proper treatment, results in numerous benefits in the prevention of visual impairment. Thus, this paper proposes an algorithm for exudate detection in retinal images, whose experimental validation is performed on retina images of the publicly available DIARETDB1 database. The reason for choosing this database is that it provides spatial coordinates of exudates in retina images which constitute ground truths for the algorithm validation. The proposed methodology combines fuzzy clustering and mathematical morphology techniques, and thus it provides a method for optic disk detection considering that it is as the convergent point of vessels. The exudate detection method presented successful rates of 73.03% and 99.41% concerning the use of the whole image and only partial regions, respectively. These results confirm the performance improvement provided by the proposed methodology, when comparing it to other methods available in the literature.

Learning of fuzzy spatial relations between handwritten patterns

It is widely admitted that modelling of spatial information is very important for interpretation and recognition of handwritten expressions. Two distinct tasks have to be addressed by spatial models in this context. Evaluationtask consists of measuring the correspondence between the relationship of two objects and a predefined model of spatial relation. Localisationtask consists of retrieving objects that are related to a reference object according to a predefined model of spatial relation. In this work, we introduce a new modelling of relative spatial positioning that handles the two tasks under a unified framework and a training scheme for learning spatial models from data. The use of fuzzy mathematical morphology allows to deal with imprecision of positioning and to adapt to varying shapes of handwritten objects. Experimentations of the evaluation task over two datasets of online handwritten patterns prove that the proposed modelling outperforms commonly used relative positioning features.

Jaw tissues segmentation in dental 3D CT images using fuzzy-connectedness and morphological processing

The success of oral surgery is subject to accurate advanced planning. In order to properly plan for dental surgery or a suitable implant placement, it is necessary an accurate segmentation of the jaw tissues: the teeth, the cortical bone, the trabecular core and over all, the inferior alveolar nerve. This manuscript presents a new automatic method that is based on fuzzy connectedness object extraction and mathematical morphology processing. The method uses computed tomography data to extract different views of the jaw: a pseudo-orthopantomographic view to estimate the path of the nerve and cross-sectional views to segment the jaw tissues. The method has been tested in a groundtruth set consisting of more than 9000 cross-sections from 20 different patients and has been evaluated using four similarity indicators (the Jaccard index, Dice's coefficient, point-to-point and point-to-curve distances), achieving promising results in all of them (0.726±0.031, 0.840±0.019, 0.144±0.023mm and 0.163±0.025mm, respectively). The method has proven to be significantly automated and accurate, with errors around 5% (of the diameter of the nerve), and is easily integrable in current dental planning systems.