Classical Morphological Operations Research Articles

Mathematical Morphology on Directional Data

We define morphological operators and filters for directional images whose pixel values are unit vectors. This requires an ordering relation for unit vectors which is obtained by using depth functions. They provide a centre-outward ordering with respect to a specified centre vector. We apply our operators on synthetic directional images and compare them with classical morphological operators for grey-scale images. As application examples, we enhance the fault region in a compressed glass foam and segment misaligned fibre regions of glass fibre-reinforced polymers.

Levellings based on spatially adaptive scale spaces using local image features

The authors propose here to overcome lacks of robustness against noise and adaptability to image features for which classical morphological operators suffer from. For doing this, they propose to deal with partial differential equations (PDEs) for generalised Cauchy problems, and they show that the proposed PDEs are equivalent to impose both robustness and adaptability to structuring functions of the corresponding sup-inf operators. This allows them to introduce spatially adaptability in levellings, and it turns out that the proposed approach constitutes a PDE formulation and a generalisation of a larger class of levellings, the so-called extended levellings, for which one of them are characterised by quasi-flat zones. They show the efficiency of the proposed approach on synthetic, grey, and colour images with different types of noises.

Neutrosophic Crisp Mathematical Morphology

In this paper, we aim to apply the concepts of the neutrosophic crisp sets and its operations to the classical mathematical morphological operations, introducing what wecall Neutrosophic Crisp Mathematical Morphology. Sever-al operators are to be developed, including the neutrosophic crisp dilation, the neutrosophic crisp erosion, the neutrosoph-ic crisp opening and the neutrosophic crisp closing. Moreover, we extend the definition of some morphological filters using the neutrosophic crisp sets concept. For instance, we introduce the neutrosophic crisp boundary extraction, the neutrosophic crisp Top-hat and the neutrosophic crisp Bot-tom-hat filters. The idea behind the new introduced operators and filters is to act on the image in the neutrosophic crisp domain instead of the spatial domain.

The design of composite adaptive morphological filter and applications to Rician noise reduction in MR images

ABSTRACTComposite filters based on morphological operators are getting considerably attractive to medical image denoising. Most of such composite filters depend on classical morphological operators. In this article, an optimal composite adaptive morphological filter (FCAMF) is developed through a genetic programming (GP) training algorithm by using new nonlocal amoeba morphological operators. On one hand, we propose a novel method for formulating and implementing nonlocal amoeba structuring elements (SEs) for input‐adaptive morphological operators. The nonlocal amoeba SEs in the proposed strategy is divided into two parts: one is the patch distance based amoeba center, and another is the geodesic distance based amoeba boundary, by which the nonlocal patch distance and local geodesic distance are both taken into consideration. On the other hand, GP as a supervised learning algorithm is employed for building the FCAMF. In GP module, FCAMF is evolved through evaluating the fitness of several individuals over certain number of generations. The proposed method does not need any prior information about the Rician noise variance. Experimental results on both standard simulated and real MRI data sets show that the proposed filter produces excellent results and outperforms existing state‐of‐the‐art filters, especially for highly noisy image. © 2015 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 25, 15–23, 2015

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.

MULTISCALE IMAGE ANALYSIS BASED ON ROBUST AND ADAPTIVE MORPHOLOGICAL SCALE-SPACES

Mathematical morphology is a powerful tool for image analysis; however, classical morphological operators suffer from lacks of robustness against noise, and also intrinsic image features are not accounted at all in the process. We propose in this work a new and different way to overcome such limits, by introducing both robustness and locally adaptability in morphological operators, which are now defined in a manner such that intrinsic image features are accounted. Dealing with partial differential equations (PDEs) for generalized Cauchy problems, we show that proposed PDEs are equivalent to impose robustness and adaptability of corresponding sup-inf operators, to structuring functions. Accurate numerical schemes are also provided to solve proposed PDEs, and experiments conducted for both synthetic and real images, show the efficiency and robustness of our approach.

基于四元数表达的模糊矢量形态学算子

Classical morphological operators cannot be extended directly to color image processing. Therefore, fuzzy vector morphological operators based on a quaternion representation are proposed in this paper. Using a quaternion polar expression combined with its decomposition characteristics, the modulus, the vertical component of the vector and the angular information of a color image are extracted, and they are used to construct the three components for lexicographical ordering. On one hand, the novel three-color components remove the correlation between the multi-channels data; on the other hand, the three components are ranked in the lexicographical ordering facility. Fuzzy mathematics is therefore introduced to solve the problem where the computation cannot be performed at deeper levels. Unlike the existing vector ordering, the new vector ordering takes the role of each component into account, and the computation arrives at the last layer of the lexicographical ordering. Based on a novel vector ordering rule, some new vector morphological operators are de ned, and they are applied to color image ltering and segmentation. Experimental results show that, when compared to the existing vector morphological operators, the new vector morphological operators can smooth the image noise while preserving the image detail, and color images can therefore be segmented correctly with high robustness and practicality.

A Novel Improved Edge Detection Method

In this paper, a novel morphological edge detection using adaptive weighted morphological operators is presented. The newly introduced operators employ weighted structuring element (SE) and apply multiplication or division in place of addition and subtraction in classical morphological operations. It judges its edge and its direction by means of training method and differentiable equivalent representations for the operators, efficient adaptive algorithms to optimize SEs are derived. The gradient of the adaptive weighted morphology utilizes a set of SEs to detect the edge strength with a view to decrease the spurious detail edge and suppressed the noise. Results will be presenting for images in comparison with the others edging detectors.

Noise gradient reduction based on morphological dual operators

Noise gradient is reduced while image details gradient is also reduced by a filter. For the image corrupted by impulse noise, a novel approach of noise gradient reduction is proposed based on a pair of morphological dual operators. The noise image is filtered by a pair of morphological dual operators respectively, and then the two filtered images are provided with the complementary characteristics of the noise gradient position. This feature results from the unsymmetric behaviour of the pair of morphological dual operators, and it can be applied to reduce the noise gradient effectively. This approach is presented in detail and the experimental results show that the approach not only reduces noise gradient effectively, but also maintains image details gradient. Compared with the classical morphological dual operators, the generalised morphology dual operators have smaller root mean square error on the premise of the close computation and time.

A general framework for tree-based morphology and its applications to self-dual filtering

This paper presents a tree-based framework for producing self-dual morphological operators, based on a tree-representation complete inf-semilattice (CISL). The idea is to use a self-dual tree transform to map a given image into the above CISL, perform one or more morphological operations there, and map the result back to the image domain using the inverse tree transform. We also present a particular case of this general framework, involving a new tree transform, the Extrema-Watershed Tree (EWT). The operators obtained by using the EWT in the above framework behave like classical morphological operators, but in addition are self-dual. Some application examples are provided: pre-processing for OCR and dust and scratch removal algorithms, and image denoising. We also explore first steps towards obtaining tree transforms that induce a CISL on the image domain as well.

잡음영상에서 아메바를 이용한 형태학적 에지검출

영상에서 에지검출은 영상처리시스템과 컴퓨터비전에서 매우 중요한 단계이다. 지금까지 형태학적 에지검출은 고정된 구조적 요소를 사용한 형태학적 연산 토대 하에서 수행되어왔다. 본 논문에서는 잡음영상에서 에지검출을 위해 영상의 다양한 형태에 맞춰 다이내믹하게 모양이 변하는 아메바라는 구조적 요소를 사용하고자 한다. 제안된 에지검출 방법의 성능을 시각적인 방법뿐만 아니라 객관적인 척도인 PFOM과 ROC 곡선을 사용하여 정성적, 정량적으로 모두 평가하였다. 영상 설험 결과 고정된 구조적 요소를 이용하는 기존의 방법보다 잡음에 덜 민감하였으며 미세한 에지까지도 검출하는 뛰어난 성능을 보여주었다. Edge detection in images has been widely used in image processing system and computer vision. Morphological edge detection has used structuring elements with fixed shapes. This paper presents morphological operators with non-fixed shape kernels, or amoebas, which take into account the image contour variations to adapt their shape. Experimental results are analyzed in both qualitative analysis through visual inspection and quantitative analysis with PFOM and ROC curves. The Experiments demonstrate that these novel operators outperform classical morphological operations with a fixed, space-invariant structuring elements for edge detection applications.

Image filtering using morphological amoebas

This paper presents morphological operators with non-fixed shape kernels, or amoebas, which take into account the image contour variations to adapt their shape. Experiments on grayscale and color images demonstrate that these novel filters outperform classical morphological operations with a fixed, space-invariant structuring element for noise reduction applications. Tests on synthetic 3D images are then performed to show the high noise-reduction capacity of amoeba-based filters.

Domain learning using Choquet integral-based morphological shared weight neural networks

Morphological shared weight networks (MSNNs) have been applied to many different problem domains, such as discriminating textures, target and hand written character recognition problems. MSNNs use morphological hit-and-miss transforms (HMT) as the activation functions in the feature extraction layer. However, conventional morphological filters have certain drawbacks. They are not robust and therefore are sensitive to noise. They may not tolerate small changes in gray values and shape. On the other hand, Choquet integral-based morphological operations (CMOs), a natural extension of classical morphological operations, are less sensitive to degradations in an image. The MSNN architecture is extended using CMOs in place of HMTs. These networks are referred to as Choquet morphological shared-weight neural networks (CMSNN). In a related paper, we compared the MSNN and CMSNN by extensive experimentation on the real world problem of land mine detection. In this paper, we discuss the problem of domain learning, which is related to feature importance. We provide examples of successes and failures of generalized mathematical morphology and the Choquet integral. These results are interesting, not only for purposes of robustness, but when viewed in the context of determining more valuable information sources.

Weighted morphological filter

A novel morphological filter using weighted morphological operators is presented. The newly introduced operators employ a weighted structuring element and apply multiplication or division in place of addition and subtraction in classical morphological operations. Experimental results prove that the new operators' performance dominates those of classical operators for signals/images buried in salt&pepper, speckle and Gaussian noise.

Design and analysis of fuzzy morphological algorithms for image processing

A general paradigm for lifting binary morphological algorithms to fuzzy algorithms is employed to construct fuzzy versions of classical binary morphological operations. The lifting procedure is based upon an epistemological interpretation of both image and filter fuzzification. Algorithms are designed via the paradigm for various fuzzifications and their performances are analyzed to provide insight into the kind of liftings that produce suitable results. Algorithms are discussed for three image processing tasks: shape detection, edge detection, and clutter removal. Detailed analyses are given for the effect of noise and its mitigation owing to fuzzy approaches. It is demonstrated how the fuzzy hit-or-miss transform can be used in conjunction with a decision procedure to achieve word recognition.

Optimal mean-square N-observation digital morphological filters : I. Optimal binary filters

The present paper places binary morphological filtering into the framework of statistical estimation, the intent being to develop the theory of mean-square (MS) optimization. Classical binary morphological operations are interpreted as numerical functionals on binary N-vectors, so that in the random setting they can be treated as estimators dependent on N binary observation random variables. For single-erosion filters, optimization is achieved by finding the structuring element that minimizes MS error. Using the Matheron representation as a guide, we generalize the analysis to morphological filters given by unions of multiple erosions and optimize by minimizing MS error over all collections of erosions, or over a prefixed number of erosions. In all cases, MS error is relative to the estimation of an unobserved variable by a morphological function of observed variables. A key element in the method is use of the basis form of the Matheron expansion to reduce significantly the structuring-element search. The technique is adapted to special morphological filters by constraining the basis representation in accordance with the class of interest. It is demonstrated that optimization in terms of erosions is equivalent to optimization in terms of dilations.