Unsupervised Morphological Multiscale Segmentation of Scanning Electron Microscopy Images

This paper deals with a problem of unsupervised multiscale segmentation in the domain of scanning electron microscopy, which is tackled by mathematical morphology techniques. The proposed approach includes various steps. First, the image is decomposed into various compact scales of representation, where objects at each scale are homogeneous in size. Multiscale decomposition is based on a morphological scale-space followed by scale merging using hierarchical clustering and earth mover distance. Then the compact scales are segmented independently using watershed transform. Finally the segmented scales are combined using a tree of objects in order to obtain a multiscale segmentation

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

A mathematical morphology approach for a qualitative exploration of drought events in space and time

Drought events occur worldwide and possibly incur severe consequences. Trying to understand and characterize drought events is of considerable importance in order to improve the preparedness for coping with future events. In this paper, we present a methodology that allows for the delineation of drought events by exploiting their spatiotemporal nature. To that end, we apply operators borrowed from mathematical morphology to represent drought events as connected components in space and time. As an illustration, we identify drought events on the basis of a 35-year data set of daily soil moisture values covering mainland Australia. We then extract characteristics reflecting the affected area, duration and intensity from the proposed representation of a drought event in order to illustrate the impact of tuning parameters in the methodology presented. Yet, this paper we refrain from comparing with other drought delineation methods

On morphological hierarchical representations for image processing and spatial data clustering

Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we briefly survey fundamental results on hierarchical clustering and then detail recent paradigms developed for the hierarchical representation of images in the framework of mathematical morphology: constrained connectivity and ultrametric watersheds. Constrained connectivity can be viewed as a way to constrain an initial hierarchy in such a way that a set of desired constraints are satis ed. The framework of ultrametric watersheds provides a generic scheme for computing any hierarchical connected clustering, in particular when such a hierarchy is constrained. The suitability of this framework for solving practical problems is illustrated with applications in remote sensing

Electrocardiogram Baseline Wander Suppression Based on the Combination of Morphological and Wavelet Transformation Based Filtering

One of the major noise components in electrocardiogram (ECG) is the baseline wander (BW). Effective methods for suppressing BW include the wavelet-based (WT) and the mathematical morphological filtering-based (MMF)algorithms. However, the T waveform distortions introduced by the WTand the rectangular/trapezoidal distortions introduced by MMF degrade the quality of the output signal. Hence, in this study, we introduce a method by combining the MMF and WTto overcome the shortcomings of both existing methods. To demonstrate the effectiveness of the proposed method, artificial ECG signals containing a clinicalBW are used for numerical simulation, and we also create a realistic model of baseline wander to compare the proposed method with other state-of-the-art methods commonly used in the literature. /e results show that the BW suppression effect of the proposed method is better than that of the others. Also, the new method is capable of preserving the outline of the BW and avoiding waveform distortions caused by the morphology filter, thereby obtaining an enhanced quality of ECG

Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology

Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale morphology. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical point of view, FMM relies on the fact that the class of all fuzzy sets over a certain universe forms a complete lattice. Recall that complete lattices provide for the most general framework in which MM can be conducted. The concept of L-fuzzy set generalizes not only the concept of fuzzy set but also the concepts of interval-valued fuzzy set and Atanassov’s intuitionistic fuzzy set. In addition, the class of L-fuzzy sets forms a complete lattice whenever the underlying set L constitutes a complete lattice. Based on these observations, we develop a general approach towards L-fuzzy mathematical morphology in this paper. Our focus is in particular on the construction of connectives for interval-valued and intuitionistic fuzzy mathematical morphologies that arise as special, isomorphic cases of L-fuzzy MM. As an application of these ideas, we generate a combination of some well-known medical image reconstruction techniques in terms of interval-valued fuzzy image processing

A Unified Algebraic Framework for Fuzzy Image Compression and Mathematical Morphology

In this paper we show how certain techniques of image processing, having different scopes, can be joined together under a common "algebraic roof"

Flat zones filtering, connected operators, and filters by reconstruction

This correspondence deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions. It is shown that from any connected operator acting on sets, one can construct a connected operator for functions (however, it is not the unique way of generating connected operators for functions). Moreover, the concept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the flat zones of the functions increase with the level of the pyramid. In other words, the flat zones are nested. Filters by reconstruction are defined and their main properties are presented. Finally, some examples of application of connected operators and use of flat zones are described.Peer ReviewedPostprint (published version