Disjoint set data structure for morphological area operators

Purpose – The purpose of this paper is to present a new geometric model based on the mathematical morphology paradigm, specialized to provide determinism to the classic morphological operations. The determinism is needed to model dynamic processes that require an order of application, as is the case for designing and manufacturing objects in CAD/CAM environments. Design/methodology/approach – The basic trajectory-based operation is the basis of the proposed morphological specialization. This operation allows the definition of morphological operators that obtain sequentially ordered sets of points from the boundary of the target objects, inexistent determinism in the classical morphological paradigm. From this basic operation, the complete set of morphological operators is redefined, incorporating the concept of boundary and determinism: trajectory-based erosion and dilation, and other morphological filtering operations. Findings – This new morphological framework allows the definition of complex three-dimensional objects, providing arithmetical support to generating machining trajectories, one of the most complex problems currently occurring in CAD/CAM. Originality/value – The model proposes the integration of the processes of design and manufacture, so that it avoids the problems of accuracy and integrity that present other classic geometric models that divide these processes in two phases. Furthermore, the morphological operative is based on points sets, so the geometric data structures and the operations are intrinsically simple and efficient. Another important value that no excessive computational resources are needed, because only the points in the boundary are processed.

Mathematical morphological operations are commonly used as a tool in image processing for extracting image components that are useful in the representation and description of region shape. In this paper, six basic morphological operations are investigated to remove noise and enhance the appearance of binary images. Dilation, erosion, opening, closing, fill and majority operations are tested on twenty-five images and subjectively evaluated based on perceived quality of the enhanced images. Results of the experiments showed that noise can be effectively removed from binary images using combinations of erode-dilate operations. Also, the binary images are significantly enhanced using combinations of majority-close operations.

ABSTACT Image segmentation has been an important and challenging issue in the field of computer vision over decades. It plays a critical role for most image analysis tasks, such as object detection and recognition. The aim of this paper is to obtain segmented image of Printed Circuit Board (PCB)’s track using mathematical morphological operation. Morphological image analysis is based on the idea that images represent a collection of spatial patterns that can be analyzed based on some predefined patterns called structuring elements. Most basic morphological operation, dilation and erosion have been employed in this research. Detail elaboration on this method will be discussed and experimental results are presented.

A novel clustering algorithm based on mathematical morphology for wind power generation prediction

In a recent paper (Escribano et al. in Discrete Geometry for Computer Imagery 2008. Lecture Notes in Computer Science, vol. 4992, pp. 81---92, 2008) we have introduced a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach, which uses multivalued functions, provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In this work we develop properties of this family of continuous functions, now concentrating on morphological operations and thinning algorithms. We show that our notion of continuity provides a suitable framework for the basic operations in mathematical morphology: erosion, dilation, closing, and opening. On the other hand, concerning thinning algorithms, we give conditions under which the existence of a retraction F:X?X?D guarantees that D is deletable. The converse is not true, in general, although it is in certain particular important cases which are at the basis of many thinning algorithms.

A familiar way to describe shapes is through their behavior under the operations of mathematical morphology. In this paper we provide a quantitative analysis of the basic operation of mathematical morphology: dilation. This operation has the important property that it transports points such that normals to surfaces are preserved. As a consequence, straight lines are eigenfunctions of morphology. A representation of the objects on a basis of these eigenfunctions should clarify the basic operation (remember how the Fourier transform illuminates linear filtering!), and finding such representations is the subject of this paper.We present two ways to convert the parallel normal transport property into a computational representation of tangential dilation, which is a suitably defined generalization of the dilation of object boundaries. One is the slope transform, designed for the dilation of functions, the other is the normal transform designed for the dilation of geometrical objects. For both transforms, we show how tangential dilation in the spatial domain becomes addition in the transformed domain (plain addition for the slope transform, radial harmonic addition for the normal transform). Though both representations are complete, there are applications in which one is preferable over the other - we give some recommendations for the selection.Key wordsmathematical morphologyeigenfunctiontangential dilationslope transformLegendre transformGauss map

A novel method of the active contour model is proposed by introducing the mathematical morphological operations on the "contour object", which is a binary image object whose outline is the contour. The contours are shrunk and expanded by simply applying the mathematical morphological operations on the contour objects. The split and fusion of contour are also carried out by the mathematical morphological operations, and no additional procedure for split or fusion is required.

Morphological perceptrons (MPs) belong to the class of morphological neural networks (MNNs) whose neuronal aggregation functions are drawn from mathematical morphology (MM). Most MNN models including MPs employ operators of gray-scale mathematical morphology as aggregation functions. Recently, a hybrid morphological/linear perceptron (HMLP) appeared in the literature. This neural network model combines the approximation capabilities of the two-layer perceptron having sigmoid activation functions with the capability of the MP to represent non-differentiable functions. For a number of reasons, that include the non-differentiability of morphological operators, it is advantageous to train HMLPs using extreme learning machine (ELM). The fact that gray-scale MM is closely related to fuzzy MM based on Lukasiewicz operators motivated us to introduce hybrid fuzzy morphological/linear perceptrons (FMLPs) and train them using ELM in this paper. We compare the performances of the HMLP and the FMLP with the ones of some related models in a number of well-known classification problems.

Morphological operators on complex signals

A great earthquake and following great tsunami occurred on 11 th March 2011 over the wide areas of the north-east of Japan. The agricultural fields along the coast were submerge d under the seawater caused by the Tsunami tidal wave for some periods. The soil in such farmland suffered from salt of sea water. As soil salinity is hindrance to the crop growth, the detection of Tsunami flooded farmland is important for ag riculture. ALOS satellite data were obtained from March 13 th including both optical sensor data and SAR data. And aerial photograph for photogrammetry was taken from the next day of the earthquake by Geospatial Information Auth ority of Japan. Many research institutes and universities performed ground survey and made Tsunami flooded extent maps in that region. But as for cloud and large areas, SAR data has advantage. Therefore the author tried detecting the Tsunami flooded extents from ALOS/PALSAR HH data. The outline procedure of the analysis is threshold method for ex tracting the low backscattering areas as a black and white color image, opening operation of mathematical morphology using a 3 by 3 filter size for clearing small islands, dilation operation of mathematical morphology using a 3 by 3 filter size to establish united areas in the scene. The obtained images are compared to aerial ph otograph and ground survey maps. Keywords: Tsunami, soil salinity, farmland, ALOS/PALSAR

Mathematical Morphology (MM) is a general method for image processing based on set theory. The two basic morphological operators are dilation and erosion. From these, several non linear filters have been developed, usually with polynomial complexity and this because the two basic operators depend strongly on the definition of the structural element. Most efforts to improve the algorithm's speed for each operator are based on structural element decomposition and/or efficient codification. In this second part, the concepts developed in part I (see Diaz de Leon and Sossa Azuela, “Mathematical morphology based on linear combined metric spaces on Z^1 (part I): Fast distance transforms,” Journal of Mathematical Imaging and Vision, Vol. 12, No. 2, pp. 137–154, 2000) are used to prove that it is possible to reduce the complexity of the morphological operators to zero complexity (constant time algorithms) for any regular discrete metric space and to eliminate the use of the structural element. In particular, this is done for an infinite family of metric spaces further defined. The use of the distance transformation is proposed for it comprises the information concerning all the discs included in a region to obtain fast morphological operators: erosions, dilations, openings and closings (of zero complexity) for an infinite (countable) family of regular metric spaces. New constant time, in contrast with the polynomial time algorithms, for the computation of these basics operators for any structural element are next derived by using this background. Practical examples showing the efficiency of the proposed algorithms, final comments and present research are also given here.

The electrocardiogram (ECG) is one of the most useful diagnostic tests in emergency medicine. The ECG is affected by large noises such as impulsive noise caused by muscle contraction, power-line interference, baseline drift due to respiration, and motion artifacts. To avoid misinterpreting the ECG, a simple and accurate QRS detection algorithm based on morphology instead of frequency, for the BSN ECG devices is presented. The uniqueness of mathematical morphology is that it does not require any prior knowledge on the frequency spectrum of the signal under investigation. The two most fundamental operators in mathematical morphology are the dilation and erosion operators which are used to reduce the computational complexity. Low power consumption is essential for ECG sensor application in BSN we go for VLSI implementation.

Fast parallel processing of gray-scale images and exact hard-clip thresholding are two important functionalities necessary in optoelectronic implementations of structural processors. The parallel nature of processing stems from optical implementation of local operations with arrays of active smart pixels. We have demonstrated a morphological image processor composed of arrays of bistable optoelectronic transceivers which are connected in differential pairs and work as comparators. The use of differential pairs of optical thyristors fabricated in GaAs technology allows to realize a dual rail architecture for this photonic morphological image processor. The processor consists of a thresholding module and a binary morphological processing module. The thresholding module decomposes gray level images into series of binary slices. In the binary morphological processing module operations are performed within a neighborhood defined by a structuring element implemented as a diffractive fan-out element. In the prototype set-up we demonstrate median filtering, dilation and erosion operations performed for an image of 8x8 pixels and threshold decomposition of 6 gray level images. In principle all rank order as well as morphological filters can be optically calculated in the set-up. Additional functionality of the processor is achieved with use of the electronic layer with digital cellular processors. The electronic layer, designed as an array of simple digital processors, realizes a set of operations on binary images using 4 bit programmable weights. Simulation results for 0.8 µm CMOS technology are presented. We discuss the limitations of the photonic morphological image processing with respect to bandwidth, parallelism and architecture of the processor.

When considering ways to automate the generation of image processing algorithms for object recognition tasks, one critical element is the availability of measures to assess the potential and actual ability of individual operations for making a set of desired discriminations. This paper discusses the analysis and evaluation of grey-level image processing operators or algorithms from the perspective of trying to search automatically through a large space of them for one which satisfactorily performs a given recognition or discrimination task. Performance of an operator may be expressed in terms of accuracy, consistency, and cost, over an entire set of training images.The major issues of evaluating and choosing between operators in this context are discussed, and examples are given of measures which can be used to evaluate classes of operators for applicability, or to evaluate individual operators or parameter settings for actual performance. The paper first describes the form of the analysis for binary morphological operators, and then shows how it may be directly extended to grey-level morphological operators. Several examples are provided to show how grey-level pixel sets may be discriminated on the basis of various combinations of grey level and spatial criteria, as calculated by the basic morphological operators of erosion, dilation, opening, and closing.

This paper describes the development of an automatic segmentation method and a novel navigation system that detect polyps using advanced image processing techniques. The segmentation method described here outlines the colon wall of the CT data set of abdomen by combining the active contouring model - level set method and the minima detection using mathematical morphology theory. The polyp detection is achieved by analysing the surface curvature and the texture information surrounded on the colon wall. As such, the polyp candidates are examined not only by their shape, size but also by their texture appearance which improves the current existing methods. The major contribution of our method is the detailed information analysis using the active contour model assisted by mathematical morphology operations and texture analysis.