International Journal of Pattern Recognition and Artificial Intelligence

Natural systems undergo several morphological changes with time. To study spatio-temporal dynamics of such natural systems, and to further understand the morphological dynamical behaviors, various images that show several macro- and micro-level phenomena, acquired by various types of sensors need to be analyzed in spatio-temporal scales. Such analyses, to facilitate the researcher to model the spatio-temporal organization of a desired phenomenon, evidently require the robust procedures to extract specific error-free features from multiscale-temporal images represented in discrete space. Geometry and topology based features, such as edges of unique type and general type, are the indicators to record the changes that occur temporally. Extraction of such information is essential prerequisite to develop cogent models to understand the spatio-temporal organization.

This paper develops a new technique for modeling and classifying a growing texture using its evolution function over time. It encompasses morphological texture classification and parameter estimation with the objective of assessing the state of growth achieved by the texture using only a small sample set to train on, consistent with many real world situations for quality control. It is assumed that the texture model evolves over time according to the way in which its evolution function determines the parameters of its defining random process. This paper considers the random Boolean model for both binary and gray-scale images. A multiple linear regression model is used to estimate the Boolean model parameters as functions of the granulometric moments of the textures. Once the texture-model parameters are estimated, the time of the process can be found via the manner in which the parameters are determined by the dynamic evolutionary model.

Examinations of the left ventricle (LV), which is the systemic ventricle and as such of paramount importance for the function of the heart, are commonly employed in cardiology. Numerous models have been developed that allow for LV parametric representation. Thanks to that, the left ventricle is better suited for all types of modeling endeavors and the correctness of the results may be relatively easily verified.

The authors present a new method for an automatic detection and evaluation of the left ventricle, which is seen as an echocardiographic image in the four-chamber projection. The method is based on computerized image analysis, and in particular, on mathematical morphology.^{4,6,8,9,11,12} Investigations and the preliminary verification of the method have been carried out on complete cycles registered on video in the course of examinations. It is the complete cycles only that allow us to follow the dynamics of cardiac function.

As a result of long-term collaboration with cardiologists, an algorithm has been developed that allows for an automatic LV detection. A precise delineation of its borders allows for an objective description of changes in geometric parameters in the course of the entire cycle and for a quantitative analysis of the left ventricular function.

In this paper, new operational definitions of binary morphological, both conditional and nonconditional, operations are proposed. The new operations are applied to detect boundary points from binary images. Comparisons of boundary detection algorithms using proposed, standard morphological, and gradient-based operations, showing the effectiveness of the proposed operations, are given. Comparative hardware implementations of standard and proposed morphological operations are also given. Main distinguishing aspects of the new operations are: speed and low hardware implementation (i.e., e.g., low number of buffers and D-Flip–Flops).

How to select a structuring element for a given task is one of the most frequently asked questions in morphology. The present work tries to find a solution for a restricted class of problems, in the domain of shape classification. In this work an algorithm that extracts distinctive structure of each of a given set of objects, which can be used as the structuring elements for object classification system employing the hit-and-miss transformation, is proposed. The proposed algorithm is based on a new measure of local shape property. The method is used to develop a system for Bengali numeral recognition.

The goal of this paper is to establish the fundamental requirements of any morphological software in such a way as to produce reliable, precise, and generic algorithm representations in order to overcome the combinatorial explosion of the code needed to deal with all possible kinds of data structures and image types. Algorithms should be built with the guarantee that the desired implementation is written once, process data in an abstract way, and is efficient at the same time. Requirements are derived from a review of some of the most used software packages and image libraries with respect to mathematical morphology including , , and . Such a review makes it possible to characterize their advantages and drawbacks. These aspects call for software for mathematical morphology that has to be generic and should support a large variety of data types.

This paper shows how mathematical morphological operators can be applied to computer go. On the one hand, mathematical morphology is a very powerful tool within image processing community. On the other hand, the Zobrist's model is well known within the computer go community for its "influence" recognition. We present a model, derived from the closing operator of mathematical morphology and from the Zobrist's model, which yields very good results for "territory" recognition. Moreover, we give efficient implementations of the dilation operator and territory recognition for computer go. This model was found when developing Indigo, our go playing program, and is now used with success in GnuGo, the go playing program of the Free Software Foundation.

This short note presents an application of an algorithm to extract two singular networks of topological interest, such as channel and ridge connectivity networks, from a contour based Digital Elevation Model (DEM) of a region with hilly terrain. From these two extracted networks, a sub-watershed map of this region has been automatically generated. This study facilitates in understanding the watershed morphological processes in a firm quantitative manner in discrete space.

Stereology and stochastic geometry can be used as auxiliary tools for diagnostic purposes in tumour pathology. The role of first-order parameters and stochastic–geometric functions for the classification of the texture of biological tissues has been investigated recently. The volume fraction and surface area per unit volume, the pair correlation function and the centred quadratic contact density function of epithelium were estimated in three case series of benign and malignant lesions of glandular tissues. This approach was further extended by applying the Laslett test, i.e. a point process statistic computed after transformation of the convex tangent points of sectioned random sets from planar images. This method has not yet been applied to histological images so far. Also the nonlinear deterministic approach to tissue texture was applied by estimating the correlation dimension as a function of embedding dimension. We used the stochastic–geometric functions, the first-order parameters and the correlation dimensions for the classification of cases using various algorithms. Learning vector quantization was applied as neural paradigm. Applications included distinction between mastopathy and mammary cancer, between benign prostatic hyperplasia and prostatic cancer, and between chronic pancreatitis and pancreatic cancer. The same data sets were also classified with discriminant analysis and support vector machines. The stereological estimates provided high accuracy in the classification of individual cases. The question: which category of estimator is the most informative, cannot be answered globally, but must be explored empirically for each specific data set. The results obtained by the three algorithms were similar.

The three-dimensional -shape is based on a mathematical formalism which determines exact relationships between points and shapes. It reconstructs surface and volume and detects 3D dot patterns for a given point cloud. -shape of a set of points is a sub-complex of Delaunay triangulation of this set. It generates a family of shapes according to the selected (a set of points). A method to compute the positions of the points of is proposed. These points are selected from the vertices of Voronoi diagram by analyzing the form of the polytopes; their elongation. This method allows the -shape to reflect different levels of detail in different parts of space. An efficient algorithm computing the three-dimensional -shape is presented, the -shape of a set of points is derived from the Delaunay triangulation of the same set. The speed of the algorithm is determined by the speed of the algorithm computing the Delaunay triangulation.

Point-, line- or boundary-sampled intercepts may be measured inside a particle as a measure of particle size. Each intercept is primarily characterized by three geometric properties: length, location and orientation. Circle and sphere models are used in the present study to analyze these properties. The probability distribution function, probability density function, expectation and coefficient of variation for each of the properties were presented based on geometric probability and mathematical statistics. Such presentation would be helpful for potential users of stereology to better understand the concept of intercepts and implement stereological intercept measurement for estimation of particle sizes in practice.