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

Spatiotemporal video segmentation and motion estimation through irregular pyramids

Abstract This paper presents a new spatiotemporal segmentation technique for video sequences. It relies on building irregular pyramids based on its homogeneity over consecutive frames. Pyramids are interlinked to keep a relationship between the regions in the frames. Its performance is good in real-world conditions because it does not depend on image constrains

Color Image Segmentation by Voronoi Partitions

We address the issue of low-level segmentation of color images. The proposed approach is based on the formulation of the problem as a generalized Voronoi partition of the image domain. In this context, a segmentation is determined by the definition of a distance between points of the image and the selection of a set of sites. The distance is defined by considering the low-level attributes of the image and, particularly, the color information. We divide the segmentation task in three successive sub-tasks, treated in the framework of Voronoi partitions : pre-segmentation, hierarchical representation and contour extraction.Nous étudions le problème de la segmentation de bas niveau pour les images couleur. L'approche proposée consiste à modéliser la segmentation d'une image comme une partition de Voronoï généralisée de son domaine. Dans ce contexte, segmenter une image couleur revient à définir une distance appropriée entre points de l'image et à choisir un ensemble de sites. La distance est définie en considérant les attributs de bas niveau de l'image et, en particulier, l'information fournie par la couleur. La démarche adoptée repose sur la division du problème de la segmentation en trois sous-tâches successives, traitées dans le cadre des partitions de Voronoï : la pré-segmentation, la représentation hiérarchique et l'extraction de contours

Data Mining Using the Crossing Minimization Paradigm

Our ability and capacity to generate, record and store multi-dimensional, apparently unstructured data is increasing rapidly, while the cost of data storage is going down. The data recorded is not perfect, as noise gets introduced in it from different sources. Some of the basic forms of noise are incorrect recording of values and missing values. The formal study of discovering useful hidden information in the data is called Data Mining. Because of the size, and complexity of the problem, practical data mining problems are best attempted using automatic means. Data Mining can be categorized into two types i.e. supervised learning or classification and unsupervised learning or clustering. Clustering only the records in a database (or data matrix) gives a global view of the data and is called one-way clustering. For a detailed analysis or a local view, biclustering or co-clustering or two-way clustering is required involving the simultaneous clustering of the records and the attributes. In this dissertation, a novel fast and white noise tolerant data mining solution is proposed based on the Crossing Minimization (CM) paradigm; the solution works for one-way as well as two-way clustering for discovering overlapping biclusters. For decades the CM paradigm has traditionally been used for graph drawing and VLSI (Very Large Scale Integration) circuit design for reducing wire length and congestion. The utility of the proposed technique is demonstrated by comparing it with other biclustering techniques using simulated noisy, as well as real data from Agriculture, Biology and other domains. Two other interesting and hard problems also addressed in this dissertation are (i) the Minimum Attribute Subset Selection (MASS) problem and (ii) Bandwidth Minimization (BWM) problem of sparse matrices. The proposed CM technique is demonstrated to provide very convincing results while attempting to solve the said problems using real public domain data. Pakistan is the fourth largest supplier of cotton in the world. An apparent anomaly has been observed during 1989-97 between cotton yield and pesticide consumption in Pakistan showing unexpected periods of negative correlation. By applying the indigenous CM technique for one-way clustering to real Agro-Met data (2001-2002), a possible explanation of the anomaly has been presented in this thesis

Design of Heuristic Algorithms for Hard Optimization

This open access book demonstrates all the steps required to design heuristic algorithms for difficult optimization. The classic problem of the travelling salesman is used as a common thread to illustrate all the techniques discussed. This problem is ideal for introducing readers to the subject because it is very intuitive and its solutions can be graphically represented. The book features a wealth of illustrations that allow the concepts to be understood at a glance. The book approaches the main metaheuristics from a new angle, deconstructing them into a few key concepts presented in separate chapters: construction, improvement, decomposition, randomization and learning methods. Each metaheuristic can then be presented in simplified form as a combination of these concepts. This approach avoids giving the impression that metaheuristics is a non-formal discipline, a kind of cloud sculpture. Moreover, it provides concrete applications of the travelling salesman problem, which illustrate in just a few lines of code how to design a new heuristic and remove all ambiguities left by a general framework. Two chapters reviewing the basics of combinatorial optimization and complexity theory make the book self-contained. As such, even readers with a very limited background in the field will be able to follow all the content

Document image processing using irregular pyramid structure

Ph.DDOCTOR OF PHILOSOPH

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set