On the Detection of Visual Features from Digital Curves using a Metaheuristic Approach

In computational shape analysis a crucial step consists in extracting meaningful features from digital curves. Dominant points are those points with curvature extreme on the curve that can suitably describe the curve both for visual perception and for recognition. Many approaches have been developed for detecting dominant points. In this paper we present a novel method that combines the dominant point detection and the ant colony optimization search. The method is inspired by the ant colony search (ACS) suggested by Yin in [1] but it results in a much more efficient and effective approximation algorithm. The excellent results have been compared both to works using an optimal search approach and to works based on exact approximation strateg

Thinning-free Polygonal Approximation of Thick Digital Curves Using Cellular Envelope

Since the inception of successful rasterization of curves and objects in the digital space, several algorithms have been proposed for approximating a given digital curve. All these algorithms, however, resort to thinning as preprocessing before approximating a digital curve with changing thickness. Described in this paper is a novel thinning-free algorithm for polygonal approximation of an arbitrarily thick digital curve, using the concept of "cellular envelope", which is newly introduced in this paper. The cellular envelope, defined as the smallest set of cells containing the given curve, and hence bounded by two tightest (inner and outer) isothetic polygons, is constructed using a combinatorial technique. This envelope, in turn, is analyzed to determine a polygonal approximation of the curve as a sequence of cells using certain attributes of digital straightness. Since a real-world curve=curve-shaped object with varying thickness, unexpected disconnectedness, noisy information, etc., is unsuitable for the existing algorithms on polygonal approximation, the curve is encapsulated by the cellular envelope to enable the polygonal approximation. Owing to the implicit Euclidean-free metrics and combinatorial properties prevailing in the cellular plane, implementation of the proposed algorithm involves primitive integer operations only, leading to fast execution of the algorithm. Experimental results that include output polygons for different values of the approximation parameter corresponding to several real-world digital curves, a couple of measures on the quality of approximation, comparative results related with two other well-referred algorithms, and CPU times, have been presented to demonstrate the elegance and efficacy of the proposed algorithm

Dominant points detection for shape analysis

The growing interest in recent years towards the multimedia and the large amount of information exchanged across the network involves the various fields of research towards the study of methods for automatic identification. One of the main objectives is to associate the information content of images, using techniques for identifying composing objects. Among image descriptors, contours reveal are very important because most of the information can be extracted from them and the contour analysis offers a lower computational complexity also. The contour analysis can be restricted to the study of some salient points with high curvature from which it is possible to reconstruct the original contour. The thesis is focused on the polygonal approximation of closed digital curves. After an overview of the most common shape descriptors, distinguished between simple descriptors and external methods, that focus on the analysis of boundary points of objects, and internal methods, which use the pixels inside the object also, a description of the major methods regarding the extraction of dominant points studied so far and the metrics typically used to evaluate the goodness of the polygonal approximation found is given. Three novel approaches to the problem are then discussed in detail: a fast iterative method (DPIL), more suitable for realtime processing, and two metaheuristics methods (GAPA, ACOPA) based on genetic algorithms and Ant Colony Optimization (ACO), more com- plex from the point of view of the calculation, but more precise. Such techniques are then compared with the other main methods cited in literature, in order to assess the performance in terms of computational complexity and polygonal approximation error, and measured between them, in order to evaluate the robustness with respect to affine transformations and conditions of noise. Two new techniques of shape matching, i.e. identification of objects belonging to the same class in a database of images, are then described. The first one is based on the shape alignment and the second is based on a correspondence by ACO, which puts in evidence the excellent results, both in terms of computational time and recognition accuracy, obtained through the use of dominant points. In the first matching algorithm the results are compared with a selection of dominant points generated by a human operator while in the second the dominant points are used instead of a constant sampling of the outline typically used for this kind of approach

Contribuciones sobre métodos óptimos y subóptimos de aproximaciones poligonales de curvas 2-D

Esta tesis versa sobre el an álisis de la forma de objetos 2D. En visión articial existen numerosos aspectos de los que se pueden extraer información. Uno de los más usados es la forma o el contorno de esos objetos. Esta característica visual de los objetos nos permite, mediante el procesamiento adecuado, extraer información de los objetos, analizar escenas, etc. No obstante el contorno o silueta de los objetos contiene información redundante. Este exceso de datos que no aporta nuevo conocimiento debe ser eliminado, con el objeto de agilizar el procesamiento posterior o de minimizar el tamaño de la representación de ese contorno, para su almacenamiento o transmisión. Esta reducción de datos debe realizarse sin que se produzca una pérdida de información importante para representación del contorno original. Se puede obtener una versión reducida de un contorno eliminando puntos intermedios y uniendo los puntos restantes mediante segmentos. Esta representación reducida de un contorno se conoce como aproximación poligonal. Estas aproximaciones poligonales de contornos representan, por tanto, una versión comprimida de la información original. El principal uso de las mismas es la reducción del volumen de información necesario para representar el contorno de un objeto. No obstante, en los últimos años estas aproximaciones han sido usadas para el reconocimiento de objetos. Para ello los algoritmos de aproximaci ón poligonal se han usado directamente para la extracci ón de los vectores de caracter ísticas empleados en la fase de aprendizaje. Las contribuciones realizadas por tanto en esta tesis se han centrado en diversos aspectos de las aproximaciones poligonales. En la primera contribución se han mejorado varios algoritmos de aproximaciones poligonales, mediante el uso de una fase de preprocesado que acelera estos algoritmos permitiendo incluso mejorar la calidad de las soluciones en un menor tiempo. En la segunda contribución se ha propuesto un nuevo algoritmo de aproximaciones poligonales que obtiene soluciones optimas en un menor espacio de tiempo que el resto de métodos que aparecen en la literatura. En la tercera contribución se ha propuesto un algoritmo de aproximaciones que es capaz de obtener la solución óptima en pocas iteraciones en la mayor parte de los casos. Por último, se ha propuesto una versi ón mejorada del algoritmo óptimo para obtener aproximaciones poligonales que soluciona otro problema de optimización alternativo.This thesis focus on the analysis of the shape of objects. In computer vision there are several sources from which we can extract information. One of the most important source of information is the shape or contour of objects. This visual characteristic can be used to extract information, analyze the scene, etc. However, the contour of the objects contains redundant information. This redundant data does not add new information and therefore, must be deleted in order to minimize the processing burden and reducing the amount of data to represent that shape. This reduction of data should be done without losing important information to represent the original contour. A reduced version of a contour can be obtained by deleting some points of the contour and linking the remaining points by using line segments. This reduced version of a contour is known as polygonal approximation in the literature. Therefore, these polygonal approximation represent a compressed version of the original information. The main use of polygonal approximations is to reduce the amount of information needed to represent the contour of an object. However, in recent years polygonal approximations have been used to recognize objects. For this purpose, the feature vectors have been extracted from the polygonal approximations. The contributions proposed in this thesis have focused on several aspects of polygonal approximations. The rst contribution has improved several algorithms to obtain polygonal approximations, by adding a new stage of preprocessing which boost the whole method. The quality of the solutions obtained has also been improved and the computation time reduced. The second contribution proposes a novel algorithm which obtains optimal polygonal approximations in a shorter time than the optimal methods found in the literature. The third contribution proposes a new method which may obtain the optimal solution after few iterations in most cases. Finally, an improved version of the optimal polygonal approximation algorithm has been proposed to solve an alternative optimization problem

Geometric-based Optimization Algorithms for Cable Routing and Branching in Cluttered Environments

The need for designing lighter and more compact systems often leaves limited space for planning routes for the connectors that enable interactions among the system’s components. Finding optimal routes for these connectors in a densely populated environment left behind at the detail design stage has been a challenging problem for decades. A variety of deterministic as well as heuristic methods has been developed to address different instances of this problem. While the focus of the deterministic methods is primarily on the optimality of the final solution, the heuristics offer acceptable solutions, especially for such problems, in a reasonable amount of time without guaranteeing to find optimal solutions. This study is an attempt to furthering the efforts in deterministic optimization methods to tackle the routing problem in two and three dimensions by focusing on the optimality of final solutions. The objective of this research is twofold. First, a mathematical framework is proposed for the optimization of the layout of wiring connectors in planar cluttered environments. The problem looks at finding the optimal tree network that spans multiple components to be connected with the aim of minimizing the overall length of the connectors while maximizing their common length (for maintainability and traceability of connectors). The optimization problem is formulated as a bi-objective problem and two solution methods are proposed: (1) to solve for the optimal locations of a known number of breakouts (where the connectors branch out) using mixed-binary optimization and visibility notion and (2) to find the minimum length tree that spans multiple components of the system and generates the optimal layout using the previously-developed convex hull based routing. The computational performance of these methods in solving a variety of problems is further evaluated. Second, the problem of finding the shortest route connecting two given nodes in a 3D cluttered environment is considered and addressed through deterministically generating a graphical representation of the collision-free space and searching for the shortest path on the found graph. The method is tested on sample workspaces with scattered convex polyhedra and its computational performance is evaluated. The work demonstrates the NP-hardness aspect of the problem which becomes quickly intractable as added components or increase in facets are considered

A discrete geometry approach for dominant point detection

International audienceWe propose two fast methods for dominant point detection and polygonal representation of noisy and possibly disconnected curves based on a study of the decomposition of the curve into the sequence of maximal blurred segments \cite{ND07}. Starting from results of discrete geometry \cite{FT99,Deb05}, the notion of maximal blurred segment of width $\nu$ \cite{ND07} has been proposed, well adapted to noisy curves. The first method uses a fixed parameter that is the width of considered maximal blurred segments. The second one is proposed based on a multi-width approach to obtain a non-parametric method that uses no threshold for working with noisy curves. Comparisons with other methods in the literature prove the efficiency of our approach. Thanks to a recent result \cite{FF08} concerning the construction of the sequence of maximal blurred segments, the complexity of the proposed methods is $O(n\log n)$. An application of vectorization is also given in this paper