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

A multi-objective approach for the segmentation issue

Special Issue: Multi-objective metaheuristics for multi-disciplinary engineering applicationsThis work presents and formalizes an explicit multi-objective evolutionary approach for the segmentation issue according to Piecewise Linear Representation, which consists in the approximation of a given digital curve by a set of linear models minimizing the representation error and the number of such models required. Available techniques are focused on the minimization of the quality of the obtained approximation, being the cost of that approximation considered, in general, only for certain comparison purposes. The multi-objective nature of the problem is analysed and its treatment in available works reviewed, presenting an a posteriori approach based on an evolutionary algorithm. Three representative curves are included in the data set, comparing the proposed technique to nine different techniques. The performance of the presented approach is tested according to single and multiobjective perspectives. The statistical tests carried out show that the experimental results are, in general, significantly better than available approaches from both perspectives.This work was supported in part by Projects CICYT TIN2008-06742-C02-02/TSI, CICYT TEC2008-06732-C02-02/TEC, CAM CONTEXTS (S2009/TIC-1485) and DPS2008-07029-C02-02.Publicad

Shape representation and coding of visual objets in multimedia applications — An overview

Emerging multimedia applications have created the need for new functionalities in digital communications. Whereas existing compression standards only deal with the audio-visual scene at a frame level, it is now necessary to handle individual objects separately, thus allowing scalable transmission as well as interactive scene recomposition by the receiver. The future MPEG-4 standard aims at providing compression tools addressing these functionalities. Unlike existing frame-based standards, the corresponding coding schemes need to encode shape information explicitly. This paper reviews existing solutions to the problem of shape representation and coding. Region and contour coding techniques are presented and their performance is discussed, considering coding efficiency and rate-distortion control capability, as well as flexibility to application requirements such as progressive transmission, low-delay coding, and error robustnes

An adaptative method for the smothing of curves edge detection application

We present a new approach to smooth discrete curves . The smoothing is realized by associating portions of regular curves which are defined on each points interval . The originality of the method consists in finding the portions of curves by minimizing the squared error over a restricted neighbourhood around each point . Adding continuity constraints at the junction points, we obtain a direct formulation of the solution . A unique parameter allows to easily control the smoothing amplitude which can be selected between two extreme cases : interpolation or approximation . It seems like a drawer behaviour trying to join points by a curve . He can choose to join each point by a curve or only take into account the global form of the set of points . The method is particularly adapted to fit contours defined on an image and is used as a final step of image segmentation process . The parameter controlling the smoothing amplitude is computed from the value of local gradient magnitude on each pixel .La méthode de lissage de courbes discrètes présentée est fondée sur la minimisation d'un critère d'erreur quadratique appliqué sur des portions jointives de la courbe à traiter. En imposant des contraintes géométriques au niveau des points de jonctions entre intervalles, on aboutit à une formulation directe de la solution. Un paramètre unique permet de façon simple de contrôler la force du lissage qui évolue ainsi entre 2 cas extrêmes: l'interpolation et l'approximation. La méthode simule le comportement d'un scripteur cherchant à unir des points par une courbe, il peut privilégier le passage du tracé par chaque point ou au contraire respecter la forme globale définie par l'ensemble des points. Cette méthode adaptative de lissage est utilisée comme étape finale d'un processus de segmentation d'images, le paramètre contrôlant la force du lissage étant défini à partir du gradient mesuré localement en chaque point

Multiresolutional Fault-Tolerant Sensor Integration and Object Recognition in Images.

This dissertation applies multiresolution methods to two important problems in signal analysis. The problem of fault-tolerant sensor integration in distributed sensor networks is addressed, and an efficient multiresolutional algorithm for estimating the sensors\u27 effective output is proposed. The problem of object/shape recognition in images is addressed in a multiresolutional setting using pyramidal decomposition of images with respect to an orthonormal wavelet basis. A new approach to efficient template matching to detect objects using computational geometric methods is put forward. An efficient paradigm for object recognition is described