A novel framework for making dominant point detection methods non-parametric

Most dominant point detection methods require heuristically chosen control parameters. One of the commonly used control parameter is maximum deviation. This paper uses a theoretical bound of the maximum deviation of pixels obtained by digitization of a line segment for constructing a general framework to make most dominant point detection methods non-parametric. The derived analytical bound of the maximum deviation can be used as a natural bench mark for the line fitting algorithms and thus dominant point detection methods can be made parameter-independent and non-heuristic. Most methods can easily incorporate the bound. This is demonstrated using three categorically different dominant point detection methods. Such non-parametric approach retains the characteristics of the digital curve while providing good fitting performance and compression ratio for all the three methods using a variety of digital, non-digital, and noisy curves

Multiorder polygonal approximation of digital curves

In this paper, we propose a quick threshold-free algorithm, which computes the angular shape of a 2D object from the points of its contour. For that, we have extended the method defined in [4, 5] to a multiorder analysis. It is based on the arithmetical definition of discrete lines [11] with variable thickness. We provide a framework to analyse a digital curve at different levels of thickness. The extremities of a segment provided at a high resolution are tracked at lower resolution in order to refine their location. The method is thresholdfree and automatically provides a partitioning of a digital curve into its meaningful parts

A New Method for Fast Computation of Moments Based on 8-neighbor Chain CodeApplied to 2-D Objects Recognition

2D moment invariants have been successfully applied in pattern recognition tasks. The main difficulty of using moment invariants is the computational burden. To improve the algorithm of moments computation through an iterative method, an approach for fast computation of moments based on the 8-neighbor chain code is proposed in this paper. Then artificial neural networks are applied for 2D shape recognition with moment invariants. Compared with the method of polygonal approximation, this approach shows higher accuracy in shape representation and faster recognition speed in experiment

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

Polygonal Approximation of Digital Planar Curve Using Novel Significant Measure

This chapter presents an iterative smoothing technique for polygonal approximation of digital image boundary. The technique starts with finest initial segmentation points of a curve. The contribution of initially segmented points toward preserving the original shape of the image boundary is determined by computing the significant measure of every initial segmentation point that is sensitive to sharp turns, which may be missed easily when conventional significant measures are used for detecting dominant points. The proposed method differentiates between the situations when a point on the curve between two points on a curve projects directly upon the line segment or beyond this line segment. It not only identifies these situations but also computes its significant contribution for these situations differently. This situation-specific treatment allows preservation of points with high curvature even as revised set of dominant points are derived. Moreover, the technique may find its application in parallel manipulators in detecting target boundary of an image with varying scale. The experimental results show that the proposed technique competes well with the state-of-the-art techniques