A. Carmona-Poyato

Polygonal approximation of digital planar curves through break point suppression

This paper presents a new algorithm that detects a set of dominant points on the boundary of an eight-connected shape to obtain a polygonal approximation of the shape itself. The set of dominant points is obtained from the original break points of the initial boundary, where the integral square is zero. For this goal, most of the original break points are deleted by suppressing those whose perpendicular distance to an approximating straight line is lower than a variable threshold value. The proposed algorithm iteratively deletes redundant break points until the required approximation, which relies on a decrease in the length of the contour and the highest error, is achieved. A comparative experiment with another commonly used algorithm showed that the proposed method produced efficient and effective polygonal approximations for digital planar curves with features of several sizes.

On candidates selection for hysteresis thresholds in edge detection

Manual determination of hysteresis thresholds is time-consuming. Several methods approach the problem of unsupervised determination of edge detector parameters, but they require human intervention to establish the initial range of values in which to detect the best parameter value and the result depends on the range of values initially used. In this paper, a method is proposed to determine candidates to hysteresis thresholds in an unsupervised manner. The method provides a criterion to reduce in a significant way the number of initial values to be considered as threshold candidates. The proposed method can be applied to any feature image provided by an edge detector upon which hysteresis must be implemented.

Characterization of empirical discrepancy evaluation measures

The quality curve concept is proposed to characterize the performance of an empirical discrepancy evaluation measure when it is used to compare color edge detection algorithms. This quality curve concept is independent of any automatic thresholding algorithm. A simple visual analysis of the quality curve allows possible drawbacks of the evaluation measure to be detected. Five classical evaluation measures and ten color edge detection algorithms have been used to confirm the usefulness of the quality curve analysis. Most evaluation measures show drawbacks when they are applied to several color edge detectors. In this case, these measures should not be used to compare that set of color edge detectors. Nevertheless, a less-cited evaluation measure gives the best performance when it is applied to color edge detectors.

Dominant point detection: A new proposal

A new method for dominant point detection is presented. This method can be classified as search corner detection using some significant measurement other than curvature category, and needs no input parameters. A new and normalized measurement is described to compute the estimated curvature and to detect dominant points, and a new algorithm is proposed to eliminate collinear points using an optimization procedure. The experimental results show that this method is efficient, effective, reduces the number of dominant points as compared to other proposed methods, and the obtained contours using this objective function are properly adjusted to the original contour.

Determining Hysteresis Thresholds for Edge Detection by Combining the Advantages and Disadvantages of Thresholding Methods

Hysteresis is an important technique for edge detection, but the unsupervised determination of its parameters is not an easy problem. In this paper, we propose a method for unsupervised determination of hysteresis thresholds using the advantages and disadvantages of two thresholding methods. The basic idea of our method is to look for the best hysteresis thresholds in a set of candidates. First, the method finds a subset and a overset of the unknown edge points set. Then, it determines the best edge map with the measure ¿2. Compared with a general method to determine the parameters of an edge detector, our method performs well and is less computationally complex. The basic idea of our method can be generalized to other pattern recognition problems.

Evaluation of global thresholding techniques in non-contextual edge detection

The performance of global thresholding techniques in edge detection is a problem that has yet to be studied in depth. Basically, an edge detection process consists of applying an edge intensity detector sequence and a thresholding technique to a given image. In this paper, we demonstrate that applying this sequence to an image and comparing it with a reference image does not constitute a valid process for the evaluation of global thresholding techniques in edge detection. Instead we propose a method that allows the performance of a global thresholding technique to be jointly or independently evaluated using a detector. Our methodology is applied to assess the performance of seven global thresholding techniques, which have been widely cited in the literature and evaluated in other contexts, using five color image edge intensity detectors. We show how the results may differ depending on the criterion selected. A new criterion is proposed that brings together different aspects, permitting a more valid evaluation of the performance of thresholding techniques both alone or in conjunction with a determined detector.

A new measurement for assessing polygonal approximation of curves

This paper presents a novel method for assessing the accuracy of unsupervised polygonal approximation algorithms. This measurement relies on a polygonal approximation called the reference approximation. The reference approximation is obtained using the method of Perez and Vidal [11] by an iterative method that optimizes an objective function. Then, the proposed measurement is calculated by comparing the reference approximation with the approximation to be evaluated, taking into account the similarity between the polygonal approximation and the original contour, and penalizing polygonal approximations with an excessive number of points. A comparative experiment by using polygonal approximations obtained with commonly used algorithms showed that the proposed measurement is more efficient than other proposed measurements at comparing polygonal approximations with different number of points.

Solving the process of hysteresis without determining the optimal thresholds

Hysteresis is an important edge detection technique, but the unsupervised determination of hysteresis thresholds is a difficult problem. Thus, hysteresis has limited practical applicability. Unimodal thresholding techniques are another edge detection method. They are useful, because the histogram of a feature image (usually the feature image is an approximation of the gradient image) is unimodal, and there are many unsupervised methods to solve this problem. But such techniques do not use spatial information to detect edge points, so their performance is worse than that of the hysteresis. In this paper, we show how to formulate the hysteresis process as a unimodal thresholding problem without determining the optimal hysteresis thresholds. Using similar steps of the Canny edge detector to obtain an approximation of the gradient image we compare the performance of our method against that of a method that determines the best parameters of an edge detector and show that our method performs relatively well. Additionally, our method can adjust its sensitivity by using different unimodal thresholding techniques.

A novel histogram transformation to improve the performance of thresholding methods in edge detection

The gradient image is used to detect edge points, and the gradient histogram is a typical case of a unimodal histogram. It is well-documented that bi-modal thresholding methods (such as the Otsu method) detect edges poorly. Therefore, specific unimodal thresholding methods are used to detect edge points. However, unimodal thresholding methods (such as the Rosin method) sometimes obtain very noisy results. In this paper, we propose a histogram transformation to improve the performance of some thresholding methods. Using the Berkeley Segmentation Dataset, we present quantitative performance results in an edge detection task to show that our transformation improves the performance of the Otsu and Rosin methods. Our histogram transformation can be used by any histogram thresholding method, but the performance of the method, using the transformed histogram, will depend of the criterion used by this method.

Keypoint descriptor fusion with Dempster-Shafer theory

Keypoint matching is the task of accurately finding the location of a scene point in two images. Many keypoint descriptors have been proposed in the literature aiming at providing robustness against scale, translation and rotation transformations, each having advantages and disadvantages. This paper proposes a novel approach to fuse the information from multiple keypoint descriptors using Dempster-Shafer theory of evidence 1], which has proven particularly efficient in combining sources of information providing incomplete, imprecise, biased, and conflictive knowledge. The matching results of each descriptor are transformed into an evidence distribution on which a confidence factor is computed making use of its entropy. Then, the evidence distributions are fused using Dempster-Shafer Theory (DST), considering its confidence. As a result of the fusion, a new evidence distribution that improves the result of the best descriptor is obtained. Our method has been tested with SIFT, SURF, ORB, BRISK and FREAK descriptors using all possible their combinations. Results on the Oxford keypoint dataset 2] show that the proposed approach obtains an improvement of up to 10 % compared to the best one (FREAK). Novel approach fusing information from multiple keypoint descriptors using the Dempster-Shafer Theory of evidence.Descriptors matches are transformed in evidence distributions assigning a confidence factor using Shannons entropy.Results on the Oxford keypoint dataset show improvements of up to 10% compared to the best keypoint descriptor.