Edge detection based on Krawtchouk polynomials

Discrete orthogonal polynomials are useful tools in digital image processing to extract visual object contours in different application contexts. This paper proposes an alternative method that extends beyond classic first-order differential operators, by using the properties of Krawtchouk orthogonal polynomials to achieve a first order differential operator. Therefore, smoothing of the image with a 2-D Gaussian filter is not necessary to regularize the ill-posed nature of differentiation. Experimentally, we provide simulation results which show that the proposed method achieves good performance in comparison with commonly used algorithms.The authors dedicate this work to the memory of their friend Pablo González Vera. First and second authors work was partially supported by Ministerio de Economía y Competitividad of Spain, under grant MTM2012-36372-C03-01

An Improved NMS-Based Adaptive Edge Detection Method and Its FPGA Implementation

For improving the processing speed and accuracy of edge detection, an adaptive edge detection method based on improved NMS (nonmaximum suppression) was proposed in this paper. In the method, the gradient image was computed by four directional Sobel operators. Then, the gradient image was processed by using NMS method. By defining a power map function, the elements values of gradient image histogram were mapped into a wider value range. By calculating the maximal between-class variance according to the mapped histogram, the corresponding threshold was obtained as adaptive threshold value in edge detection. Finally, to be convenient for engineering application, the proposed method was realized in FPGA (Field Programmable Gate Array). The experiment results demonstrated that the proposed method was effective in edge detection and suitable for real-time application

Generalized antisymmetric filters for edge detection

A large number of filters has been proposed to compute local gradients in grayscale images, usually having as goal the adequate characterization of edges. A significant portion of such filters are antisymmetric with respect to the origin. In this work we propose to generalize those filters by incorporating an explicit evaluation of the tonal difference. More specifically, we propose to apply restricted dissimilarity functions to appropriately measure the tonal differences. We present the mathematical developments, as well as quantitative experiments that indicate that our proposal offers a clear option to improve the performance of classical edge detection filters

A bilateral schema for interval-valued image differentiation

Differentiation of interval-valued functions is an intricate problem, since it cannot be defined as a direct generalization of differentiation of scalar ones. Literature on interval arithmetic contains proposals and definitions for differentiation, but their semantic is unclear for the cases in which intervals represent the ambiguity due to hesitancy or lack of knowledge. In this work we analyze the needs, tools and goals for interval-valued differentiation, focusing on the case of interval-valued images. This leads to the formulation of a differentiation schema inspired by bilateral filters, which allows for the accommodation of most of the methods for scalar image differentiation, but also takes support from interval-valued arithmetic. This schema can produce area-, segment-and vector-valued gradients, according to the needs of the image processing task it is applied to. Our developments are put to the test in the context of edge detection

A Novel Multiscale Edge Detection Approach Based on Nonsubsampled Contourlet Transform and Edge Tracking

Edge detection is a fundamental task in many computer vision applications. In this paper, we propose a novel multiscale edge detection approach based on the nonsubsampled contourlet transform (NSCT): a fully shift-invariant, multiscale, and multidirection transform. Indeed, unlike traditional wavelets, contourlets have the ability to fully capture directional and other geometrical features for images with edges. Firstly, compute the NSCT of the input image. Secondly, the K-means clustering algorithm is applied to each level of the NSCT for distinguishing noises from edges. Thirdly, we select the edge point candidates of the input image by identifying the NSCT modulus maximum at each scale. Finally, the edge tracking algorithm from coarser to finer is proposed to improve robustness against spurious responses and accuracy in the location of the edges. Experimental results show that the proposed method achieves better edge detection performance compared with the typical methods. Furthermore, the proposed method also works well for noisy images

Evaluation of New Gaussian Wavelet Functions in Signal Edge Detection

Edge detection is a fundamental tool in image processing, machine vision and computer vision, particularly in the areas of feature detection and feature extraction. The same problem of finding discontinuities in 1D signals is known as step detection and the problem of finding signal discontinuities over time is known as change detection. In this paper, a new set of wavelet basis functions for the edge detection issue is introduced in 1D space. First, we develop the Gaussian wavelet and present new bases by the derivation of Gaussian smoothing filter. It is proven that these filters have the necessities of the wavelet basis. After that, for proposed wavelet functions, three Canny criteria (signal-to-noise ratio, localization and low spurious response) and spatial and frequency width, which are surveys for edge detectors are discussed and formulated. For the better understanding the behavior of bases, the formulas are presented in the parametric form and compared with each other in relevant tables. The unit step and line edge are modeled as two particular types of edges and detected in the wavelet domain via introduced wavelet functions. Moreover, the effect of smooth filtering as a denoising preprocessing stage in the edge detection is discussed, and relevant formulas are derived

Fuzzy Image Segmentation based upon Hierarchical Clustering

In this paper we introduce the concept of Fuzzy Image Segmentation, providing an algorithm to build fuzzy boundaries based on the existing relations between the fuzzy boundary set problem and the (crisp) hierarchical image segmentation problem. In particular, since a crisp image segmentation can be characterized in terms of the set of edges that separates the adjacent regions of the segmentation, from these edges we introduce the concept of fuzzy image segmentation. Hence,each fuzzy image segmentation is characterized by means of a fuzzy set over the set of edges, which can be then understood as the fuzzy boundary of the image. Some computational experiences are included in order to show the obtained fuzzy boundaries of some digital images