Monogenic Signal Associated with Linear Canonical Transform and Application to Edge Detection Problems

Monogenic signal is regarded as a generalization of analytic signal from the one dimensional space to the high dimensional space. It is defined by an original signal with the combination of Riesz transform. Then it provides the signal features representation, such as the local attenuation and the local phase vector. The main objective of this study is to analyze the local phase vector and the local attenuation in the high dimensional spaces. The differential phase congruency is applied for the edge detection problems.Comment: 11 pages, 2 figure

The Poisson Scale-Space: A Unified Approach to Phase-Based Image Processing in Scale-Space

In this paper we address the topics of scale-space and phase-based signal processing in a common framework. The involved linear scale-space is no longer based on the Gaussian kernel but on the Poisson kernel. The resulting scale-space representation is directly related to the monogenic signal, a 2D generalization of the analytic signal. Hence, the local phase arises as a natural concept in this framework which results in several advanced relationships that can be used in image processing

The Color Clifford Hardy Signal: Application to Color Edge Detection and Optical Flow

This paper introduces the idea of the color Clifford Hardy signal, which can be used to process color images. As a complex analytic function's high-dimensional analogue, the color Clifford Hardy signal inherits many desirable qualities of analyticity. A crucial tool for getting the color and structural data is the local feature representation of a color image in the color Clifford Hardy signal. By looking at the extended Cauchy-Riemann equations in the high-dimensional space, it is possible to see the connection between the different parts of the color Clifford Hardy signal. Based on the distinctive and important local amplitude and local phase generated by the color Clifford Hardy signal, we propose five methods to identify the edges of color images with relation to a certain color. To prove the superiority of the offered methodologies, numerous comparative studies employing image quality assessment criteria are used. Specifically by using the multi-scale structure of the color Clifford Hardy signal, the proposed approaches are resistant to a variety of noises. In addition, a color optical flow detection method with anti-noise ability is provided as an example of application.Comment: 13 page

Visualisation of Articular Cartilage Microstructure

This thesis developed image processing techniques enabling the detection and segregation of biological three dimensional images into its component features based upon shape and relative size of the features detected. The work used articular cartilage images and separated fibrous components from the cells and background noise. Measurement of individual components and their recombination into a composite image are possible. Developed software was used to analyse the development of hyaline cartilage in developing sheep embryos

Vector extension of monogenic wavelets for geometric representation of color images

14 pagesInternational audienceMonogenic wavelets offer a geometric representation of grayscale images through an AM/FM model allowing invariance of coefficients to translations and rotations. The underlying concept of local phase includes a fine contour analysis into a coherent unified framework. Starting from a link with structure tensors, we propose a non-trivial extension of the monogenic framework to vector-valued signals to carry out a non marginal color monogenic wavelet transform. We also give a practical study of this new wavelet transform in the contexts of sparse representations and invariant analysis, which helps to understand the physical interpretation of coefficients and validates the interest of our theoretical construction

Signal Modeling for Two-Dimensional Image Structures and Scale-Space Based Image Analysis

Model based image representation plays an important role in many computer vision tasks. Consequently, it is of high significance to model image structures with more powerful representation capabilities. In the literature, there exist bulk of researches for intensity based modeling. However, most of them suffer from the illumination variation. On the other hand, phase information, which carries most essential structural information of the original signal, has the advantage of being invariant to the brightness change. Therefore, phase based image analysis is advantageous when compared to purely intensity based approaches. This thesis aims to propose novel image representations for 2D image structures, from which useful local features can be extracted, which are useful for phase based image analysis. The first approach presents a 2D rotationally invariant quadrature filter. This model is able to handle superimposed intrinsically two-dimensional (i2D) patterns with flexible angles of intersection. Hence, it can be regarded as an extension of the structure multivector. The second approach is the monogenic curvature tensor. Coupling methods of differential geometry, tensor algebra, monogenic signal and quadrature filter, we can design a general model for 2D structures as the monogenic extension of a curvature tensor. Based on it, local representations for the intrinsically one-dimensional (i1D) and i2D structures are derived as the monogenic signal and the generalized monogenic curvature signal, respectively. From them, independent features of local amplitude, phase and orientation are simultaneously extracted. Besides, a generalized monogenic curvature scale-space can be built by applying a Poisson kernel to the monogenic curvature tensor. Compared with other related work, the remarkable advantage of our approach lies in the rotationally invariant phase evaluation of 2D structures in a multi-scale framework, which delivers access to phase-based processing in many computer vision tasks. To demonstrate the efficiency and power of the theoretic framework, some computer vision applications are presented, which include the phase based image reconstruction, detecting i2D image structures using local phase and monogenic curvature tensor for optical flow estimation