1,019 research outputs found

    Vector extension of monogenic wavelets for geometric representation of color images

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    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

    A Novel Representation for Two-dimensional Image Structures

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    This paper presents a novel approach towards two-dimensional (2D) image structures modeling. To obtain more degrees of freedom, a 2D image signal is embedded into a certain geometric algebra. 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, a local representation for the intrinsically two-dimensional (i2D) structure is derived as the monogenic curvature signal. From it, independent features of local amplitude, phase and orientation are simultaneously extracted. Besides, a monogenic curvature scale-space can be built by applying a Poisson kernel to the monogenic curvature signal. Compared with the 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

    The development of the quaternion wavelet transform

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    The purpose of this article is to review what has been written on what other authors have called quaternion wavelet transforms (QWTs): there is no consensus about what these should look like and what their properties should be. We briefly explain what real continuous and discrete wavelet transforms and multiresolution analysis are and why complex wavelet transforms were introduced; we then go on to detail published approaches to QWTs and to analyse them. We conclude with our own analysis of what it is that should define a QWT as being truly quaternionic and why all but a few of the “QWTs” we have described do not fit our definition

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

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    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

    AM-FM methods for image and video processing

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    This dissertation is focused on the development of robust and efficient Amplitude-Modulation Frequency-Modulation (AM-FM) demodulation methods for image and video processing (there is currently a patent pending that covers the AM-FM methods and applications described in this dissertation). The motivation for this research lies in the wide number of image and video processing applications that can significantly benefit from this research. A number of potential applications are developed in the dissertation. First, a new, robust and efficient formulation for the instantaneous frequency (IF) estimation: a variable spacing, local quadratic phase method (VS-LQP) is presented. VS-LQP produces much more accurate results than current AM-FM methods. At significant noise levels (SNR \u3c 30dB), for single component images, the VS-LQP method produces better IF estimation results than methods using a multi-scale filterbank. At low noise levels (SNR \u3e 50dB), VS-LQP performs better when used in combination with a multi-scale filterbank. In all cases, VS-LQP outperforms the Quasi-Eigen Approximation algorithm by significant amounts (up to 20dB). New least squares reconstructions using AM-FM components from the input signal (image or video) are also presented. Three different reconstruction approaches are developed: (i) using AM-FM harmonics, (ii) using AM-FM components extracted from different scales and (iii) using AM-FM harmonics with the output of a low-pass filter. The image reconstruction methods provide perceptually lossless results with image quality index values bigger than 0.7 on average. The video reconstructions produced image quality index values, frame by frame, up to more than 0.7 using AM-FM components extracted from different scales. An application of the AM-FM method to retinal image analysis is also shown. This approach uses the instantaneous frequency magnitude and the instantaneous amplitude (IA) information to provide image features. The new AM-FM approach produced ROC area of 0.984 in classifying Risk 0 versus Risk 1, 0.95 in classifying Risk 0 versus Risk 2, 0.973 in classifying Risk 0 versus Risk 3 and 0.95 in classifying Risk 0 versus all images with any sign of Diabetic Retinopathy. An extension of the 2D AM-FM demodulation methods to three dimensions is also presented. New AM-FM methods for motion estimation are developed. The new motion estimation method provides three motion estimation equations per channel filter (AM, IF motion equations and a continuity equation). Applications of the method in motion tracking, trajectory estimation and for continuous-scale video searching are demonstrated. For each application, we discuss the advantages of the AM-FM methods over current approaches
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