Phase-shifting Haar Wavelets For Image-based Rendering Applications

In this thesis, we establish the underlying research background necessary for tackling the problem of phase-shifting in the wavelet transform domain. Solving this problem is the key to reducing the redundancy and huge storage requirement in Image-Based Rendering (IBR) applications, which utilize wavelets. Image-based methods for rendering of dynamic glossy objects do not truly scale to all possible frequencies and high sampling rates without trading storage, glossiness, or computational time, while varying both lighting and viewpoint. This is due to the fact that current approaches are limited to precomputed radiance transfer (PRT), which is prohibitively expensive in terms of memory requirements when both lighting and viewpoint variation are required together with high sampling rates for high frequency lighting of glossy material. At the root of the above problem is the lack of a closed-form run-time solution to the nontrivial problem of rotating wavelets, which we solve in this thesis. We specifically target Haar wavelets, which provide the most efficient solution to solving the tripleproduct integral, which in turn is fundamental to solving the environment lighting problem. The problem is divided into three main steps, each of which provides several key theoretical contributions. First, we derive closed-form expressions for linear phase-shifting in the Haar domain for one-dimensional signals, which can be generalized to N-dimensional signals due to separability. Second, we derive closed-form expressions for linear phase-shifting for two-dimensional signals that are projected using the non-separable Haar transform. For both cases, we show that the coefficients of the shifted data can be computed solely by using the coefficients of the original data. We also derive closed-form expressions for non-integer shifts, which has not been reported before. As an application example of these results, we apply the new formulae to image shifting, rotation and interpolation, and demonstrate the superiority of the proposed solutions to existing methods. In the third step, we establish a solution for non-linear phase-shifting of two-dimensional non-separable Haar-transformed signals, which is directly applicable to the original problem of image-based rendering. Our solution is the first attempt to provide an analytic solution to the difficult problem of rotating wavelets in the transform domain

Comments on "phase-shifting for nonseparable 2-D haar wavelets"

In their recent paper, Alnasser and Foroosh derive a wavelet-domain (in-band) method for phase-shifting of 2-D "nonseparable" Haar transform coefficients. Their approach is parametrical to the (a priori known) image translation. In this correspondence, we show that the utilized transform is in fact the separable Haar discrete wavelet transform (DWT). As such, wavelet-domain phase shifting can be performed using previously-proposed phase-shifting approaches that utilize the overcomplete DWT (ODWT), if the given image translation is mapped to the phase component and in-band position within the ODWT

An auditory classifier employing a wavelet neural network implemented in a digital design

This thesis addresses the problem of classifying audio as either voice or music. The goal was to solve this problem by means of digital logic circuit, capable of performing the classification in real time. Since digital audio is essentially a discrete non-periodic timeseries, it was necessary to extract features from the audio which are suitable for classification. The discrete wavelet transform combined with a feature extraction method was found to produce such features. The task of classifying these features was found to be best performed by an artificial neural network. Collectively known as a wavelet neural network, the digital logic design implementation of this architecture was effective in correctly identifying the test data sets. The wavelet neural network was first implemented as a software model, to develop the network architecture and parameters, and to determine ideal results. The unconstrained software simulation was capable of correctly classifying test data sets with greater than 90% accuracy. This model was not feasible as a digital logic design however, as the size of the implementation would have been prohibitive. The size of the resulting hardware model was constrained by reducing the widths of the data paths and storage registers. The hardware implementation of the wavelet processor consisted of a novel pipelined design with a novel data-flow control structure. The neural network training was performed entirely in software by way of a novel training algorithm, and the resulting weights were made to be available to be uploaded to the hardware model. The digital design of the wavelet neural network was modeled in VHDL and was synthesized with Synplicity Synplify, using Actel ProASICPlus APA600 synthesized library cells with a target clock frequency of 11.025 KHz, to match the sampling rate of the digital audio. The results of the synthesis indicated that the design could operate at 15.6 MHz, and required 96,265 logic cells. The resulting constrained wavelet neural network processor was capable of correctly classifying test data sets with greater than 70% accuracy. Additional modeling showed that with a reasonable increase in hardware size, greater than 86% accuracy is attainable. This thesis focused on classifying audio as either voice or music, and future research could readily extend this work to the problem of speaker recognition and multimedia indexing

Pruned Continuous Haar Transform of 2D Polygonal Patterns with Application to VLSI Layouts

We introduce an algorithm for the efficient computation of the continuous Haar transform of 2D patterns that can be described by polygons. These patterns are ubiquitous in VLSI processes where they are used to describe design and mask layouts. There, speed is of paramount importance due to the magnitude of the problems to be solved and hence very fast algorithms are needed. We show that by techniques borrowed from computational geometry we are not only able to compute the continuous Haar transform directly, but also to do it quickly. This is achieved by massively pruning the transform tree and thus dramatically decreasing the computational load when the number of vertices is small, as is the case for VLSI layouts. We call this new algorithm the pruned continuous Haar transform. We implement this algorithm and show that for patterns found in VLSI layouts the proposed algorithm was in the worst case as fast as its discrete counterpart and up to 12 times faster.Comment: 4 pages, 5 figures, 1 algorith