Orthogonal wavelet transforms have recently become a popular representation for multiscale signal and image analysis. One of the major drawbacks of these representations is their lack of translation invariance: the content of wavelet subbands is unstable under translations of the input signal. Wavelet transforms are also unstable with respect to dilations of the input signal, and in two dimensions, rotations of the input signal. We formalize these problems by defining a type of translation invariance that we call "shiftability". In the spatial domain, shiftability corresponds to a lack of aliasing; thus, the conditions under which the property holds are specified by the sampling theorem. Shiftability may also be considered in the context of other domains, particularly orientation and scale. We explore "jointly shiftable" transforms that are simultaneously shiftable in more than one domain. Two examples of jointly shiftable transforms are designed and implemented: a one-dimensional tran...

A new nonlinear noise reduction method is presented that uses the discrete wavelet transform. Similar to Donoho and Johnstone, we employ thresholding in the wavelet transform domain but, following a suggestion by Coifman, we use an undecimated, shift-invariant, nonorthogonal wavelet transform instead of the usual orthogonal one. This new approach can be interpreted as a repeated application of the original Donoho and Johnstone method for different shifts. The main feature of the new algorithm is a significantly improved noise reduction compared to the original wavelet based approach, both the l 2 error and visually, for a large class of signals. This is shown both theoretically as well as by experimental results. 1 Introduction Recently a powerful approach for noise reduction has been proposed by Donoho and Johnstone [3, 4, 5]. It employs thresholding in the wavelet domain and has been shown to be asymptotically near optimal for a wide class of signals corrupted by additive white Gaus...

Abstract—Unlike other biometrics such as fingerprints and face, the distinct aspect of iris comes from randomly distributed features. This leads to its high reliability for personal identification, and at the same time, the difficulty in effectively representing such details in an image. This paper describes an efficient algorithm for iris recognition by characterizing key local variations. The basic idea is that local sharp variation points, denoting the appearing or vanishing of an important image structure, are utilized to represent the characteristics of the iris. The whole procedure of feature extraction includes two steps: 1) a set of one-dimensional intensity signals is constructed to effectively characterize the most important information of the original two-dimensional image; 2) using a particular class of wavelets, a position sequence of local sharp variation points in such signals is recorded as features. We also present a fast matching scheme based on exclusive OR operation to compute the similarity between a pair of position sequences. Experimental results on 2 255 iris images show that the performance of the proposed method is encouraging and comparable to the best iris recognition algorithm found in the current literature. Index Terms—Biometrics, iris recognition, local sharp variations, personal identification, transient signal analysis, wavelet transform. I.

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Future large visual information systems (such as image databases and video servers) require effective and efficient methods for indexing, accessing, and manipulating images based on visual content. This paper focuses on automatic extraction of low-level visual features such as texture, color, and shape. Continuing our prior work in compressed video manipulation, we also propose to explore the possibility of deriving visual features directly from the compressed domain, such as the DCT and wavelet transform domain. By stressing at the low-level features, we hope to achieve generic techniques applicable to general applications. By exploring the compressed-domain content extractability, we hope to reduce the computational complexity. We also propose a quad-tree based data structure to bind various signal features. Integrated feature maps are proposed to improve the overall effectiveness of the feature-based image query system. Current technical progress and system prototypes are also descr...

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A novel approach for noise reduction is presented. Similar to Donoho, we employ thresholding in some wavelet transform domain but use a nondecimated and consequently redundant wavelet transform instead of the usual orthogonal one. Another difference is the shift invariance as opposed to the traditional orthogonal wavelet transform. We show that this new approach can be interpreted as a repeated application of Donoho's original method. The main feature is, however, a dramatically improved noise reduction compared to Donoho's approach, both in terms of the l 2 error and visually, for a large class of signals. This is shown by theoretical and experimental results, including synthetic aperture radar (SAR) images.

In this work, a shifted wavelet packet (SWP) library, containing all the time shifted wavelet packet bases, is defined. A corresponding shift-invariant wavelet packet decomposition (SIWPD) search algorithm for a "best basis" is introduced. The search algorithm is representable by a binary tree, in which a node symbolizes an appropriate subspace of the original signal. We prove that the resultant "best basis" is orthonormal and the associated expansion, characterized by the lowest information cost, is shift-invariant. The shift-invariance stems from an additional degree of freedom, generated at the decomposition stage and incorporated into the search algorithm. The added dimension is a relative shift between a given parent-node and its respective children-nodes. We prove that for any subspace it suffices to consider one of two alternative decompositions, made feasible by the SWP library. These decompositions correspond to a zero shift and a 2 - relative shift where denotes the resolution level.

We propose invariant formulations that can potentially be combined into a single system. In particular# we describe a framework for computing invariant features which are insensitiveto rigid motion# a#ne transform# changes of parameterization and scene illumination# perspective transform# and view point change. This is unlike most current research on image invariants which concentrates on either geometric or illumination invariants exclusively. The formulations are widely applicable to many popular basis representations# such as wavelets #3# 4# 24# 25## short#time Fourier analysis #13#35## and splines #2# 5#37#. Exploiting formulations that examine information about shape and color at di#erent resolution levels# the new approachisneither strictly global nor local. It enables a quasi#localized# hierarchical shape analysis which is rarely found in other known invariant techniques# such as global invariants. Furthermore# it does not require estimating high#order derivatives in computing i...

Experience suggests the existence of a connection between the contrast of a grayscale image and the gradient magnitude of intensity edges in the neighborhood where the contrast is measured. This observation motivates the development of edge-based contrast enhancement techniques. In this paper, we present a simple and effective method for image contrast enhancement based on the multiscale edge representation of images. The contrast of an image can be enhanced simply by stretching or upscaling the multiscale gradient maxima of the image. This method offers flexibility to selectively enhance features of different sizes and ability to control noise magnification. We present some experimental results from enhancing medical images and discuss the advantages of this wavelet approach over other edge-based techniques.