General stereo image matching provides an adequate but hard problem with sufficient complexity, with which the potential of wavelets may be exploited to a full extend. An ideal stereo image matching algorithm is suppo...
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ISBN:
(纸本)0819422134
General stereo image matching provides an adequate but hard problem with sufficient complexity, with which the potential of wavelets may be exploited to a full extend. An ideal stereo image matching algorithm is supposed to be invariant to the scale, translation, rotation, and partial correspondence between two given stereo images. While the multi-resolution of wavelets is good at scale adaptivity, we also require the wavelet transform and pyramids to be translation- and rotation-invariant. This paper is intended to serve for three purposes: (1) To present the general problem of stereo image matching in a sufficient depth and extent, so that pure wavelet mathematicians could think on adequate and efficient solutions, (2) To present a complete algorithm for top-down image matching including surface reconstruction by using wavelet pyramids, (3) To search for a wavelet family optimal for image matching. It is expected that a family of adequately designed wavelets could provide a generic and robust solution to the stereo image matching problem, which could be an important breakthrough in computer vision, photogrammetry, and pattern recognition.
We give an explicit expression for the transform of a signal in an arbitrary representation which has first been filtered in another representation. Using thus formula we connect the work of Cohen for obtaining convol...
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ISBN:
(纸本)0819441929
We give an explicit expression for the transform of a signal in an arbitrary representation which has first been filtered in another representation. Using thus formula we connect the work of Cohen for obtaining convolution and correlation theorems in arbitrary representations with the work of Lindsey and Suter for partitioning the space of integral transforms.
Malvar wavelets or lapped orthogonal transform has been recognized as a useful tool in eliminating block effects in transform coding. Suter and Oxley extended the Malvar wavelets to more general forms, which enable on...
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ISBN:
(纸本)0819416274;9780819416278
Malvar wavelets or lapped orthogonal transform has been recognized as a useful tool in eliminating block effects in transform coding. Suter and Oxley extended the Malvar wavelets to more general forms, which enable one to construct an arbitrary orthonormal basis on different intervals. In this paper, we generalize the idea in Suter and Oxley from 1D to 2D cases and construct nonseparable Malvar wavelets, which is potentially important in multidimensional signal analysis. With nonseparable Malvar wavelets, we then construct nonseparable Lemarie-Meyer wavelets which are band-limited.
We propose formal analytical models for identification of tumors in medical images based on the hypothesis that the tumors have a fractal (self-similar) growth behavior. Therefore, the images of these tumors may be ch...
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ISBN:
(纸本)0819450804
We propose formal analytical models for identification of tumors in medical images based on the hypothesis that the tumors have a fractal (self-similar) growth behavior. Therefore, the images of these tumors may be characterized as Fractional Brownian motion (fBm) processes with a fractal. dimension (D) that is distinctly different than that of the image of the surrounding tissue. In order to extract the desired features that delineate different tissues in a MR image, we study multiresolution signal decomposition and its relation to fBm. The fBm has proven successful to modeling a variety of physical phenomena and non-stationary processes, such as medical images, that share essential properties such as self-similarity, scale invariance and fractal dimension (D). We have developed the theoretical framework that combines wavelet analysis with multiresolution fBm to compute D.
In the scalar-valued setting, it is well-known that the two-scale sequences {q(k)} of Daubechies orthogonal wavelets can be given explicitly by the two-scale sequences {p(k)} of their corresponding orthogonal scaling ...
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ISBN:
(纸本)0819450804
In the scalar-valued setting, it is well-known that the two-scale sequences {q(k)} of Daubechies orthogonal wavelets can be given explicitly by the two-scale sequences {p(k)} of their corresponding orthogonal scaling functions, such as q(k) = (-1)(k)p(1-k). However, due to the non-commutativity of matrix multiplication, there is little such development in the multi-wavelet literature to express the two-scale matrix sequence {Q(k)} of an orthogonal multi-wavelet in terms of the two-scale matrix sequence {P-k} of its corresponding multi-scaling function vector. This paper, in part, is devoted to this study for the setting of orthogonal multi-wavelets of dimension r = 2. We will apply our results to constructing a family of the most recently introduced notion of armlet of order n and a family of the n-balanced orthogonal multi-wavelets.
The construction of smooth, orthogonal compactly supported wavelets is accomplished using fractal interpolation functions and splines. These give rise to multiwavelets. In the latter case piecewise polynomial wavelets...
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ISBN:
(纸本)0819416274;9780819416278
The construction of smooth, orthogonal compactly supported wavelets is accomplished using fractal interpolation functions and splines. These give rise to multiwavelets. In the latter case piecewise polynomial wavelets are exhibited using an intertwining multiresolution analysis.
Spherical filters have recently been introduced in order to avoid the spherical harmonic transform. Spherical filtering can be used in a variety of applications, such as climate modelling, electromagnetic and acoustic...
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ISBN:
(纸本)0819450804
Spherical filters have recently been introduced in order to avoid the spherical harmonic transform. Spherical filtering can be used in a variety of applications, such as climate modelling, electromagnetic and acoustic scattering, and several other areas. However, up to now these methods have been restricted to special grids on the sphere. The main reason for this was to enable the use of FFT techniques. In this paper we extend the spherical filter to arbitrary grids by using the the Nonequispaced Fast Fourier Transform (NFFT).(1) The new algorithm can be applied to a variety of different distributions on the sphere, equidistributions on the sphere being an important example. The algorithm's performance is illustrated with several numerical examples.
Typical neuroimaging studies place great emphasis on not only the estimation but also the standard error estimates of underlying parameters derived from a temporal model. This is principally done to facilitate the use...
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ISBN:
(纸本)0819450804
Typical neuroimaging studies place great emphasis on not only the estimation but also the standard error estimates of underlying parameters derived from a temporal model. This is principally done to facilitate the use of t-statistics. Due to the spatial correlations in the data, it can often be more advantageous to interrogate models in the wavelet domain than in the image domain. However, widespread acceptance of these wavelet techniques has been hampered due to the limited ability to generate both parametric and error estimates in the image domain from these temporal models in the wavelet domain, without which comparison to current standard non-wavelet methods can prove difficult.
The discrete wavelet transform was introduced as a linear operator. It works on signals that are modeled as functions from the integers into the real or complex numbers. Since many signals have finite function values,...
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ISBN:
(纸本)0819441929
The discrete wavelet transform was introduced as a linear operator. It works on signals that are modeled as functions from the integers into the real or complex numbers. Since many signals have finite function values, a linear discrete wavelet transform over a finite ring has been proposed recently. Another recent development is the research of nonlinear wavelet transforms triggered by the introduction of Sweldens' lifting scheme. This paper builds on these developments and defines an essentially nonlinear translation invariant discrete wavelet transform that works on signals that are functions from the integers into any finite set. As only discrete arithmetic is needed, such transforms can be calculated very time efficiently. The basic properties of these generalized discrete wavelet transforms are given along with explicit examples.
We present a coder that yields good quality images at very high compression rates. It performs embedded coding and can carry out both lossy and lossless compression, properties which are suitable for progressive trans...
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ISBN:
(纸本)0819441929
We present a coder that yields good quality images at very high compression rates. It performs embedded coding and can carry out both lossy and lossless compression, properties which are suitable for progressive transmission;It is based on an integer to integer wavelet transform, and uses augmented zerotrees with a hybrid technique that incorporates bitplane coding as well.
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