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
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.
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
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.
This paper develops a steerable multiscale analysis theory. A number of models based on the wavelet theory are proposed for multiscale TV scene analysis and imageprocessing, including image representation, image edge...
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ISBN:
(纸本)0819415464
This paper develops a steerable multiscale analysis theory. A number of models based on the wavelet theory are proposed for multiscale TV scene analysis and imageprocessing, including image representation, image edge detection, and noise analysis and removal. A multiscale interpretation method is discussed that makes full use of multiresolution images and edge feature. In order to employ multiple information and all relative information reasonably and effectively, information fusion has been investigated. The idea of geometric reasoning has been also proposed for interpreting objects in TV scenes. Finally, some experiments have illustrated that the proposals described above are feasible.
An important step in imageprocessing tasks involves the identification of certain desired attributes in an image. Traditionally, this is done by transforming the image into a domain where the desired attributes or fe...
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ISBN:
(纸本)0444818707
An important step in imageprocessing tasks involves the identification of certain desired attributes in an image. Traditionally, this is done by transforming the image into a domain where the desired attributes or features are easily identifiable. In this paper, we discuss the parallel implementation of one such image transform-the 2-D Gabor based Wavelet Transform. Individual components of this transform are sensitive to particular ranges of frequencies and the orientation of features in an image. The transform is formed by computing convolutions of the image with a family of wavelets. Each member of the wavelet family is a 2-D Gabor Function, We describe how this 2-D Wavelet Transform can be computed efficiently on a fine-grained, Single Instruction, Multiple Data Stream (SIMD) computer, the Connection Machine (CM-2). The transform of a 128 x 128 pixel image using 40 wavelets (sensitive to different frequency levels and orientations of features) takes 2.43 seconds on the CM-2 as compared to 240 seconds on a Sun 4/200 and 55 seconds on a SPARCsystem 10. The gains achieved by these speed-ups are even more dramatic when hundreds of images have to be transformed (as in the Face Recognition problem [1]).
In this paper, we develop a theory to design weighted order statistic filters with structural approach and discuss their applications in image filtering. By introducing a set of parameters, called Mis, the statistical...
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ISBN:
(纸本)0819414778
In this paper, we develop a theory to design weighted order statistic filters with structural approach and discuss their applications in image filtering. By introducing a set of parameters, called Mis, the statistical properties of weighted order statistic filters are analyzed. A theorem is presented to show that any symmetric weighted order statistic filter will drive the input to a root or oscillate in a cycle of period 2. This result was proven to hold only for some weighted order statistic filters. A condition is provided to guarantee the convergence of weighted order statistic filters.
Clusters of fine, granular microcalcifications in mammograms may be an early sign of disease. Individual grains are difficult to detect and segment due to size and shape variability and because the background mammogra...
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ISBN:
(纸本)0819416274;9780819416278
Clusters of fine, granular microcalcifications in mammograms may be an early sign of disease. Individual grains are difficult to detect and segment due to size and shape variability and because the background mammogram texture is typically inhomogeneous. We present a two-stage method based on wavelet transforms for detecting and segmenting calcifications. The first stage consists of a full resolution wavelet transform, which is simply the conventional filter bank implementation without downsampling, so that all sub-bands remain at full size. Four octaves are computed with two inter-octave voices for finer scale resolution. By appropriate selection of the wavelet basis the detection of microcalcifications in the relevant size range can be nearly optimized in the details sub-bands. In fact, the separable 2D filters which transform the input image into the HH details sub-bands are closely related to pre-whitening matched filters for detecting Gaussian objects (idealized microcalcifications) in Markov noise (background noise). The second stage is designed to overcome the limitations of the simplistic Gaussian assumption and provides a useful segmentation of calcifications boundaries. Detected pixel sites in the LH, HL, and HH sub-bands are heavily weighted before computing the inverse wavelet transform. The LL component is omitted since gross spatial variations are of little interest. Individual microcalcifications are often greatly enhanced in the output image, to the point where straightforward thresholding can be applied to segment them. FROC curves are computed from tests using a well-known database of digitized mammograms. A true positive fraction of 85% is achieved at 0.5 false positives per image.
Recently, we demonstrated the use of orthonormal wavelets as desirable waveforms for baseband waveform coding application in digital communications. In this paper, we examine the use of generalized biorthogonal wavele...
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ISBN:
(纸本)0819416274
Recently, we demonstrated the use of orthonormal wavelets as desirable waveforms for baseband waveform coding application in digital communications. In this paper, we examine the use of generalized biorthogonal wavelets for waveform coding. Though the transmit and receive waveforms have different supports in the biorthogonal case, it is shown that binary symbols can be extracted easily at the receiver. Spectral characteristics of several types of biorthogonal wavelets are examined and resulting codecs' bandwidth efficiencies (in bits/sec/Hz) are provided. An M-band wavelet codec is also proposed. Preliminary results indicate that the M-band codec (used in this study) will be out-performed by a two-band codec of the same order.
In this paper, we describe a new approach to radar target discrimination. Specifically, we will apply it to the problem of exo-atmospheric object discrimination from UHF radar returns. The method uses wavelet transfor...
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ISBN:
(纸本)0819415391
In this paper, we describe a new approach to radar target discrimination. Specifically, we will apply it to the problem of exo-atmospheric object discrimination from UHF radar returns. The method uses wavelet transforms, pattern recognition techniques such as feature spaces, vectors and neural net classifiers. Feature vectors for each object are constructed from the wavelet transforms of the input data samples. The feature vectors are based on energies at each scale of the wavelet transforms and therefore effectively circumvent the problem of noncoherence due to target and ionospheric effects. This is a very important consideration when coherent signalprocessing is not feasible. The feature vectors are input to an unsupervised learning neural network for classification of the objects. In unsupervised learning, the network output is not forced towards a desired response for each input pattern but allowed to learn proximity to past input patterns. Limited results from simulated radar cross-section (RCS) data indicate that most objects can be correctly classified. The results also show that the overall scheme is quite immune to fair amounts of gaussian as well as uniformly distributed noise. Further efforts are under way to test the methodology against real object data as well as more extensive simulations.
Low bit rate image coding at 10 kbit/s and less is a difficult problem and does not appear possible with the current generation of block transform based methods. Current research efforts center around the use of trans...
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ISBN:
(纸本)0819414824
Low bit rate image coding at 10 kbit/s and less is a difficult problem and does not appear possible with the current generation of block transform based methods. Current research efforts center around the use of transforms with less objectionable artifacts such as wavelets or model based methods. We examine a method that is transform based but captures specific features of the image to be represented. The transform uses principal component analysis to generate a basis set specific to the particular class of images to be coded. We present results from a transform designed for use in a `talking head' sequence. Significant improvement in reconstructed quality is shown when perceptual weighting is used in generating the basis set. The appendix includes details of computationally efficient methods for deriving the basis set as well as a description of the weighting method.
In this paper we are concerned with the design of 2D biorthogonal, 2-channel filter banks where the sampling is on the quincunx lattice. Such systems can be used to implement the nonseparable Discrete Wavelet Transfor...
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ISBN:
(纸本)0819416274;9780819416278
In this paper we are concerned with the design of 2D biorthogonal, 2-channel filter banks where the sampling is on the quincunx lattice. Such systems can be used to implement the nonseparable Discrete Wavelet Transform and also to construct the nonseparable scaling and wavelet functions. One important consideration of such systems (brought into attention by wavelet theory) is the regularity or smoothness of the scaling and wavelet functions. The regularity is related to the zero-property - the number of zeros of the filter transfer function at the aliasing frequency ((Ω1, Ω2) = (π,π) for the quincunx lattice). In general the greater the number of zeros, the greater the regularity. It has been shown previously by the authors that the transformation of variables is an effective and flexible way of designing multidimensional filter banks. However the wavelet aspects of the filter banks (i.e., regularity) were not considered. In this paper we shall show how the zero-property can be easily imposed through the transformation of variables technique. A large number of zeros can be imposed with ease. Arbitrarily smooth scaling and wavelet functions can be constructed. Several design examples will be given to illustrate this.
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