We give characterizations of stable scaling functions with compact band regions, which have the oversampling property.

We propose a modification of the generalized gradient vector flow field techniques based on multiresolution analysis and phase portrait techniques. The original image is subjected to mutliresolutional analysis to create a sequence of approximation and detail images. The approximations are converted into an edge map and subsequently into a gradient field subjected to the generalized gradient vector flow transformation. The procedure removes noise and extends large gradients. At every iteration the algorithm obtains a new, improved vector field being filtered using the phase portrait analysis. The phase portrait is applied to a window with a variable size to find possible boundary points and the noise. As opposed to previous phase portrait techniques based on binary rules our method generates a continuous adjustable score. The score is a function of the eigenvalues of the corresponding linearized system of ordinary differential equations. The salient feature of the method is continuity: when the score is high it is likely to be the noisy part of the image, but when the score is low it is likely to be the boundary of the object. The score is used by a filter applied to the original image. In the neighbourhood of the points with a high score the gray level is smoothed whereas at the boundary points the gray level is increased. Next, a new gradient field is generated and the result is incorporated into the iterative gradient vector flow iterations. This approach combined with multiresolutional analysis leads to robust segmentations with an impressive improvement of the accuracy. Our numerical experiments with synthetic and real medical ultrasound images show that the proposed technique outperforms the conventional gradient vector flow method even when the filters and the multiresolution are applied in the same fashion. Finally, we show that the proposed algorithm allows the initial contour to be much farther from the actual boundary than possible with the conventional methods.

In this paper, we propose a new approach to rotation invariant texture analysis. This method uses the Radon transform with some considerations in direction estimation of textural images. Furthermore, it utilizes the information obtained from the number of peaks in the variance array of the Radon transform as a realty feature. The textural features are then generated after rotation of texture along principle direction. Also, to eliminating the introduced error due to rotation of texture, a simple technique is presented. Experimental results on a set of images from the Brodatz album show a good performance achieved by the proposed method in comparison with some recent texture analysis methods.

This paper proposes an approach to image segmentation using Iterated Graph Cuts based on local texture features of wavelet coefficients. Using Haar Wavelet based Multiresolution Analysis, the low-frequency range (smoothed image) is used for the n-link and the high-frequency range (local texture features) is used for the t-link along with the color histogram. The proposed method can segment an object region having not only noisy edges and colors similar to the background, but also heavy texture change. Experimental results illustrate the validity of our method.

Although watermarking techniques have been extensively developed for natural videos, little progress is made in the area of graphics animation. Following the former successful MPEG-1 and MPEG-2 coding standards that provide efficient representations of natural videos, the emerging MPEG-4 standard incorporates new coding tools for 2D mesh animation. Graphics animation information is crucial for many applications and may need proper protection. In this paper, we develop a watermarking technique suitable for MPEG-4 2D mesh animation. The proposed method is based on the multiresolution analysis of 2D dynamic mesh. We perform wavelet transform on the temporal sequence of the node points to extract the significant spectral components of mesh movement, which we term the "feature motions. " A binary watermark invisibly resides in the feature motions based on the spread-spectrum principle. Before watermark detection, a spatial-domain least-squares registration technique is used to restore the possibly geometrically distorted mesh data. Each watermark bit is then detected by hard decision with cryptographically secure keys. We have tested the proposed method with a variety of attacks, including affine transformations, temporal smoothing, spectral enhancement and attenuation, additive random noise, and a combination of the above. Experimental results show that the proposed watermarks can withstand the aforementioned attacks.

Recent advances of Web information systems such as e-commerce and e-learning have created very large but hidden demands on conceptual multiresolution analysis for more generalized information analysis, cognition and modeling. To meet the demands in a general way, its modeling is formulated based on modern algebraic topology. To be specific, the modeling formulation is worked out in an incrementally modular abstraction hierarchy with emphasis on the two levels of the hierarchy appropriate for conceptual modeling: the adjunction space level and the cellular structured space level. Examples are shown to demonstrate the usefulness of the presented model as well as an implementation of a flower structure case.

We show that characteristic functions of elements of self-similar tilings can be used as scaling functions of multiresolution analysis of L2(Rn). This multiresolution analysis is a generalization of a self-affine tiling multiresolution analysis using a characteristic function of element of self-affine tiling as a scaling function. We give a method of constructing a wavelet basis which realizes such an MRA.

This paper proves a general sampling theorem, which is an extension of Shannon's classical theorem. Let o be a closed subspace of square integrable functions and call o a signal space. The main aim of this paper is giving a necessary and sufficient condition for unique existence of the sampling basis {Sn}o without band-limited assumption. Using the general sampling theorem we rigorously discuss a frequency domain treatment and a general signal space spanned by translations of a single function. Many known sampling theorems in signal spaces, which have applications for multiresolution analysis in wavelets theory are corollaries of the general sampling theorem.

We propose concepts of Paley-Wiener multiresolution analysis and Paley-Wiener wavelet frame based on general, not limited to dyadic, dilations of functions. Such a wavelet frame is an extension both of the Shannon wavelet basis and the Journe-Meyer wavelet basis. A concept of "natural" Paley-Wiener wavelet frame is also proposed to clarify whether a Paley-Wiener wavelet frame can naturally express functions from the point of view of the multiresolution analysis. A method of constructing a natural Paley-Wiener wavelet frame is given. By using this method, illustrative examples of Paley-Wiener wavelet frames with general scales are provided. Finally, we show that functions can be more efficiently expressed by using a Paley-Wiener wavelet frame with general scales.

Scattering data from radar targets are analyzed in the time-frequency domain by using wavelet transform, and the scattering mechanisms are investigated. The wavelet transform used here is a powerful tool for the analysis of scattering data, because it can provide better insights into scattering mechanisms that are not immediately apparent in either the time or frequency domain. First, two types of wavelet transforms that are applied to the time domain data and to the frequency domain data are defined, and the multi-resolution characteristics of them are discussed. Next, the scattering data from a conducting cylinder, two parallel conducting cylinders, a parallel-plate waveguide cavity, and a rectangular cavity in the underground are analyzed by using these wavelet transforms to reveal the scattering mechanisms. In the resulting time-frequency displays, the scattering mechanisms including specular reflection, creeping wave, resonance, and dispersion are clearly observed and identified.

We propose a theory of general frame multiresolution analysis (GFMRA) which generalizes both the theory of multiresolution analysis based on an affine orthonormal basis and the theory of frame multiresolution analysis based on an affine frame to a general frame. We also discuss the problem of perfectly representing a function by using a wavelet frame which is not limited to being of affine type. We call it a "generalized affine wavelet frame." We then characterize the GFMRA and provide the necessary and sufficient conditions for the existence of a generalized affine wavelet frame.

In this paper, subband image coding with symmetric biorthogonal wavelet filters is studied. In order to implement the symmetric biorthogonal wavelet basis, we use the Laplacian Pyramid Model (LPM) and the trigonometric polynomial solution method. These symmetric biorthogonal wavelet basis are used to form filters in each subband. Also coefficients of the filter are optimized with respect to the coding efficiency. From this optimization, we show that the values of a in the LPM generating kernel have the best coding efficiency in the range of 0.7 to 0.75. We also present an optimal bit allocation method based on considerations of the reconstruction filter characteristics. The step size of each subband uniform quantizer is determined by using this bit allocation method. The coding efficiency of the symmetric biorthogonal wavelet filter is compared with those of other filters: QMF, SSKF and Orthonormal wavelet filter. Simulation results demonstrate that the symmetric biorthogonal wavelet filter is useful as a basic means for image analysis/synthesis filters and can give better coding efficiency than other filters.