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

In this paper, we propose a novel coding scheme for the geometry of the triangular mesh model. The geometry coding schemes can be classified into two groups: schemes with perfect reconstruction property that maintains their connectivity, and schemes without it in which the remeshing procedure is performed to change the mesh to semi-regular or regular mesh. The former schemes have good coding performance at higher coding rate, while the latter give excellent coding performance at lower coding rate. We propose a geometry coding scheme that maintains the connectivity and has a perfect reconstruction property. We apply a method that successively structures on 2-D plane the surrounding vertices obtained by expanding vertex sequences neighboring the previous layer. Non-separable component decomposition is applied, in which 2-D structured data are decomposed into four components depending on whether their location was even or odd on the horizontal and vertical axes in the 2-D plane. And a prediction and update are performed for the decomposed components. In the prediction process the predicted value is obtained from the vertices, which were not processed, neighboring the target vertex in the 3-D space. And the zero-tree coding is introduced in order to remove the redundancies between the coefficients at similar positions in different resolution levels. SFQ (Space-Frequency Quantization) is applied, which gives the optimal combination of coefficient pruning for the descendant coefficients of each tree element and a uniform quantization for each coefficient. Experiments applying the proposed method to several polygon meshes of different resolutions show that the proposed method gives a better coding performance at lower bit rate when compared to the conventional schemes.

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.

A new hierarchical isosurface reconstruction scheme from a set of tomographic cross sectional images is presented. From the input data, we construct a hierarchy of volume, called the volume pyramid, based on a 3D dilation filter. After extracting the base mesh from the volume at the coarsest level by the cell-boundary method, we iteratively fit the mesh to the isopoints representing the actual isosurface of the volume. The SWIS (Shrink-wrapped isosurface) algorithm is adopted in this process, and a mesh subdivision scheme is utilized to reconstruct fine detail of the isosurface. According to experiments, our method is proved to produce a hierarchical isosurface which can be utilized by various multiresolution algorithms such as interactive visualization and progressive transmission.

This paper introduces a texture analysis mechanism utilizing multiresolution technique to reduce false motion detection and hence thoroughly improve the interpolation results for high-quality deinterlacing. Conventional motion-adaptive deinterlacing algorithm selects from inter-field and intra-field interpolations according to motion. Accurate determination of motion information is essential for this purpose. Fine textures, having high local pixel variation, tend to cause false detection of motion. Based on hierarchical wavelet analysis, this algorithm provides much better perceptual visual quality and considerably higher PSNR than other motion adaptive deinterlacers as shown. In addition, a recursive 3-field motion detection algorithm is also proposed to achieve better performance than the traditional 2-field motion detection algorithm with little memory overhead.

Displaced subdivision surface representation [13] is a new form of representing a polygonal surface model, where a detailed surface model is defined as a scaler-valued displacement map over a smooth domain surface; it puts forth a number of attractive features for editing, geometry compression, animation, scalability, and adaptive rendering of polygonal models. The construction of the smooth domain surface is a challenging task in the conversion process of a detailed polygonal surface model into this representation. In this paper, we propose a new efficient method for defining the smooth domain surface based on -subdivision scheme. The proposed algorithm not only performs better in terms of the quality of the generated surfaces but is computationally more efficient and occupies less memory as compared to the original algorithm [13] and generates surfaces with more levels of detail due to the specific nature of -subdivision when the prescribed target complexity of the generated mesh must not be exceeded. To corroborate the efficiency and the quality of the new technique, the conversion results for several public domain models have been presented.

We present a new method in multiresolution rendering of a complex object. Our method uses viewer-centered features including the silhouette in generating multiresolution model. Because the silhouette of an object depends on the position of the viewer, the silhouette has difficulties in real-time generation. We propose the AGSphere for real-time management of the silhouette. The AGSphere easily identifies silhouette parts and manages it in multiresolution manner. The primary applicable feature of the AGSphere is the silhouette from the viewer, but we can also use the AGSphere for other directional features like light silhouette. In this paper, we show experimental results for the silhouette either from the viewer or the light. The efficiency of the proposed method is compared with other methods. We also propose new texture map generation method to use with the multiresolution geometry. Generated texture map has valid mapping function for the multiresolution geometry minimizing texture distortions.

In this paper, a novel Wold decomposition algorithm is proposed to address the issue of deterministic component extraction for texture images. This algorithm exploits the wavelet-based singularity detection theory to process both harmonic a nd evanescent features from frequency domain. This exploitation is based on the 2D Lebesgue decomposition theory. When applying multiresolution analysis techniq ue to the power spectrum density (PSD) of a regular homogeneous random field, its indeterministic component will be effectively smoothed, and its deterministic component will remain dominant at coarse scale. By means of propagating these positions to the finest scale, the deterministic component can be properly extracted. From experiment, the proposed algorithm can obtain results that satisfactorily ensure its robustness and efficiency.

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.

This article describes a new method for converting an arbitrary topology mesh into one having subdivision connectivity. First, a base mesh is produced by applying a sequence of edge collapse operations to the original mesh with irregular connectivity. Then, the base mesh is iteratively subdivided. Each subdivided mesh is optimized to reduce its distance from the original mesh and to improve its global smoothness and compactness. A set of corresponding point pairs, which is required to compute the distance from the original mesh to the subdivided mesh, is determined by combining the initial parameterization and the multi-resolution projection. Experimental results show that the proposed method yields good performance in terms of global smoothness, small distortion, and good compactness, compared with conventional methods.

In this paper, a new Hierarchical Sum of Double Difference metric, HSDD, is introduced. It is shown, as opposed to conventional Sum of Absolute Difference (SAD) metric, how this zerotree coding aware metric can jointly constrain the motion vector searching for both temporal and spatial (quad-tree) directions under multiresolution motion estimation framework. The reward from the temporal-spatial co-optimization concept of HSDD is that fewer bits are spent later for describing the isolated zeros. The embedded wavelet video coder using HSDD metric was tested with a set of video sequences and the compression performance seems to be promising.

We consider the classification problem as a problem of approximation of a given training set. This approximation is constructed in a multiresolution framework, and organized in a tree-structure. It allows efficient training and query, both in constant time per training point. The proposed method is efficient for low-dimensional classification and regression estimation problems with large data sets.

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.

Finding corresponding edges is considered being the most difficult part of edge-based stereo matching algorithms. Usually, correspondence for a feature point in the first image is obtained by searching in a predefined region of the second image, based on epipolar line and maximum disparity. Reduction of search region can increase performances of the matching process, in the context of execution time and accuracy. Traditionally, hierarchical multiresolution techniques, as the fastest methods are used to decrease the search space and therefore increase the processing speed. Considering maximum of directional derivative of disparity in real scenes, we formulated some relations between maximum search space in the second images with respect to relative displacement of connected edges (as the feature points), in successive scan lines of the first images. Then we proposed a new matching strategy to reduce the search space for edge-based stereo matching algorithms. Afterward, we developed some fast stereo matching algorithms based on the proposed matching strategy and the hierarchical multiresolution techniques. The proposed algorithms have two stages: feature extraction and feature matching. We applied these new algorithms on some stereo images and compared their results with those of some hierarchical multiresolution ones. The execution times of our proposed methods are decreased between 30% to 55%, in the feature matching stage. Moreover, the execution time of the overall algorithms (including the feature extraction and the feature matching) is decreased between 15% to 40% in real scenes. Meanwhile in some cases, the accuracy is increased too. Theoretical investigation and experimental results show that our algorithms have a very good performance with real complex scenes, therefore these new algorithms are very suitable for fast edge-based stereo applications in real scenes like robotic applications.

We present an efficient scheme for progressive fractal coding in a wavelet multiresolution pyramid. In our proposed scheme, range blocks are selectively coded, based on energy localization in wavelet bands. In order to form domain pools with blocks yielding less distortion, domain blocks are also selectively searched in the wavelet bands of either the same or a different orientation from that of each range block at the next lower resolution. It is shown that the performance of the non-hybrid fractal coder presented is much better than that of predictive pyramid coding (PPC).

This paper presents a novel image coding scheme based on separate coding of region and residue sources. In a subband image coding scheme, quantization errors in each subimage spread over the reconstructed image and result in a blurring or a boundary artifact. To obtain high compression ratio without considerable degradation, an input image, in our scheme, is separated into region and residue sources which are coded using different coding schemes. The region source is coded by adaptive arithmetic coder. The residue source is coded using multiresolution subimages generated by applying a subband filter. Each block in the subimages is predicted by an affine transformation of blocks in lower resolution subimages. Experimental results show that a high coding efficiency is achieved using the proposed scheme, especially in terms of the subjective visual quality and PSNR at low bit-rate compression.

In this paper, a Wiener filtering method in wavelet domain is proposed for restoring an image corrupted by additive white noise. The proposed method utilizes the multiscale characteristics of wavelet transform and the local statistics of each subband. The size of a filter window for estimating the local statistics in each subband varies with each scale. The local statistics for every pixel in each wavelet subband are estimated by using only the pixels which have a similar statistical property. Experimental results show that the proposed method has better performance over the Lee filter with a window of fixed size.

This paper describes a highly performance scalable video coder. Wavelet transform is employed to decompose the video frame into different resolutions. Novel features of this coder are 1) a highly efficient multi-resolution motion estimation that requires minimum compuation and overhead motion information is embedded in this scheme; 2) the wavelet coefficients are organized in an extended zero tree (EZT) which is much more efficient than the simple zerotree. We show with experimental results that this video coder achieves good performances both in processing time and compression ratio when applied to typical test video sequences.