In this paper, we present a numerical method for the equiripple approximation of minimum phase FIR digital filters. Many methods have been proposed for the design of such filters. Many of them first design a linear phase filter whose length is twice as long, and then factorize the filter to obtain the minimum phase. Although these methods theoretically guarantee its optimality, it is difficult to control the ratio of ripples between different bands. In the conventional lowpass filter design, for example, when different weights are given for its passband and stopband, one needs to iteratively design the filter by trial and error to achieve the ratio of the weights exactly. To address this problem, we modifies well-known Parks-McClellan algorithm and make it possible to directly control the ripple ratios. The method iteratively solves a set of linear equations with controlling the ratio of ripples. Using this method, the equiripple solutions are obtained quickly.

Due to the rapid development of computer and information technology, 3D modeling and rendering capabilities are becoming increasingly important in many applications, including industrial design, architecture, CAD/CAM, video games, and medical imaging. Since 3D mesh models often have huge amounts of the data, it is time-consuming to retrieve from a storage device or to download from the network. Most 3D viewing applications need to obtain the entire file of a 3D model in order to display the model, even when the user is interested only in a low-resolution version of the model. Therefore, progressive coding that enables multiresolution transmission of 3D models is desired. In this paper, we propose the progressive coding scheme of 3D meshes with texture, in which we convert irregular meshes to semi-regular using texture coordinates, map them on planes, and apply 2D image coding algorithm to mesh compression. As our method uses the wavelet transform, the encoded bitstream has a progressive nature. We gain high compression rate with the same visual quality as original models.

Since IIR filters have lower computational complexity than FIR filters, some design methods for IIR filter banks have been presented in the recent literatures. Smith et al. have proposed a class of linear phase IIR filter banks. However this method restricts the order of the numerator to be odd and has some drawbacks. In this paper, we present two design methods for linear phase IIR filter banks. One is based on Lagrange-Multiplier method, and optimal IIR filter banks in least squares sense are obtained. In an other approach, IIR filter banks with the maximum number of zeros are derived analytically.

In this paper, we propose a new design algorithm for nearly linear phase IIR digital filters with prescribed log magnitude response. The error function used here is the sum of the weighted log magnitude-squared error and phase -squared error, and so it is possible to control log magnitude and phase response directly. The gradient vector of the proposed error function is easily calculated as the closed form solution because of its nature, in which the real and imaginary part of the logarithm of a complex transfer transfer function corresponds to the log magnitude and phase response, respectively. This algorithm is simple and converges quickly. Finally, we show the validity of the proposed algorithm with some examples.

Files of 3D mesh models are often large and hence time-consuming to retrieve from a storage device or to download through the network. Most 3D viewing applications need to obtain the entire file of a 3D model in order to display the model, even when the user is interested only in a small part, or a low-resolution version, of the model. Therefore, coding that enables multiresolution and ROI (Region Of Interest) transmission of 3D models is desired. In this paper, we propose a coding algorithm of 3D models based on partitioning schemes. The algorithm actually partitions the 3D meshes into some small sub-meshes according to some geometric criteria (such as curvatures), and then codes each small sub-meshes separately to transmit it progressively to users on demand. The key idea of this paper lies in the mesh partitioning procedure prior to its LOD control, which enables good compression ratio of the mesh data as well as some other good capable properties through network transmission such as ROI coding, view-adaptive transmission, error resilient coding, etc.

Due to the explosive growth of the network technologies, 3D models and animations have led to a great interest in various media. Especially 3D mesh models (3D meshes), which approximate surfaces by polygonal meshes are widely used to model 3D objects. In 1D and 2D signals such as speech, audio, images, video, etc., the signal values are located on "grids", for example the signals of images are defined on pixels. Thus, the errors of such signals can be explicitly defined by differences of the values on the "grids". However since in the 3D meshes, vertices are located on arbitrary positions in a 3D space and are triangulated in arbitrary ways, the grids cannot be defined. This makes it difficult to measure error on the 3D meshes. In this paper, we propose a new numerical method to measure the errors between two different 3D meshes.

Most natural images are well modeled as smoothed areas segmented by edges. The smooth areas can be well represented by a wavelet transform with high regularity and with fewer coefficients which requires highpass filters with some vanishing moments. However for the regions around edges, short highpass filters are preferable. In one recently proposed approach, this problem was solved by switching filter banks using longer filters for smoothed areas of the images and shorter filters for areas with edges. This approach was applied to lossy image coding resulting in a reduction of ringing artifacts. As edges were predicted using neighboring pixels, the nonlinear transforms made the decorrelation more flexible. In this paper we propose a time-varying filterbank and apply it to lossless image coding. In this scheme, we estimate the standard deviation of the neighboring pixels of the current pixel by solving the maximum likelihood problem. The filterbank is switched between three filter banks, depending on the estimated standard deviation.

In this paper, we present a new numerical method for the complex approximation of FIR digital filters. Our objective is to design FIR filters with equiripple magnitude and phase errors. The proposed method solves the least squares (LS) problem iteratively. At each iteration, the desired response is updated so as to have an equiripple error. The proposed methods do not require any time-consuming optimization procedure such as the quasi-Newton methods and converge to equiripple solutions quickly. We show some examples to illustrate the advantages of our proposed methods.