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.

In this paper, we present a numerical method for the equiripple approximation of IIR digital filters. The conventional rational Remez algorithm quickly finds the squared magnitude response of the optimal IIR digital filters, and then by factorizing it the equiripple filter is obtained. Unlike the original Remez algorithm for FIR filters, it is difficult for the rational Remez algorithm to explicitly 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 manually changing the weights in order to achieve the ratio of the weights exactly. To address this problem, we modify the conventional algorithm and make it possible to directly control the ripple ratio. The method iteratively solves eigenvalue problems with controlling the ripple ratio. Using this method, the equiripple solutions with desired weights are obtained automatically.

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.

In this paper we propose a new tone mapping method for HDR video. Two types of gamma tone mapping are blended to preserve local contrast in the entire range of luminance. Our method achieves high quality tone mapping especially for the HDR video that has a nonlinear response to scene radiance. Additionally, we apply it to an object-aware tone mapping method for camera surveillance. This method achieves high visibility of target objects in the tone mapped HDR video. We examine the validity of our methods through simulation and comparison with conventional work.

In this paper, we propose a coding method for camera raw images with high dynamic ranges. Our encoder has two layers. In the first layer, 24 bit low dynamic range image is encoded by a conventional codec, and then the residual image that represents the difference between the raw image and its approximation is encoded in the second layer. The approximation is derived by a polynomial fitting. The main advantage of this approach is that applying the polynomial model reduces the correlation between the raw and 24 bit images, which increases coding efficiency. Experiments shows compression efficiency is significantly improved by taking an inverse tone mapping into account.

High Dynamic Range (HDR) images have been widely applied in daily applications. However, HDR image is a special format, which needs to be pre-processed known as tone mapping operators for display. Since the visual quality of HDR images is very sensitive to luminance value variations, conventional watermarking methods for low dynamic range (LDR) images are not suitable and may even cause catastrophic visible distortion. Currently, few methods for HDR image watermarking are proposed. In this paper, two watermarking schemes targeting HDR images are proposed, which are based on µ-Law and bilateral filtering, respectively. Both of the subjective and objective qualities of watermarked images are greatly improved by the two methods. What's more, these proposed methods also show higher robustness against tone mapping operations.

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.

In this paper, we propose a coding algorithm for High Dynamic Range Images (HDRI). Our encoder applies a tone mapping model based on scaled µ-Law encoding, followed by a conventional Low Dynamic Range Image (LDRI) encoder. The tone mapping model is designed to minimize the difference between the tone-mapped HDRI and its LDR version. By virtue of the nature of the µ-Law model, not only the quality of the HDRI but also the one of the LDRI is improved, compared with a state of the art in conventional HDRI coding methods. Furthermore the error limit caused by our encoding is theoretically analyzed.

This paper proposes a method for evaluating visual differences caused by decimation. In many applications it is important to evaluate visual differences of two different images. There exist many image assessment methods that utilize the model of the human visual system (HVS), such as the visual difference predictor (VDP) and the Sarnoff visual discrimination model. In this paper, we extend and elaborate on the conventional image assessment method for the purpose of evaluating the visual difference caused by the image decimation. Our method matches actual human evaluation more and requires less computational complexity than the conventional method.

Using a flash/no-flash image pair, we propose a novel white-balancing technique that can effectively correct the color balance of a complex scene under multiple light sources. In the proposed method, by using multiple images of the same scene taken under different lighting conditions, we estimate the reflectance component of the scene and the multiple shading components of each image. The reflectance component is a specific object color which does not depend on scene illumination and the shading component is a shading effect caused by the illumination lights. Then, we achieve white balancing by appropriately correcting the estimated shading components. The proposed method achieves better performance than conventional methods, especially under colored illumination and mixed lighting conditions.

The Retinex theory assumes that large intensity changes correspond to reflectance edges, while smoothly-varying regions are due to shading. Some algorithms based on the theory adopt simple thresholding schemes and achieve adequate results for reflectance estimation. In this paper, we present a practical reflectance estimation technique for hyperspectral images. Our method is realized simply by thresholding singular values of a matrix calculated from scaled pixel values. In the method, we estimate the reflectance image by measuring spectral similarity between two adjacent pixels. We demonstrate that our thresholding scheme effectively estimates the reflectance and outperforms the Retinex-based thresholding. In particular, our methods can precisely distinguish edges caused by reflectance change and shadows.

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.

We propose an image restoration technique that uses multiple image integration. The detail of the dark area when acquiring a dark scene is often deteriorated by sensor noise. Simple image integration inherently has the capability of reducing random noises, but it is especially insufficient in scenes that have a dark area. We introduce a novel image integration technique that optimizes the weights for the integration. We find the optimal weight map by solving a convex optimization problem for the weight optimization. Additionally, we apply the proposed weight optimization scheme to a single-image super-resolution problem, where we slightly modify the weight optimization problem to estimate the high-resolution image from a single low-resolution one. We use some of our experimental results to show that the weight optimization significantly improves the denoising and super-resolution performances.

Classical designs of maximally flat finite impulse response digital filters need to perform inverse discrete Fourier transformation of the frequency responses, in order to calculate the impulse response coefficients. Several attempts have been made to simplify the designs by obtaining explicit formulas for the impulse response coefficients. Such formulas have been derived for digital differentiators having maximal linearity at zero frequency, using different techniques including interpolating polynomials and the Taylor series etc. We show that these formulas can be obtained directly by application of maximal linearity constraints on the frequency response. The design problem is formulated as a system of linear equations, which can be solved to achieve maximal linearity at an arbitrary frequency. Certain special characteristics of the determinant of the coefficients matrix of these equations are explored for designs centered at zero frequency, and are used in derivation of explicit formulas for the impulse response coefficients of digital differentiators of both odd and even lengths.

We propose an algorithm for the constrained design of FIR filters with sparse coefficients. In general filter design approaches, as the length of the filter increases, the number of multipliers used to construct the filter increases. This is a serious problem, especially in two-dimensional FIR filter designs. The FIR filter coefficients designed by the least-squares method with peak error constraint are optimal in the sense of least-squares within a given order, but not necessarily optimal in terms of constructing a filter that meets the design specification under the constraints on the number of coefficients. That is, a higher-order filter with several zero coefficients can construct a filter that meets the specification with a smaller number of multipliers. We propose a two-step approach to design constrained sparse FIR filters. Our method minimizes the number of non-zero coefficients while the frequency response of the filter that meets the design specification. It achieves better performance in terms of peak error than conventional constrained least-squares designs with the same or higher number of multipliers in both one-dimensional and two-dimensional filter designs.

Recently, we have discovered wave propagation phenomena which are continuously existing waves of changing phase states between two adjacent oscillators from in-phase to anti-phase or from anti-phase to in-phase in van der Pol oscillators coupled by inductors as a ladder. We named the phenomena as "phase-inversion waves." In this study, phase-inversion waves which exist in the state of in-and-anti-phase synchronization have been found. We observe the phenomena by circuit experiments and computer calculations, and investigate them.

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.