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This paper introduces a new method of converting interlaced video to a progressively scanned video and image. The new method is derived from Bayesian framework with the spatial-temporal smoothness constraint and the MAP is done by minimizing the energy functional. The half-quadratic regularization method is used to solve the corresponding partial differential equations (PDEs). This approach gives the improved results over the conventional de-interlacing methods. Two criteria are proposed in the paper, and they can be used to evaluate the performance of the de-interlacing algorithms.

This paper presents a video-tracking system composed of two cameras. One camera acts for producing an in-focus image of the object and the other one ensures an extended vision field under monitoring. Such a system scheme can achieve an excellent tracking performance, especially under various unfavorable conditions. A projection algorithm is used for the calculation of the displacement of the moving object. As a result, the computational cost is reduced greatly. In order that the tracking action of the system persists even if the object is sheltered or its acceleration is larger than a specified threshold, a dedicated tracking algorithm on the basis of the α-β filtering is designed. Experiments show that the algorithm is efficient and the system works very well.

Deconvolution techniques currently available for application in spectroscopy must presuppose a known system response function. An inexactly presupposed response function can degrade the obtainable resolution of instruments. In this paper we propose a practical method of blind deconvolution that can eliminate such an irrational presupposition. Simulations show that an improved resolution of instruments can be achieved by this new method. An advantage of the method is that it is easily implemented in an on-line way or by using modern digital signal processors.

It is known that discretization of a continuous deconvolution problem can alleviate the ill-posedness of the problem. The currently used circulant matrix model, however, does not play such a role. Moreover, the approximation of deconvolution problems by circulant matrix model is rational only if the size of the kernel function is very small. We propose an aperiodic model of deconvolution. For discrete and finite deconvolution problems the new model is an exact one. In the general case, the new model can lead to a nonsingular system of equations that has a lower condition number than the circulant one, and the related computations in the deconvolution can be done efficiently by means of the DFT technique, as in the ease for circulant matrices. The rationality of the new model holds without regard to the size of the kernel and the image. The use of the aperiodic model is illustrated by gradient-based algorithms. >

An increment iterative blind deconvolution (IIBD) algorithm in the frequency domain is proposed for simultaneous identification of blurs and restoration of images. The algorithm is simple and efficient, and one does not need to impose a statistic presumption on the image. The a priori knowledge can be easily incorporated into the algorithm. Experiments show that the IIBD algorithms may be a practical solution to the identification and restoration problems.

The aperiodic matrix deconvolution model has been shown to have a better condition number than the popularly used circulant matrix model. In this paper, we illustrate that the restoration algorithms in a weighted space using the block circulant matrices can be modified into the aperiodic model based algorithms and we have more possibilities to reduce the computational cost for the modified algorithms. Examples are used to show the modified algorithm. We address that more interesting is the use of the model to develop some new algorithms, for example, for the unknown blur case. >

Texture segmentation is a typical difficult problem in image processing. This paper presents a new textural oscillatory feature based on image decomposition. The oscillatory feature together with other textural features based on the structure tensor and nonlinear diffusion constructs a 5 dimensional textural feature space. The last result can be obtained by segmenting the feature space using level set and non-parametric active contours technology. The validity of the method in this paper is proved by different texture segmentation tests.

We establish a theory of embedability of supports of two-dimensional sequences. We found that the embedability of a support plays an essential role in the reducibility or irreducibility of the support. The theory can offer a new insight and a geometric visuality to the support problems. For example, the irreducibility of a class of supports including Eisenstein’s support can be checked by use of a simple lemma and by inspection. Based on convolution and embedability arguments, a new description of support irreducibility is suggested. As an application, we propose a new method for determining a reliable and tight bound on object support from its autocorrelation support.

We propose a few new algorithms of two-dimensional blind deconvolution. It is known that discretization of a continuous deconvolution problem can alleviate its ill-posedness. This philosophy can be embodied by using the aperiodic convolution model. We illustrate a few gradient algorithms of blind deconvolution using the aperiodic model and show that the main calculations can be accomplished efficiently by means of the discrete Fourier transform (DFT) technique. We present an increment Wiener filter that can further improve the solution of the frequency domain deconvolution. The increment Wiener filter has an iterative form and therefore the object domain constraints can be efficiently incorporated. We propose a multiframe combination scheme of blind deconvolution that can stabilize the solution of the iterative algorithms and suggest two useful techniques: the numerical level adjustment and the updating of the support constraints. We propose that the combination of the Wiener filter, the increment Wiener filter, and the new gradient algorithm is a reasonable choice for practical blind deconvolution applications.

In this paper, some approaches are presented for the approximate factorization of unfactorable multivariable polynomials. An iterative algorithm which can be shown to be convergent is developed on the basis of coefficient matching in the least-squares sense. For the approximate separation of polynomials—a special case of approximate factorization—a noniterative algorithm is proposed by means of the singular value decomposition concept. Examples of the two-variable case are presented to illustrate the utility of the approaches. The techniques described can directly be utilized for the design of 2-D digital filters (see, e.g., Antoniou and Lu, 1987).

A general procedure is presented to realize a two-port impedance matrix by a generalized transformerless LC ladder network including the classical LC ladder structure as a special case. the realization process consists of repeatedly applying a subnetwork removal cycle for which six different cases are to be considered. the feasibility of the various subnetwork removals is characterized by formulating necessary and sufficient conditions on the impedance matrix. the application of the procedure is illustrated by a numerical example.

An approach to the evaluation of two-dimensional (2-D) correlation sequences and complex integrals is discussed. It is demonstrated that the system of rational function equations given by Hwang can be solved by making use of the unit circle polynomial interpolation. Thus, a general computer algorithm becomes available for handling the problem.

A method is presented for the approximate factorization of unfactorable bivariate polynomials. An efficient iterative algorithm is developed to minimize an appropriate criterion. The approximate separation of bivariate polynomials may be considered as a special case of the approximate factorization for which a non-iterative algorithm is developed on the basis of the singular value decomposition concept. The basic ideas can be easily extended to the case of polynomials in more than two independent variables. Examples are presented to illustrate the utility of the methods.

Second-order 2-D recursive digital filters are frequently used as building blocks in computer-aided design by means of optimisation techniques. An efficient, simple and exact procedure to test the stability of such filters is presented.