Digital cameras are widely used in many applications, such as digital still cameras, camcorders, camera phones, and
video surveillance. Advances in large resolution CCD/CMOS sensors coupled with the availability of low-power image
signal processors have led to the development of digital cameras with both high resolution image and short visual clip
capabilities. The red, green, or blue color values obtained from a camera sensor are device-dependent. Thus there is a
need to characterize these values in a device-independent fashion and provide a color correction. For simplicity,
common methods presume a linear transformation to perform the color conversion. The problem translates to finding the
transformation matrix and the offset vector. One well known approach uses a white-preserving constraint in the
optimization. This approach requires that source data and reference data have the same exposure values. However,
source data and reference data usually have different exposure values, and exposure information is either unavailable or
inaccurate. We propose a new method that provides color conversion by linear transformation optimization with gray
preservation. Our method allows for differing exposures between images from the target sensor and the color reference.
Experiments show that images resulted from our method look more colorful than those from previous methods.
We present two-dimensional filter banks with directional vanishing moments. The directional-vanishing-moment condition is crucial for
the regularity of directional filter banks. However, it is a challenging task to design orthogonal filter banks with directional vanishing moments. Due to the lack of multidimensional factorization theorems, traditional one-dimensional methods cannot be extended to higher dimensional cases. Kovacevic and Vetterli investigated the design of two-dimensional orthogonal filter banks and proposed a set of closed-form solutions called the lattice structure, where the polyphase matrix of the filter bank is characterized with a set of rotation parameters. Orthogonal filter banks with lattice structures have simple implementation. We propose a method of designing orthogonal filter banks with directional vanishing moments based on this lattice structure. The constraint of directional vanishing moments is imposed on the rotation parameters. We find the solutions of rotation parameters have special structure. Based on this structure, we find the closed-form solution for orthogonal filter banks with directional vanishing moments.
We present the characterization and design of multidimensional oversampled FIR filter banks. In the polyphase domain, the perfect reconstruction condition for an oversampled filter bank amounts to the invertibility of the analysis polyphase matrix, which is a rectangular FIR matrix. For a nonsubsampled FIR filter bank, its analysis polyphase matrix is the FIR vector of analysis filters. A major challenge is how to extend algebraic geometry techniques, which only deal with polynomials (that is, causal filters), to handle general FIR filters. We propose a novel method to map the FIR representation of the nonsubsampled filter bank into a polynomial one by simply introducing a new variable. Using algebraic geometry and Groebner bases, we propose the existence, computation, and characterization of FIR synthesis filters given FIR analysis filters. We explore the design problem of MD nonsubsampled FIR filter banks by a mapping approach. Finally, we extend these results to general oversampled FIR filter banks.
It is a challenging task to design orthogonal filter banks, especially multidimensional (MD) ones. In the one-dimensional (1D) two-channel finite impulse response (FIR) filter bank case, several design methods exist. Among them, designs based on spectral factorizations (by Smith and Barnwell) and designs based on lattice
factorizations (by Vaidynanathan and Hoang) are the most effective and widely used. The 1D two-channel infinite impulse response (IIR) filter banks and associated wavelets were considered by Herley and Vetterli. All of these design methods are based on spectral factorization. Since in multiple dimensions, there is no factorization
theorem, traditional 1D design methods fail to generalize. Tensor products can be used to construct MD orthogonal filter banks from 1D orthogonal filter banks, yielding separable filter banks. In contrast to separable filter banks, nonseparable filter banks are designed directly, and result in more freedom and better frequency selectivity. In the FIR case, Kovacevic and Vetterli designed specific two-dimensional and three-dimensional nonseparable FIR orthogonal filter banks. In the IIR case, there are few design results (if any) for MD orthogonal IIR filter banks. To design orthogonal filter banks, we must design paraunitary matrices,
which leads to solving sets of nonlinear equations. The Cayley transform establishes a one-to-one mapping between paraunitary
matrices and para-skew-Hermitian matrices. In contrast to nonlinear equations, the para-skew-Hermitian condition amounts to linear constraints on the matrix entries which are much easier to
solve. We present the complete characterization of both paraunitary FIR matrices and paraunitary IIR matrices in the Cayley domain. We also propose efficient design methods for MD orthogonal filter banks and corresponding methods to impose the vanishing-moment condition.
Block motion estimation is one of the key technologies in video compression and has been widely adopted by several existing video coding international standards. Many popular block motion estimation methods, including three-step search (TSS), new three-step search (NTSS), and four-step search (4SS), have assumed that the error surface is unimodal over the search area or the motion vector is center-biased. However, these assumptions do not hold for most MPEG-1,2 video frames. As a result, the schemes with these assumptions will exhibit degraded performance as they applied to MPEG-1,2 video frames. In this paper, we propose a fast block matching motion estimation scheme based on an integration of pixel subsampling and search candidate subsampling. Comparing with the well- known TSS algorithm, the proposed scheme visits more candidates so that it can significantly avoid trapping into the local minima and therefore is more robust. Experimental results using typical MPEG-1 video frames show that the proposed algorithm can achieve better PSNR as well as higher speed-up ratios than the well-known TSS. In addition, the combined subsampling scheme has a regular structure that facilitates easy hardware implementation.