This paper develops a practical method for image resolution enhancement. The method optimizes the spatially constrained Wiener filter for an efficiently parameterized model of the image autocorrelation based on a Markov random field (MRF) with affine transformation. The paper presents a closed-form solution to parameterize the model for an image. The enhancement method is computationally efficient, because it is formulated as convolution with a small kernel. Because the kernel is small, it can be optimized efficiently and only a small portion of the MRF autocorrelation model is required. Because the autocorrelation model parameters and optimal filter can be computed quickly, the method can be optimized locally for adaptive processing. Experimental results indicate that the new method can balance the error-budget tradeoff between signal error and aliasing error.

Cubic convolution is a popular method for image interpolation. Traditionally, the piecewise-cubic kernel has been derived in one dimension with one parameter and applied to two-dimensional (2-D) images in a separable fashion. However, images typically are statistically nonseparable, which motivates this investigation of nonseparable cubic convolution. This paper derives two new nonseparable, 2-D cubic-convolution kernels. The first kernel, with three parameters (designated 2D-3PCC), is the most general 2-D, piecewise-cubic interpolator defined on [-2, 2] x [-2, 2] with constraints for biaxial symmetry, diagonal (or 90 degrees rotational) symmetry, continuity, and smoothness. The second kernel, with five parameters (designated 2D-5PCC), relaxes the constraint of diagonal symmetry, based on the observation that many images have rotationally asymmetric statistical properties. This paper also develops a closed-form solution for determining the optimal parameter values for parametric cubic-convolution kernels with respect to ensembles of scenes characterized by autocorrelation (or power spectrum). This solution establishes a practical foundation for adaptive interpolation based on local autocorrelation estimates. Quantitative fidelity analyses and visual experiments indicate that these new methods can outperform several popular interpolation methods. An analysis of the error budgets for reconstruction error associated with blurring and aliasing illustrates that the methods improve interpolation fidelity for images with aliased components. For images with little or no aliasing, the methods yield results similar to other popular methods. Both 2D-3PCC and 2D-5PCC are low-order polynomials with small spatial support and so are easy to implement and efficient to apply.

This paper studies how biologically meaningful landmarks extracted from face images can be exploited for face recognition using the bidimensional regression. Incorporating the correlation statistics of landmarks, this paper also proposes a new approach called eigenvalue weighted bidimensional regression. Complex principal component analysis is used for computing eigenvalues and removing correlation among landmarks. We evaluate our approach using two standard face databases: the Purdue AR and the NIST FERET. Experimental results show that the bidimensional regression is an efficient method to exploit geometry information of face images.

This paper formulates a two-dimensional, piecewise-cubic interpolator that accounts for non-separable and rotationally asymmetric scene statistics. The resulting kernel has five parameters and is designated 2D-5PCC. As a low-order polynomial with small spatial support, the kernel is easy to implement and efficient to apply. A closed-form solution, developed in this paper, yields the optimal parameter values for scene ensembles characterized by autocorrelation or power spectrum. Experiments indicate that 2D-5PCC yields higher fidelity interpolations than several other popular methods.

This paper formulates two-dimensional parametric cubic convolution for one-pass image restoration and reconstruction and derives a closed-form solution for the mean-square optimal parameters. The approach improves on traditional separable cubic convolution and relaxes the interpolation constraint to support restoration. The resulting kernel has five parameters and is designated 2D-5PCC-R. The closed-form solution for the optimal parameters is based on a continuous-discrete-continuous system model that accounts for the scene ensemble, acquisition blurring, sampling, noise, and processing. The analysis of the model leads to a simultaneous solution for five linear equations in the five parameters

We present the design and implementation of a real-time model for the global control of robotic highway safety markers. Problems addressed in the system are: 1) poor scalability and predictability as the number of markers increases, 2) jerky movement of markers, and 3) false-hits caused by environment objects. We extensively analyze the system and offer two solutions: a basic solution and an enhanced solution. They are built respectively upon two task models: the periodic task model and the variable rate execution task model. The former is characterized by four static parameters: phase, period, worst case execution time and relative deadline. The latter has similar parameters. Its parameter values, however, are allowed to change at arbitrary times. We then examine two typical real-time scheduling approaches: rate monotonic (RM) priority driven and earliest deadline first (EDF). Analysis of their sufficient conditions shows that our system is feasibly schedulable under either RM or EDF. This conclusion justifies that the path for each safety marker can be guaranteed to be smooth under the designed real-time system. For the scalability issue, we present a sufficient condition for the upper bound on the number of barrel robots that can be reliably controlled. One key technique integrated into our real-time system is the Hough transform. We refine its traditional implementation so that, for the task of detecting safety markers, the time complexity decreases and the reliability increases with only slight additional storage for search windows. The basic idea behind our improvements is to limit the search window for safety markers.