Image interpolation by two-dimensional parametric cubic convolution
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]/spl times/[-2,2] with constraints for biaxial symmetry, diagonal (or 90/spl deg/ 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.

title: A real-time model for the robotic highway safety marker system
abstract: 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.

title: Normalized cuts and image segmentation
abstract: We propose a novel approach for solving the perceptual grouping problem in vision. Rather than focusing on local features and their consistencies in the image data, our approach aims at extracting the global impression of an image. We treat image segmentation as a graph partitioning problem and propose a novel global criterion, the normalized cut, for segmenting the graph. The normalized cut criterion measures both the total dissimilarity between the different groups as well as the total similarity within the groups. We show that an efficient computational technique based on a generalized eigenvalue problem can be used to optimize this criterion. We have applied this approach to segmenting static images and found results very encouraging.

title: Starvation mitigation through multi-channel coordination in CSMA multi-hop wireless networks
abstract: Existing multi-channel protocols have been demonstrated to significantly increase aggregate throughput compared to single-channel protocols. However, we show that despite such improvements in aggregate throughput, existing protocols can lead to flow starvation in a multi-hop network, a phenomenon that also occurs with single-channel protocols. In this paper, we devise Asynchronous Multi-channel Coordination Protocol (AMCP), a distributed medium access protocol that not only increases aggregate throughput, but more importantly, addresses the fundamental coordination problems that lead to starvation. Based on AMCP's counter-starvation mechanisms, we analytically derive and experimentally validate an ap-proximate lower bound on the throughput of any flow in an arbitrary topology. We also demonstrate that AMCP can deliver significantly higher per-flow throughput than both IEEE 802.11 and existing multi-channel solutions. In addition to its performance properties, AMCP is both simple in that it operates using the primitives of IEEE 802.11 DCF, and cost-effective in that it requires only a single half-duplex transceiver and no infrastructure support.

title: Segmentation with Pairwise Attraction and Repulsion
abstract: We propose a method of image segmentation by integrating pairwise attraction and directional repulsion derived from local grouping and figure-ground cues. These two kinds of pairwise relationships are encoded in the real and imaginary parts of an Hermitian graph weight matrix, through which we can directly generalize the normalized cuts criterion. With bi-graph constructions, this method can be readily extended to handle nondirectional repulsion that captures dissimilarity. We demonstrate the use of repulsion in image segmentation with relative depth cues, which allows segmentation and figure-ground segregation to be computed simultaneously. As a general mechanism to represent the dual measures of attraction and repulsion, this method can also be employed to solve other constraint satisfaction and optimization problems.

title: Left cells containing a fully commutative element
abstract: Let W be a finite or an affine Coxeter group and Wc the set of all the fully commutative elements in W. For any left cell L of W containing some fully commutative element, our main result of the paper is to prove that there exists a unique element (say wL) in L ∩ Wc such that any z ∈ L has the form z = xwL with l(z) = l(x) + l(wL) for some x ∈ W. This implies that L is left connected, verifying a conjecture of Lusztig in our case.

title: Understanding popout through repulsion
abstract: Perceptual popout is defined by both feature similarity and local feature contrast. We identify these two measures with attraction and repulsion, and unify the dual processes of association by attraction and segregation by repulsion in a single grouping framework. We generalize normalized cuts to multi-way partitioning with these dual measures. We expand graph partitioning approaches to weight matrices with negative entries, and provide a theoretical basis for solution regularization in such algorithms. We show that attraction, repulsion and regularization each contributes in a unique way to popout. Their roles are demonstrated in various salience detection and visual search scenarios. This work opens up the possibilities of encoding negative correlations in constraint satisfaction problems, where solutions by simple and robust eigendecomposition become possible.