The use of mathematical morphology in low and mid-level image processing and computer vision applications has allowed the development of a class of techniques for analyzing shape information in monochrome images. In this paper these techniques are extended to color images. We investigate two approaches for \color morphology": a vector approach, in which color vectors are ranked using a multivariate ranking concept known as reduced ordering, and a component-wise approach, in which grayscale morphological operations are applied to each of the three color component images independently. New vector morphological ltering operations are de ned, and a set-theoretic analysis of these vector operations is presented. We also present experimental results comparing the performance of the vector approach and the component-wise approach for two applications: multiscale color image analysis and noise suppression in color images.

We present a new algorithm for segmentation of textured images using a multiresolution Bayesian approach. The new algorithm uses a multiresolution Gaussian autoregressive (MGAR) model for the pyramid representation of the observed image, and assumes a multiscale Markov random field model for the class label pyramid. The models used in this paper incorporate correlations between different levels of both the observed image pyramid and the class label pyramid. The criterion used for segmentation is the minimization of the expected value of the number of misclassified nodes in the multiresolution lattice. The estimate which satisfies this criterion is referred to as the "multiresolution maximization of the posterior marginals" (MMPM) estimate, and is a natural extension of the single-resolution "maximization of the posterior marginals" (MPM) estimate. Previous multiresolution segmentation techniques have been based on the maximum a posterior (MAP) estimation criterion, which has been shown to be less appropriate for segmentation than the MPM criterion. It is assumed that the number of distinct textures in the observed image is known. The parameters of the MGAR model-the means, prediction coefficients, and prediction error variances of the different textures-are unknown. A modified version of the expectation-maximization (EM) algorithm is used to estimate these parameters. The parameters of the Gibbs distribution for the label pyramid are assumed to be known. Experimental results demonstrating the performance of the algorithm are presented.

In this paper we present new results relative to the "expectation-maximization/maximization of the posterior marginals" (EM/MPM) algorithm for simultaneous parameter estimation and segmentation of textured images. The EM/MPM algorithm uses a Markov random field model for the pixel class labels and alternately approximates the MPM estimate of the pixel class labels and estimates parameters of the observed image model. The goal of the EM/MPM algorithm is to minimize the expected value of the number of misclassified pixels. We present new theoretical results in this paper which show that the algorithm can be expected to achieve this goal, to the extent that the EM estimates of the model parameters are close to the true values of the model parameters. We also present new experimental results demonstrating the performance of the EM/MPM algorithm.

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Abstract-A primary challenge in multicasting video in a wireless LAN to multiple clients is to deal with the client diversity -clients may have different channel characteristics and hence receive different numbers of transmissions from the AP. A promising approach to overcome this problem is to combine multi-resolution (layered) video coding with interlayer network coding. The fundamental challenge in such an approach is to determine the strategy of coding the packets across different layers that maximizes the number of decoded layers at all clients. This paper makes three contributions.(1) We first show that even for one client, the previously proposed canonical triangular scheme for inter-layer network coding can perform poorly. We show how to enhance the triangular scheme by incorporating the estimated target number of layers which significantly improves its effectiveness. (2) We show that such an enhanced triangular scheme still performs poorly for multiple clients with diverse channel characteristics, which motivates the need for searching for the optimal coding strategy. The naive way of searching for the optimal strategy is computationally prohibitive. We present several optimizations that drastically reduce the complexity of exhaustively searching for the optimal strategy, making it feasible in real time. (3) Finally, we design and evaluate an online video delivery scheme, Percy, to be deployed at a proxy behind the AP of a wireless LAN. Our simulation results show that Percy outperforms the previous inter-layer coding heuristic by up to 22-80% with varying numbers of clients.