Lossy compression of discrete sources via Viterbi algorithm

We present a new lossy compressor for discrete-valued sources. For coding a sequence $x^n$, the encoder starts by assigning a certain cost to each possible reconstruction sequence. It then finds the one that minimizes this cost and describes it losslessly to the decoder via a universal lossless compressor. The cost of each sequence is a linear combination of its distance from the sequence $x^n$ and a linear function of its $k^{\rm th}$ order empirical distribution. The structure of the cost function allows the encoder to employ the Viterbi algorithm to recover the minimizer of the cost. We identify a choice of the coefficients comprising the linear function of the empirical distribution used in the cost function which ensures that the algorithm universally achieves the optimum rate-distortion performance of any stationary ergodic source in the limit of large $n$, provided that $k$ diverges as $o(\log n)$. Iterative techniques for approximating the coefficients, which alleviate the computational burden of finding the optimal coefficients, are proposed and studied.Comment: 26 pages, 6 figures, Submitted to IEEE Transactions on Information Theor

Parametric Inference for Biological Sequence Analysis

One of the major successes in computational biology has been the unification, using the graphical model formalism, of a multitude of algorithms for annotating and comparing biological sequences. Graphical models that have been applied towards these problems include hidden Markov models for annotation, tree models for phylogenetics, and pair hidden Markov models for alignment. A single algorithm, the sum-product algorithm, solves many of the inference problems associated with different statistical models. This paper introduces the \emph{polytope propagation algorithm} for computing the Newton polytope of an observation from a graphical model. This algorithm is a geometric version of the sum-product algorithm and is used to analyze the parametric behavior of maximum a posteriori inference calculations for graphical models.Comment: 15 pages, 4 figures. See also companion paper "Tropical Geometry of Statistical Models" (q-bio.QM/0311009

ENHANCEMENTS TO THE MODIFIED COMPOSITE PATTERN METHOD OF STRUCTURED LIGHT 3D CAPTURE

The use of structured light illumination techniques for three-dimensional data acquisition is, in many cases, limited to stationary subjects due to the multiple pattern projections needed for depth analysis. Traditional Composite Pattern (CP) multiplexing utilizes sinusoidal modulation of individual projection patterns to allow numerous patterns to be combined into a single image. However, due to demodulation artifacts, it is often difficult to accurately recover the subject surface contour information. On the other hand, if one were to project an image consisting of many thin, identical stripes onto the surface, one could, by isolating each stripe center, recreate a very accurate representation of surface contour. But in this case, recovery of depth information via triangulation would be quite difficult. The method described herein, Modified Composite Pattern (MCP), is a conjunction of these two concepts. Combining a traditional Composite Pattern multiplexed projection image with a pattern of thin stripes allows for accurate surface representation combined with non-ambiguous identification of projection pattern elements. In this way, it is possible to recover surface depth characteristics using only a single structured light projection. The technique described utilizes a binary structured light projection sequence (consisting of four unique images) modulated according to Composite Pattern methodology. A stripe pattern overlay is then applied to the pattern. Upon projection and imaging of the subject surface, the stripe pattern is isolated, and the composite pattern information demodulated and recovered, allowing for 3D surface representation. In this research, the MCP technique is considered specifically in the context of a Hidden Markov Process Model. Updated processing methodologies explained herein make use of the Viterbi algorithm for the purpose of optimal analysis of MCP encoded images. Additionally, we techniques are introduced which, when implemented, allow fully automated processing of the Modified Composite Pattern image

Antiextensive connected operators for image and sequence processing

This paper deals with a class of morphological operators called connected operators. These operators filter the signal by merging its flat zones. As a result, they do not create any new contours and are very attractive for filtering tasks where the contour information has to be preserved. This paper shows that connected operators work implicitly on a structured representation of the image made of flat zones. The max-tree is proposed as a suitable and efficient structure to deal with the processing steps involved in antiextensive connected operators. A formal definition of the various processing steps involved in the operator is proposed and, as a result, several lines of generalization are developed. First, the notion of connectivity and its definition are analyzed. Several modifications of the traditional approach are presented. They lead to connected operators that are able to deal with texture. They also allow the definition of connected operators with less leakage than the classical ones. Second, a set of simplification criteria are proposed and discussed. They lead to simplicity-, entropy-, and motion-oriented operators. The problem of using a nonincreasing criterion is analyzed. Its solution is formulated as an optimization problem that can be very efficiently solved by a Viterbi (1979) algorithm. Finally, several implementation issues are discussed showing that these operators can be very efficiently implemented.Peer ReviewedPostprint (published version