Hierarchical Methods in Graphics and Image Processing

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Hierarchical multi-resolution models are powerful tools for robust and effective computation in computer graphics and image processing, in an adaptive and progressive style. I will focus on the following specific topics:- To apply the hybrid hierarchical modeling method developed for hair rendering to a dynamic water simulation problem. Examples include a waterfall's dynamic shape as influenced by the features of the cliff face and wind factors, or large waves splashing onto rocks. In this work, our goal is to develop a unified framework for water state transition between liquid, droplets, and mist.- To extend the mathematical formulation of an emerging region portioning method, achieved through the mean shift algorithm, by introducing a variation factor, and to explore this method in scale-space resulting in a hierarchical representation and two novel applications in the areas of texture analysis and no-reference image metrics.- To investigate an adaptive partitioning algorithm for edge detection in images that groups edge points hierarchically according to their natural spatial clustering. An extension of this work will result in a novel sparse matrix representation for the high-dimensional accumulators used by the Hough Transform in handling curves.My long-term goals are:- To generalize my hybrid hierarchical modeling method into a framework that can handle a variety of complex natural phenomena for computer graphics.- To develop a general framework for extracting and organizing object boundaries from complex images as piecewise lines and arc segments for the general purpose of object recognition.- To develop a content-based, no-reference image and video-quality metric.