All technical report files are in compressed (gzip) postscript format. The file names are of the sort BU-CE-YYXX.pdf


BU-CE-0601

TITLE: On the Convergence of a Class of Multilevel Methods for Large, Sparse Markov Chains
AUTHORS: Peter Buchholz, Tugrul Dayar

ABSTRACT: This paper investigates the theory behind the steady state analysis of large, sparse Markov chains (MCs) with a recently proposed class of multilevel (ML) methods using concepts from algebraic multigrid and iterative aggregation-disaggregation. The motivation is to better understand the convergence characteristics of the class of ML methods and to have a clearer formulation that will aid their implementation. In doing this, restriction (or aggregation) and prolongation (or disaggregation) operators of multigrid are used, and the Kronecker based approach for hierarchical Markovian models (HMMs) is employed, since it suggests a natural and compact definition of grids (or levels). However, the HMM formalism used to describe the class of ML methods for large, sparse MCs has no influence on the theoretical results derived.

Keywords: Markov chains, multilevel methods, multigrid, aggregation-disaggregation, Kronecker based numerical techniques



BU-CE-0602

TITLE: Conservative Occlusion Culling for Urban Visualization using a Slice-wise Data Structure
AUTHORS: Turker Yilmaz and Ugur Gudukbay

ABSTRACT: In this paper, we propose a new shrinking process for conservative from-point occlusion culling algorithms and a data structure for the visualization of urban environments. The visible geometry in a typical urban walkthrough mainly consists of partially visible buildings. Occlusion-culling algorithms, in which the granularity is based on buildings, render these partially visible buildings completely. We observe that the visibility in urban walkthroughs shows certain characteristics. The proposed \textit {slice-wise data structure} represents the buildings, exploiting these characteristics, in terms of slices parallel to the coordinate axes. This forms the base for occlusion culling where the occlusion granularity is at slice level. The proposed slice-wise data structure has minimal storage requirements. The visible parts can be accessed at constant time during navigation with the help of a preprocessing stage. We also propose to shrink the occluders in a scene. This is necessary for a conservative from-point occlusion culling algorithm, which can also be applied to nonconvex general 3D occluders. Empirical results show that a 54\% decrease in the number of processed polygons and 46\% speed-up in frame-rate can be achieved by using the proposed conservative occlusion-culling algorithm with rather than an occlusion-culling method where the granularity is based on individual buildings.

Keywords: octree, occluder shrinking, from-point occlusion culling, urban visualization, visibility preprocessing.



BU-CE-0603

TITLE: Motion Capture from Single Video Sequence
AUTHORS: Ibrahim Demir

ABSTRACT: 3D human pose reconstruction is a popular research area since it can be used in various applications. Currently most of the methods work for constrained environments, where multi camera views are available and camera calibration is known, or a single camera view is available, which requires intensive user effort. However most of the currently available data do not satisfy these constraints, thus they cannot be processed by these algorithms. In this thesis a framework is proposed to reconstruct 3D pose of a human for animation from a sequence of single view video frames. The framework for pose construction starts with background estimation. Once the image background is estimated, the body silhouette is extracted by using image subtraction for each frame. Then the body silhouettes are automatically labeled by using a model-based approach. Finally, the 3D pose is constructed from the labeled human silhouette by assuming orthographic projection. The proposed approach does not require camera calibration. The proposed framework assumes that the input video has a static background and it has no significant perspective effects and the performer is in upright position.

Keywords: motion capture, framework, single camera, uncalibrated camera, vision-based, animation.