On Visualization and Reconstruction from Non-uniform Point Sets

thesis

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• Publication Type: PhD-Thesis
• Month: November
• Rigorosum: 27.11.2009

Processing of non-uniform data is a non-trivial task and hence more difficult when compared to processing of regular data. Transforming from non-uniform to uniform representations is a well-accepted paradigm in the signal processing community. In this thesis we advocate such a concept. The main motivation for adopting this paradigm is that most of the techniques and methods related to signal processing, data mining and data exploration are well-defined and stable for Cartesian data, but generally are non-trivial to apply to non-uniform data. Among other things, this will allow us to better exploit the capabilities of modern GPUs.

In non-uniform representations sampling rates can vary drastically even by several orders of magnitude, making the decision on a target resolution a non-trivial trade-off between accuracy and efficiency. In several cases the points are spread non-uniformly with similar density across the volume, while in other cases the points have an enormous variance in distribution. In this thesis we present solutions to both cases. For the first case we suggest computing reconstructions of the same volume in different resolutions based on the level of detail we are interested in. The second case scenario is the main motivation for proposing a multi-resolution scheme, where the scale of reconstruction is decided adaptively based on the number of points in each subregion of the whole volume.

We introduce a novel framework for 3D reconstruction and visualization from non-uniform scalar and vector data. We adopt a variational reconstruction approach. In this method non-uniform point sets are transformed to a uniform representation consisting of B-spline coefficients that are attached to the grid. With these coefficients we can define a C2 continuous function across the whole volume. Several testings were performed in order to analyze and fine-tune our framework. All the testings and the results of this thesis offer a view from a new and different perspective to the visualization and reconstruction from non-uniform point sets.

@phdthesis\{vucini-2009-phd,
  title =      "On Visualization and Reconstruction from Non-uniform Point
               Sets",
  author =     "Erald  Vu{\c c}ini",
  year =       "2009",
  abstract =   "Technological and research advances in both acquisition and
               simulation devices provide continuously increasing
               high-resolution volumetric data that by far exceed today's
               graphical and display capabilities. Non-uniform
               representations offer a way of balancing this deluge of data
               by adaptively measuring (sampling) according to the
               importance (variance) of the data. Also, in many real-life
               situations the data are known only on a non-uniform
               representation.   Processing of non-uniform data is a
               non-trivial task and hence more difficult when compared to
               processing of regular data. Transforming from non-uniform to
               uniform representations is a well-accepted paradigm in the
               signal processing community. In this thesis we advocate such
               a concept. The main motivation for adopting this paradigm is
               that most of the techniques and methods related to signal
               processing, data mining and data exploration are
               well-defined and stable for Cartesian data, but generally
               are non-trivial to apply to non-uniform data. Among other
               things,  this will allow us to better exploit the
               capabilities of modern GPUs.  In non-uniform representations
               sampling rates can vary drastically even by several orders
               of magnitude, making the decision on a target resolution a
               non-trivial trade-off between accuracy and efficiency. In
               several cases the points are spread non-uniformly with
               similar density across the volume, while in other cases the
               points have an enormous variance in distribution. In this
               thesis we present solutions to both cases. For the first
               case we suggest computing reconstructions of the same volume
               in different resolutions based on the level of detail we are
               interested in. The second case scenario is the main
               motivation for proposing a multi-resolution scheme, where
               the scale of reconstruction is decided adaptively based on
               the number of points in each subregion of the whole volume. 
               We introduce a novel framework for 3D reconstruction and
               visualization from non-uniform scalar and vector data. We
               adopt a variational reconstruction approach. In this method
               non-uniform point sets are transformed to a uniform
               representation consisting of B-spline coefficients that are
               attached to the grid. With these coefficients we can define
               a C2 continuous function across the whole volume. Several
               testings were performed in order to analyze and fine-tune
               our framework. All the testings and the results of this
               thesis offer a view from a new and different perspective to
               the visualization and reconstruction from non-uniform point
               sets.",
  address =    "Favoritenstrasse 9-11/186, A-1040 Vienna, Austria",
  school =     "Institute of Computer Graphics and Algorithms, Vienna
               University of Technology",
  month =      nov,
  URL =        "http://www.cg.tuwien.ac.at/research/publications/2009/vucini-2009-phd/",
}