IStar: A Raster Representation for Scalable Image and Volume Data

Topology has been an important tool for analyzing scalar data and flow fields in visualization. In this work, we analyze the topology of multivariate image and volume data sets with discontinuities in order to create an efficient, raster-based representation we call IStar. Specifically, the topology information is used to create a dual structure that contains nodes and connectivity information for every segmentable region in the original data set. This graph structure, along with a sampled representation of the segmented data set, is embedded into a standard raster image which can then be substantially downsampled and compressed. During rendering, the raster image is upsampled and the dual graph is used to reconstruct the original function. Unlike traditional raster approaches, our representation can preserve sharp discontinuities at any level of magnification, much like scalable vector graphics. However, because our representation is raster-based, it is well suited to the real-time rendering pipeline. We demonstrate this by reconstructing our data sets on graphics hardware at real-time rates.

[1]  In-kyeong Choi.  On straight line representations of random planar graphs , 1992 .

[2]  David E. Breen,et al.  A framework for Level Set segmentation of volumetric datasets , 2001 .

[3]  Jörn Loviscach,et al.  Efficient magnification of bi-level textures , 2005, SIGGRAPH '05.

[4]  Suyash P. Awate,et al.  MRI Tissue Classification with Neighborhood Statistics: A Nonparametric, Entropy-Minimizing Approach , 2005, MICCAI.

[5]  Bernd Hamann,et al.  Material Interface Reconstruction , 2003, IEEE Trans. Vis. Comput. Graph..

[6]  Bernd Hamann,et al.  Topology-based simplification for feature extraction from 3D scalar fields , 2005, VIS 05. IEEE Visualization, 2005..

[7]  David E. Breen,et al.  Segmentation of Biological Volume Datasets Using a Level-Set Framework , 2001, VG.

[8]  R. Marik,et al.  The Color Adjacency GraphRepresentation of Multi-Coloured , 1995 .

[9]  Stefan Friedrich,et al.  Topology , 2019, Arch. Formal Proofs.

[10]  David E. Breen,et al.  A Framework for Level Set Segmentation of Volume Datasets , 2001 .

[11]  Charles Hansen,et al.  The Visualization Handbook , 2011 .

[12]  Adobe Press,et al.  PostScript Language Reference Manual , 1985 .

[13]  Jack Tumblin,et al.  Bixels: Picture Samples with Sharp Embedded Boundaries , 2004, Rendering Techniques.

[14]  Tamara G. Kolda,et al.  Optimization by Direct Search: New Perspectives on Some Classical and Modern Methods , 2003, SIAM Rev..

[15]  Joe Michael Kniss,et al.  Statistically quantitative volume visualization , 2005, VIS 05. IEEE Visualization, 2005..

[16]  Charles T. Loop,et al.  Resolution independent curve rendering using programmable graphics hardware , 2005, ACM Trans. Graph..

[17]  Sudipta Sengupta,et al.  ε-optimization schemes and L-bit precision (extended abstract): alternative perspectives in combinatorial optimization , 2000, STOC '00.

[18]  Xavier Tricoche,et al.  Topological Methods for Flow Visualization , 2005, The Visualization Handbook.

[19]  Azriel Rosenfeld,et al.  Digital topology: Introduction and survey , 1989, Comput. Vis. Graph. Image Process..

[20]  Alexander Russell,et al.  Computational topology: ambient isotopic approximation of 2-manifolds , 2003, Theor. Comput. Sci..

[21]  John C. Hart,et al.  Computational topology for shape modeling , 1999, Proceedings Shape Modeling International '99. International Conference on Shape Modeling and Applications.

[22]  R. Ho.  Algebraic Topology , 2022 .

[23]  Lambertus Hesselink,et al.  Representation and display of vector field topology in fluid flow data sets , 1989, Computer.

[24]  Leo Grady,et al.  Multilabel random walker image segmentation using prior models , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[25]  Sudipta Sengupta,et al.  epsilon-optimization schemes and L-bit precision: alternative perspectives in combinatorial optimization (extended abstract) , 2000, STOC 2000.

[26]  Nicolas Ray,et al.  Vector Texture Maps on the GPU , 2006 .

[27]  A. W. Roscoe,et al.  Concepts of digital topology , 1992 .

[28]  David H. Laidlaw,et al.  Geometric model extraction from magnetic resonance volume data , 1996 .

[29]  Pradeep Sen,et al.  Silhouette maps for improved texture magnification , 2004, Graphics Hardware.

[30]  Pat Hanrahan,et al.  Shadow silhouette maps , 2003, ACM Trans. Graph..