Projected tetrahedra revisited: a barycentric formulation applied to digital radiograph reconstruction using higher-order attenuation functions

This paper presents a novel method for volume rendering of unstructured grids. Previously, we introduced an algorithm for perspective-correct interpolation of barycentric coordinates and computing polynomial attenuation integrals for a projected tetrahedron using graphics hardware. In this paper, we enhance the algorithm by providing a simple and efficient method to compute the projected shape (silhouette) and tessellation of a tetrahedron, in perspective and orthographic projection models. Our tessellation algorithm is published for the first time. Compared with works of other groups on rendering unstructured grids, the main contributions of this work are: 1) A new algorithm for finding the silhouette of a projected tetrahedron. 2) A method for interpolating barycentric coordinates and thickness on the faces of the tetrahedron. 3) Visualizing higher-order attenuation functions using GPU without preintegration. 4) Capability of applying shape deformations to a rendered tetrahedral mesh without significant performance loss. Our visualization model is independent of depth-sorting of the cells. We present imaging and timing results of our implementation, and an application in time-critical "2D-3D" deformable registration of anatomical models. We discuss the impact of using higher-order functions on quality and performance.

[1]  Rajiv Gupta,et al.  Linear Pushbroom Cameras , 1994, ECCV.

[2]  Timothy F. Cootes,et al.  Active Shape Models-Their Training and Application , 1995, Comput. Vis. Image Underst..

[3]  Joseph S. B. Mitchell,et al.  An exact interactive time visibility ordering algorithm for polyhedral cell complexes , 1998, IEEE Symposium on Volume Visualization (Cat. No.989EX300).

[4]  Takeo Kanade,et al.  Iterative x-ray/ct registration using accelerated volume rendering , 2001 .

[5]  Russell H. Taylor,et al.  A statistical bone density atlas and deformable medical image registration , 2002 .

[6]  Martin Kraus,et al.  Hardware-accelerated volume and isosurface rendering based on cell-projection , 2000, Proceedings Visualization 2000. VIS 2000 (Cat. No.00CH37145).

[7]  David S. Ebert,et al.  Projecting tetrahedra without rendering artifacts , 2004, IEEE Visualization 2004.

[8]  Jerry L. Prince,et al.  Mjolnir: deformable image registration using feature diffusion , 2006, SPIE Medical Imaging.

[9]  Marc Levoy,et al.  Light field rendering , 1996, SIGGRAPH.

[10]  Peter L. Williams.  Visibility-ordering meshed polyhedra , 1992, TOGS.

[11]  Martin Kraus,et al.  Hardware-accelerated volume and isosurface rendering based on cell-projection , 2000 .

[12]  P. Shirley,et al.  A polygonal approximation to direct scalar volume rendering , 1990, VVS.

[13]  Richard Szeliski,et al.  The lumigraph , 1996, SIGGRAPH.

[14]  Russell H. Taylor,et al.  Rendering tetrahedral meshes with higher-order attenuation functions for digital radiograph reconstruction , 2005, VIS 05. IEEE Visualization, 2005..

[15]  Cláudio T. Silva,et al.  Hardware-assisted visibility sorting for unstructured volume rendering , 2005, IEEE Transactions on Visualization and Computer Graphics.

[16]  Nelson L. Max,et al.  Hardware-accelerated simulated radiography , 2005, VIS 05. IEEE Visualization, 2005..

[17]  Kenneth Moreland,et al.  Tetrahedral projection using vertex shaders , 2002, Symposium on Volume Visualization and Graphics, 2002. Proceedings. IEEE / ACM SIGGRAPH.

[18]  Kenneth Moreland,et al.  A fast high accuracy volume renderer for unstructured data , 2004, 2004 IEEE Symposium on Volume Visualization and Graphics.

[19]  Ricardo Farias,et al.  ZSWEEP: An Efficient and Exact Projection Algorithm for Unstructured Volume Rendering , 2000, 2000 IEEE Symposium on Volume Visualization (VV 2000).

[20]  Thomas Ertl,et al.  Hardware-based view-independent cell projection , 2002, VVS '02.