Reconstruction issues in volume visualization

Although volume visualization has already grown out of its infancy, the most commonly used reconstruction techniques are still trilinear interpolation for function reconstruction and central differences (most often in conjunction with trilinear interpolation) for gradient reconstruction. Nevertheless, quite some research in the last few years was devoted to improve this situation. This paper surveys the more important methods, emphasizing selected work in function and gradient reconstruction, and gives an overview over the rather new development of exploiting second-order derivatives for volume visualization purposes.

[1]  G. Kindlmann,et al.  Semi-automatic generation of transfer functions for direct volume rendering , 1998, IEEE Symposium on Volume Visualization (Cat. No.989EX300).

[2]  Ken Turkowski,et al.  Filters for common resampling tasks , 1990 .

[3]  Arun N. Netravali,et al.  Reconstruction filters in computer-graphics , 1988, SIGGRAPH.

[4]  Guido Gerig,et al.  3D Multi-scale line filter for segmentation and visualization of curvilinear structures in medical images , 1997, CVRMed.

[5]  William H. Press,et al.  Numerical recipes in C , 2002 .

[6]  László Neumann,et al.  Gradient Estimation in Volume Data using 4D Linear Regression , 2000, Comput. Graph. Forum.

[7]  Jiri Hladuvka.  Derivatives and Eigensystems for Volume-Data Analysis and Visualization , 2001 .

[8]  Raghu Machiraju,et al.  Reconstruction Error Characterization and Control: A Sampling Theory Approach , 1996, IEEE Trans. Vis. Comput. Graph..

[9]  Markus Hadwiger,et al.  Hardware-Accelerated High-Quality Reconstruction on PC Hardware , 2001, VMV.

[10]  H. Hauser,et al.  Mastering Windows: Improving Reconstruction , 2000, 2000 IEEE Symposium on Volume Visualization (VV 2000).

[11]  Marc Levoy,et al.  Display of surfaces from volume data , 1988, IEEE Computer Graphics and Applications.

[12]  J. A. Parker,et al.  Comparison of Interpolating Methods for Image Resampling , 1983, IEEE Transactions on Medical Imaging.

[13]  David Marr,et al.  VISION A Computational Investigation into the Human Representation and Processing of Visual Information , 2009 .

[14]  Victoria Interrante,et al.  Illustrating surface shape in volume data via principal direction-driven 3D line integral convolution , 1997, SIGGRAPH.

[15]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[16]  Valerio Pascucci,et al.  The contour spectrum , 1997, Proceedings. Visualization '97 (Cat. No. 97CB36155).

[17]  Rafael Wiemker,et al.  Fast detection of meaningful isosurfaces for volume data visualization , 2001, Proceedings Visualization, 2001. VIS '01..

[18]  Thomas Malzbender,et al.  Frequency Analysis of Gradient Estimators in Volume Rendering , 1996, IEEE Trans. Vis. Comput. Graph..

[19]  Klaus Mueller,et al.  A comparison of normal estimation schemes , 1997 .

[20]  R. Keys.  Cubic convolution interpolation for digital image processing , 1981 .

[21]  Carl-Fredrik Westin,et al.  Tissue Classification Based on 3D Local Intensity Structures for Volume Rendering , 2000, IEEE Trans. Vis. Comput. Graph..

[22]  Hanspeter Pfister,et al.  Cube-4-a scalable architecture for real-time volume rendering , 1996, Proceedings of 1996 Symposium on Volume Visualization.

[23]  Gérard G. Medioni,et al.  Robust estimation of curvature information from noisy 3D data for shape description , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[24]  Roger Crawfis,et al.  Spatial domain filter design , 1999 .

[25]  Guido Gerig,et al.  Three-dimensional multi-scale line filter for segmentation and visualization of curvilinear structures in medical images , 1998, Medical Image Anal..

[26]  Robert A. Schowengerdt,et al.  Image reconstruction by parametric cubic convolution , 1982, Comput. Graph. Image Process..

[27]  Donald E. Troxel,et al.  Transformation Between Continuous and Discrete Representations of Images: A Perceptual Approach , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[28]  T. Moller,et al.  Design of accurate and smooth filters for function and derivative reconstruction , 1998, IEEE Symposium on Volume Visualization (Cat. No.989EX300).

[29]  Klaus Mueller,et al.  Evaluation and Design of Filters Using a Taylor Series Expansion , 1997, IEEE Trans. Vis. Comput. Graph..

[30]  Alejandro F. Frangi,et al.  Muliscale Vessel Enhancement Filtering , 1998, MICCAI.

[31]  Steve Marschner,et al.  An evaluation of reconstruction filters for volume rendering , 1994, Proceedings Visualization '94.

[32]  Eduard Gröller,et al.  Smallest second-order derivatives for efficient volume-data representation , 2002, Comput. Graph..

[33]  Max A. Viergever,et al.  Quantitative evaluation of convolution-based methods for medical image interpolation , 2001, Medical Image Anal..