Implicit surface visualization of reconstructed biological molecules

An implicit surface of a density function is the set of points at which the value of the function is equal to a fixed threshold. An object that is defined as the collection of points at which the density function value is above the threshold can be visualized by displaying the implicit surface. Some methods for the reconstruction of biological macromolecules from their electron microscopic projections produce density functions that are specified by a linear combination of smoothly-varying radially-symmetric basis functions of finite support, also known as blobs. When density functions are determined by such a blob representation, the implicit surfaces are smoothly varying and the normal at any point on such a surface can be analytically calculated. This property can be utilized to produce high-quality visualizations by raycasting. While raycasting tends to be computationally expensive, we present a methodology that uses techniques of computer graphics and image processing to significantly reduce the cost of visualization.

[1]  Shigeru Muraki,et al.  Multiscale Volume Representation by a DoG Wavelet , 1995, IEEE Trans. Vis. Comput. Graph..

[2]  Matthias Zwicker,et al.  Surface splatting , 2001, SIGGRAPH.

[3]  R M Lewitt,et al.  Multidimensional digital image representations using generalized Kaiser-Bessel window functions. , 1990, Journal of the Optical Society of America. A, Optics and image science.

[4]  J. van Leeuwen,et al.  Theoretical Computer Science , 2003, Lecture Notes in Computer Science.

[5]  Cornelius T. Leondes,et al.  Medical Imaging Systems Techniques and Applications , 1998 .

[6]  Teresa Ruiz,et al.  The DnaB·DnaC complex: a structure based on dimers assembled around an occluded channel , 2001, The EMBO journal.

[7]  Robert M. Lewitt,et al.  Practical considerations for 3-D image reconstruction using spherically symmetric volume elements , 1996, IEEE Trans. Medical Imaging.

[8]  A Leith,et al.  SPIDER and WEB: processing and visualization of images in 3D electron microscopy and related fields. , 1996, Journal of structural biology.

[9]  Xiaogang Jin,et al.  Subdivision interpolating implicit surfaces , 2003, Comput. Graph..

[10]  A. Ardeshir Goshtasby,et al.  Approximating Digital 3D Shapes by Rational Gaussian Surfaces , 2003, IEEE Trans. Vis. Comput. Graph..

[11]  J M Carazo,et al.  Three-dimensional reconstruction from reduced sets of very noisy images acquired following a single-axis tilt schema: application of a new three-dimensional reconstruction algorithm and objective comparison with weighted backprojection. , 1997, Journal of structural biology.

[12]  Gordon L. Kindlmann,et al.  Hue-balls and lit-tensors for direct volume rendering of diffusion tensor fields , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

[13]  T. N. Bhat,et al.  The Protein Data Bank , 2000, Nucleic Acids Res..

[14]  Lloyd Treinish,et al.  An extended data-flow architecture for data analysis and visualization , 1995, COMG.

[15]  J M Carazo,et al.  3D reconstruction in electron microscopy using ART with smooth spherically symmetric volume elements (blobs). , 1998, Ultramicroscopy.

[16]  Markus Wagner,et al.  Interactive Rendering with Coherent Ray Tracing , 2001, Comput. Graph. Forum.

[17]  Matthias Zwicker,et al.  3 Ideal Resampling 3 . 1 Sampling and Aliasing , 2022 .

[18]  W. Kühlbrandt,et al.  Bacteriorhodopsin — the movie , 2000, Nature.

[19]  Geoff Wyvill,et al.  Data structure forsoft objects , 1986, The Visual Computer.

[20]  Roger Phillips,et al.  Implicit Fitting Using Radial Basis Functions with Ellipsoid Constraint , 2004, Comput. Graph. Forum.

[21]  William E. Lorensen,et al.  The Transfer Function Bake-Off , 2001, IEEE Computer Graphics and Applications.

[22]  Marc Alexa,et al.  Computing and Rendering Point Set Surfaces , 2003, IEEE Trans. Vis. Comput. Graph..

[23]  Arie E. Kaufman,et al.  Mixing translucent polygons with volumes , 1999, Proceedings Visualization '99 (Cat. No.99CB37067).

[24]  Richard K. Beatson,et al.  Reconstruction and representation of 3D objects with radial basis functions , 2001, SIGGRAPH.

[25]  Alan Watt,et al.  3D Computer Graphics , 1993 .

[26]  Eduard Gröller,et al.  Two-Level Volume Rendering , 2001, IEEE Trans. Vis. Comput. Graph..

[27]  Robert M. Lewitt,et al.  A comparison of transform and iterative reconstruction techniques for a volume-imaging PET scanner with a large axial acceptance angle , 1995 .

[28]  William E. Lorensen,et al.  Surface Rendering Versus Volume Rendering In Medical Imaging: Techniques And Applications , 1996, Proceedings of Seventh Annual IEEE Visualization '96.

[29]  G J Williams,et al.  The Protein Data Bank: a computer-based archival file for macromolecular structures. , 1978, Archives of biochemistry and biophysics.

[30]  In-Kwon Lee,et al.  Component-based polygonal approximation of soft objects , 2001, Comput. Graph..

[31]  John C. Hart,et al.  Sphere tracing: a geometric method for the antialiased ray tracing of implicit surfaces , 1996, The Visual Computer.

[32]  Devendra Kalra,et al.  Guaranteed ray intersections with implicit surfaces , 1989, SIGGRAPH.

[33]  T. K. Narayan,et al.  Evaluation of task-oriented performance of several fully 3D PET reconstruction algorithms. , 1994, Physics in medicine and biology.

[34]  Chandrajit L. Bajaj,et al.  Spline Approximations of Real Algebraic Surfaces , 1997, J. Symb. Comput..

[35]  James F. O'Brien,et al.  Shape transformation using variational implicit functions , 1999, SIGGRAPH Courses.

[36]  David Middleton,et al.  Sampling and Reconstruction of Wave-Number-Limited Functions in N-Dimensional Euclidean Spaces , 1962, Inf. Control..

[37]  Jon C. Helton,et al.  Numerical methods in engineering and science , 1986 .

[38]  Peter D. Richardson,et al.  Numerical Methods in Engineering and Science , 1987 .

[39]  Brian Wyvill,et al.  Introduction to Implicit Surfaces , 1997 .

[40]  James F. Blinn,et al.  A generalization of algebraic surface drawing , 1982, SIGGRAPH.

[41]  R. Lewitt.  Alternatives to voxels for image representation in iterative reconstruction algorithms , 1992, Physics in medicine and biology.

[43]  J. Frank.  Three-Dimensional Electron Microscopy of Macromolecular Assemblies , 2006 .

[44]  AbramGreg,et al.  An extended data-flow architecture for data analysis and visualization , 1995 .

[45]  Samuel Matej,et al.  A comparison of transform and iterative reconstruction techniques for a volume-imaging PET scanner with a large axial acceptance angle , 1994, Proceedings of 1994 IEEE Nuclear Science Symposium - NSS'94.

[46]  Edgar Garduño,et al.  Optimization of basis functions for both reconstruction and visualization , 2001, IWCIA.

[47]  Samir Akkouche,et al.  Incremental Polygonization of Implicit Surfaces , 2000, Graph. Model..

[48]  Samir Akkouche,et al.  Adaptive Implicit Surface Polygonization Using Marching Triangles , 2001, Comput. Graph. Forum.

[49]  Adi Ben-Israel,et al.  Generalized inverses: theory and applications , 1974 .

[50]  Marco,et al.  Xmipp: An Image Processing Package for Electron Microscopy , 1996, Journal of structural biology.

[51]  D. P. Mitchell.  Robust ray intersection with interval arithmetic , 1990 .

[52]  Gabor T. Herman,et al.  ALGEBRAIC RECONSTRUCTION TECHNIQUES IN MEDICAL IMAGING , 1998 .

[53]  Kellogg S. Booth,et al.  Report from the chair , 1986 .

[54]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[55]  Gordon L. Kindlmann,et al.  Strategies for Direct Volume Rendering of Diffusion Tensor Fields , 2000, IEEE Trans. Vis. Comput. Graph..