Multi-Scale Surface Descriptors

Local shape descriptors compactly characterize regions of a surface, and have been applied to tasks in visualization, shape matching, and analysis. Classically, curvature has be used as a shape descriptor; however, this differential property characterizes only an infinitesimal neighborhood. In this paper, we provide shape descriptors for surface meshes designed to be multi-scale, that is, capable of characterizing regions of varying size. These descriptors capture statistically the shape of a neighborhood around a central point by fitting a quadratic surface. They therefore mimic differential curvature, are efficient to compute, and encode anisotropy. We show how simple variants of mesh operations can be used to compute the descriptors without resorting to expensive parameterizations, and additionally provide a statistical approximation for reduced computational cost. We show how these descriptors apply to a number of uses in visualization, analysis, and matching of surfaces, particularly to tasks in protein surface analysis.

[1]  Stefan Gumhold,et al.  Maximum entropy light source placement , 2002, IEEE Visualization, 2002. VIS 2002..

[2]  W. Todd Wipke,et al.  Quadratic Shape Descriptors. 1. Rapid Superposition of Dissimilar Molecules Using Geometrically Invariant Surface Descriptors , 2000, J. Chem. Inf. Comput. Sci..

[3]  John C. Hart,et al.  Seamster: inconspicuous low-distortion texture seam layout , 2002, IEEE Visualization, 2002. VIS 2002..

[4]  Marcel Körtgen,et al.  3D Shape Matching with 3D Shape Contexts , 2003 .

[5]  Victoria Interrante,et al.  Line direction matters: an argument for the use of principal directions in 3D line drawings , 2000, NPAR '00.

[6]  Steven J. Gortler,et al.  Fast exact and approximate geodesics on meshes , 2005, ACM Trans. Graph..

[7]  Pascal Barla,et al.  Apparent relief: a shape descriptor for stylized shading , 2008, NPAR.

[8]  Vaughan R. Pratt,et al.  Direct least-squares fitting of algebraic surfaces , 1987, SIGGRAPH.

[9]  Andrew E. Johnson,et al.  Spin-Images: A Representation for 3-D Surface Matching , 1997 .

[10]  Amitabh Varshney,et al.  Geometry-dependent lighting , 2006, IEEE Transactions on Visualization and Computer Graphics.

[11]  Joonki Paik,et al.  Normal Vector Voting: Crease Detection and Curvature Estimation on Large, Noisy Meshes , 2002, Graph. Model..

[12]  Jarek Rossignac,et al.  Blowing Bubbles for Multi-Scale Analysis and Decomposition of Triangle Meshes , 2003, Algorithmica.

[13]  Szymon Rusinkiewicz,et al.  Illustration of complex real-world objects using images with normals , 2007, NPAR '07.

[14]  Ross T. Whitaker,et al.  Partitioning 3D Surface Meshes Using Watershed Segmentation , 1999, IEEE Trans. Vis. Comput. Graph..

[15]  Cindy Grimm,et al.  Estimating Curvature on Triangular Meshes , 2006, Int. J. Shape Model..

[16]  Chin Seng Chua,et al.  Point Signatures: A New Representation for 3D Object Recognition , 1997, International Journal of Computer Vision.

[17]  Michael Garland,et al.  Curvature maps for local shape comparison , 2005, International Conference on Shape Modeling and Applications 2005 (SMI' 05).

[18]  Peter J. Huber,et al.  Robust Statistics , 2005, Wiley Series in Probability and Statistics.

[19]  Daniel Cohen-Or,et al.  Salient geometric features for partial shape matching and similarity , 2006, TOGS.

[20]  Feng Dong,et al.  Surface hatching for medical volume data , 2005, International Conference on Computer Graphics, Imaging and Visualization (CGIV'05).

[21]  B. Ripley,et al.  Robust Statistics , 2018, Encyclopedia of Mathematical Geosciences.

[22]  Ross T. Whitaker,et al.  Curvature-based transfer functions for direct volume rendering: methods and applications , 2003, IEEE Visualization, 2003. VIS 2003..

[23]  Samuel R. Buss,et al.  Spherical averages and applications to spherical splines and interpolation , 2001, TOGS.

[24]  Sylvain Petitjean,et al.  A survey of methods for recovering quadrics in triangle meshes , 2002, CSUR.

[25]  Victoria Interrante,et al.  A novel cubic-order algorithm for approximating principal direction vectors , 2004, TOGS.

[26]  Brian B. Goldman,et al.  QSD quadratic shape descriptors. 2. Molecular docking using quadratic shape descriptors (QSDock) , 2000, Proteins.

[27]  John G. Griffiths,et al.  Least squares ellipsoid specific fitting , 2004, Geometric Modeling and Processing, 2004. Proceedings.

[28]  C. Grimm,et al.  Interactive decal compositing with discrete exponential maps , 2006, SIGGRAPH 2006.

[29]  Adam Finkelstein,et al.  Suggestive contours for conveying shape , 2003, ACM Trans. Graph..

[30]  D. Souvaine,et al.  An intuitive approach to measuring protein surface curvature , 2005, Proteins.

[31]  Derek Nowrouzezahrai,et al.  Data-driven curvature for real-time line drawing of dynamic scenes , 2009, ACM Trans. Graph..

[32]  Ernest M. Stokely,et al.  Surface Parametrization and Curvature Measurement of Arbitrary 3-D Objects: Five Practical Methods , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[33]  Guillermo Sapiro,et al.  Texture Synthesis for 3D Shape Representation , 2003, IEEE Trans. Vis. Comput. Graph..

[34]  Jean-Claude Spehner,et al.  Fast and robust computation of molecular surfaces , 1995, SCG '95.

[35]  Adam Finkelstein,et al.  Real-time hatching , 2001, SIGGRAPH.

[36]  Rafael C. González,et al.  Local Determination of a Moving Contrast Edge , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[37]  Szymon Rusinkiewicz,et al.  Estimating curvatures and their derivatives on triangle meshes , 2004, Proceedings. 2nd International Symposium on 3D Data Processing, Visualization and Transmission, 2004. 3DPVT 2004..