Three-dimensional object recognition
ACM Computing Surveys (CSUR) - Annals of discrete mathematics, 24
Shape and motion of nonrigid bodies
Computer Vision, Graphics, and Image Processing
Numerical recipes in C: the art of scientific computing
Numerical recipes in C: the art of scientific computing
Hyperquadrics: smoothly deformable shapes with convex polyhedral bounds
Computer Vision, Graphics, and Image Processing
Epicardial surface estimation from coronary angiograms
Computer Vision, Graphics, and Image Processing
Recovery of Parametric Models from Range Images: The Case for Superquadrics with Global Deformations
IEEE Transactions on Pattern Analysis and Machine Intelligence
On Three-Dimensional Surface Reconstruction Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
Three-dimensional shape representation
Handbook of pattern recognition and image processing (vol. 2)
Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Parametric Model Fitting: From Inlier Characterization to Outlier Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Description of three-dimensional gray-level objects by the harmonic analysis approach
Pattern Recognition Letters
Spherical Diffusion for 3D Surface Smoothing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Detection of Deformable Objects in 3D Images Using Markov-Chain Monte Carlo and Spherical Harmonics
MICCAI '08 Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention, Part II
Representing images of a rotating object with cyclic permutation for view-based pose estimation
Computer Vision and Image Understanding
Sparse representation of deformable 3D organs with spherical harmonics and structured dictionary
Journal of Biomedical Imaging - Special issue on Machine Learning in Medical Imaging
Surface alignment of 3d spherical harmonic models: application to cardiac MRI analysis
MICCAI'05 Proceedings of the 8th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Non-rigid shape comparison of implicitly-defined curves
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
| Hi-index | 0.14 |
The use of spherical harmonics for rigid and nonrigid shape representation is well known. This paper extends the method to surface harmonics defined on domains other than the sphere and to four-dimensional spherical harmonics. These harmonics enable us to represent shapes which cannot be represented as a global function in spherical coordinates, but can be in other coordinate systems. Prolate and oblate spheroidal harmonics and cylindrical harmonics are examples of surface harmonics which we find useful. Nonrigid shapes are represented as functions of space and time either by including the time-dependence as a separate factor or by using four-dimensional spherical harmonics. This paper compares the errors of fitting various surface harmonics to an assortment of synthetic and real data samples, both rigid and nonrigid. In all cases we use a linear least-squares approach to find the best fit to given range data. It is found that for some shapes there is a variation among geometries in the number of harmonics functions needed to achieve a desired accuracy. In particular, it was found that four-dimensional spherical harmonics provide an improved model of the motion of the left ventricle of the heart.