Geodesics between 3d closed curves using path-straightening

Authors:
Eric Klassen;Anuj Srivastava
Affiliations:
Department of Mathematics, Florida State University, Tallahassee, FL;Department of Statistics, Florida State University, Tallahassee, FL
Venue:
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
Year:
2006

Citing 7
Cited 16

Computational anatomy: an emerging discipline

Quarterly of Applied Mathematics - Special issue on current and future challenges in the applications of mathematics
Matching 3D Models with Shape Distributions

SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
A Geometric Approach to 3D Object Comparison

SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces

IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape representations and algorithms for three-dimensional model retrieval

Shape representations and algorithms for three-dimensional model retrieval
Three-Dimensional Face Recognition

International Journal of Computer Vision
Elastic-string models for representation and analysis of planar shapes

CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition

Intrinsic Bayesian Active Contours for Extraction of Object Boundaries in Images

International Journal of Computer Vision
An Intrinsic Framework for Analysis of Facial Surfaces

International Journal of Computer Vision
Shape of Elastic Strings in Euclidean Space

International Journal of Computer Vision
Elastic Shape Models for Face Analysis Using Curvilinear Coordinates

Journal of Mathematical Imaging and Vision
Nasal Region Contribution in 3D Face Biometrics Using Shape Analysis Framework

ICB '09 Proceedings of the Third International Conference on Advances in Biometrics
Elastic Morphing of 2D and 3D Objects on a Shape Manifold

ICIAR '09 Proceedings of the 6th International Conference on Image Analysis and Recognition
Removing shape-preserving transformations in square-root elastic (SRE) framework for shape analysis of curves

EMMCVPR'07 Proceedings of the 6th international conference on Energy minimization methods in computer vision and pattern recognition
Local visual patch for 3d shape retrieval

Proceedings of the ACM workshop on 3D object retrieval
Manifold valued statistics, exact principal, geodesic analysis and the effect of linear, approximations

ECCV'10 Proceedings of the 11th European conference on Computer vision: Part VI
Silhouette-based gesture and action recognition via modeling trajectories on Riemannian shape manifolds

Computer Vision and Image Understanding
Shape analysis of local facial patches for 3D facial expression recognition

Pattern Recognition
Shape matching by variational computation of geodesics on a manifold

DAGM'06 Proceedings of the 28th conference on Pattern Recognition
On advances in differential-geometric approaches for 2D and 3D shape analyses and activity recognition

Image and Vision Computing
Selecting 3D curves on the nasal surface using AdaBoost for person authentication

EG 3DOR'11 Proceedings of the 4th Eurographics conference on 3D Object Retrieval
Statistical analysis of manual segmentations of structures in medical images

Computer Vision and Image Understanding
Elastic shapes models for improving segmentation of object boundaries in synthetic aperture sonar images

Computer Vision and Image Understanding

Quantified Score

Hi-index	0.00

Visualization

Abstract

In order to analyze shapes of continuous curves in ℝ3, we parameterize them by arc-length and represent them as curves on a unit two-sphere. We identify the subset denoting the closed curves, and study its differential geometry. To compute geodesics between any two such curves, we connect them with an arbitrary path, and then iteratively straighten this path using the gradient of an energy associated with this path. The limiting path of this path-straightening approach is a geodesic. Next, we consider the shape space of these curves by removing shape-preserving transformations such as rotation and re-parametrization. To construct a geodesic in this shape space, we construct the shortest geodesic between the all possible transformations of the two end shapes; this is accomplished using an iterative procedure. We provide step-by-step descriptions of all the procedures, and demonstrate them with simple examples.