Smoothing and matching of 3-D space curves

Andre P. Gueziec; Nicholas Ayache

doi:10.1117/12.131083

22 September 1992 Smoothing and matching of 3-D space curves

Andre P. Gueziec, Nicholas Ayache

Proceedings Volume 1808, Visualization in Biomedical Computing '92; (1992) https://doi.org/10.1117/12.131083
Event: Visualization in Biomedical Computing, 1992, Chapel Hill, NC, United States

Abstract

We present a new approach to the problem of matching 3-D curves. The approach has an algorithmic complexity sublinear with the number of models, and can operate in the presence of noise and partial occlusions. We make use of non-uniform B-spline approximations, which permits us to better retain information at high curvature locations. The spline approximations are controlled (i.e., regularized) by making use of normal vectors to the surface in 3-D on which the curves lie, and by an explicit minimization of a bending energy. These measures allow a more accurate estimation of position, curvature, torsion, and Frenet frames along the curve. The computational complexity of the recognition process is considerably decreased with explicit use of the Frenet frame for hypotheses generation. As opposed to previous approaches, the method better copes with partial occlusion. Moreover, following a statistical study of the curvature and torsion covariances, we optimize the hash table discretization and discover improved invariants for recognition, different than the torsion measure. Finally, knowledge of invariant uncertainties is used to compute an optimal global transformation using an extended Kalman filter. We present experimental results using synthetic data and also using characteristic curves extracted from 3-D medical images. An earlier version of this paper was presented at ECCV'92.

Citation Download Citation

Andre P. Gueziec and Nicholas Ayache "Smoothing and matching of 3-D space curves", Proc. SPIE 1808, Visualization in Biomedical Computing '92, (22 September 1992); https://doi.org/10.1117/12.131083

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available