Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Solid shape
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Tracking level sets by level sets: a method for solving the shape from shading problem
Computer Vision and Image Understanding
International Journal of Computer Vision
Scale-Space Properties of the Multiscale Morphological Dilation-Erosion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computable elastic distances between shapes
SIAM Journal on Applied Mathematics
Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford-Shah Functional
International Journal of Computer Vision
International Journal of Computer Vision
A Distance for Elastic Matching in Object Recognition
ICPR '96 Proceedings of the 1996 International Conference on Pattern Recognition (ICPR '96) Volume I - Volume 7270
A Geometric Approach to Segmentation and Analysis of 3D Medical Images
MMBIA '96 Proceedings of the 1996 Workshop on Mathematical Methods in Biomedical Image Analysis (MMBIA '96)
Analysis of Planar Shapes Using Geodesic Paths on Shape Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
2D-shape analysis using conformal mapping
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Generation of myocardial wall surface meshes from Segmented MRI
Journal of Biomedical Imaging
Hi-index | 0.00 |
We present a novel representation of shape for closed contours in 驴2 or for compact surfaces in 驴3 explicitly designed to possess a linear structure. This greatly simplifies linear operations such as averaging, principal component analysis or differentiation in the space of shapes when compared to more common embedding choices such as the signed distance representation linked to the nonlinear Eikonal equation. The specific choice of implicit linear representation explored in this article is the class of harmonic functions over an annulus containing the contour. The idea is to represent the contour as closely as possible by the zero level set of a harmonic function, thereby linking our representation to the linear Laplace equation. We note that this is a local represenation within the space of closed curves as such harmonic functions can generally be defined only over a neighborhood of the embedded curve. We also make no claim that this is the only choice or even the optimal choice within the class of possible linear implicit representations. Instead, our intent is to show how linear analysis of shape is greatly simplified (and sensible) when such a linear representation is employed in hopes to inspire new ideas and additional research into this type of linear implicit representations for curves. We conclude by showing an application for which our particular choice of harmonic representation is ideally suited.