Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
The Eikonal equation: some results applicable to computer vision
Shape from shading
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
International Journal of Computer Vision
Shape from shading: level set propagation and viscosity solutions
International Journal of Computer Vision
Extraction of shape skeletons from grayscale images
Computer Vision and Image Understanding
Geometric shock-capturing eno schemes for subpixel interpolation, computation and curve evolution
Graphical Models and Image Processing
Shock Graphs and Shape Matching
International Journal of Computer Vision
The Morphological Structure of Images: The Differential Equations of Morphological Scale-Space
IEEE Transactions on Pattern Analysis and Machine Intelligence
Complete Dense Stereovision Using Level Set Methods
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
Scale-Space Vector Fields for Feature Analysis
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
A Common Framework for Curve Evolution, Segmentation and Anisotropic Diffusion
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
A Schrödinger Equation for the Fast Computation of Approximate Euclidean Distance Functions
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
A Schrödinger Wave Equation Approach to the Eikonal Equation: Application to Image Analysis
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
The complex wave representation of distance transforms
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
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The eikonal equation and variants of it are of significant interest for problems in computer vision and image processing. It is the basis for continuous versions of mathematical morphology, stereo, shape-from-shading and for recent dynamic theories of shape. Its numerical simulation can be delicate, owing to the formation of singularities in the evolving front, and is typically based on level set methods introduced by Osher and Sethian. However, there are more classical approaches rooted in Hamiltonian physics, which have received little consideration in the computer vision literature. Here the front is interpreted as minimizing a particular action functional. In this context, we introduce a new algorithm for simulating the eikonal equation, which offers a number of computational advantages over the earlier methods. In particular, the locus of shocks is computed in a robust and efficient manner. We illustrate the approach with several numerical examples.