Visual reconstruction
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A common framework for image segmentation
International Journal of Computer Vision
A Hamiltonian Approach to the Eikonal Equation
EMMCVPR '99 Proceedings of the Second International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Image Parsing: Unifying Segmentation, Detection, and Recognition
International Journal of Computer Vision
Neural Computation
Medial Representations: Mathematics, Algorithms and Applications
Medial Representations: Mathematics, Algorithms and Applications
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
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Deformable templates using large deformation kinematics
IEEE Transactions on Image Processing
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The complex wave representation (CWR) converts unsigned 2D distance transforms into their corresponding wave functions. The underlying motivation for performing this maneuver is as follows: the normalized power spectrum of the wave function is an excellent approximation (at small values of Planck's constant--here a free parameter τ) to the density function of the distance transform gradients. Or in colloquial terms, spatial frequencies are gradient histogram bins. Since the distance transform gradients have only orientation information, the Fourier transform values mainly lie on the unit circle in the spatial frequency domain. We use the higher-order stationary phase approximation to prove this result and then provide empirical confirmation at low values of τ. The result indicates that the CWR of distance transforms is an intriguing and novel shape representation.