Distance transformations in digital images
Computer Vision, Graphics, and Image Processing
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A Representation Theory for Morphological Image and Signal Processing
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Multiscanning Approach Based on Morphological Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pattern Spectrum and Multiscale Shape Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
An approximation scheme for the minimum time function
SIAM Journal on Control and Optimization
Toward a computational theory of shape: an overview
ECCV 90 Proceedings of the first european conference on Computer vision
Shading from shape, the eikonal equation solved by grey-weighted distance transform
Pattern Recognition Letters
Decomposition of gray-scale morphological structuring elements
Pattern Recognition
Watersheds in Digital Spaces: An Efficient Algorithm Based on Immersion Simulations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
International Journal of Computer Vision
DigiDu¨rer—a digital engraving system
The Visual Computer: International Journal of Computer Graphics
Morphological systems: slope transforms and max-min difference and differential equations
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Morphological signal processing and the slope transform
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Watershed of a continuous function
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Topographic distance and watershed lines
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Level sets of viscosity solutions: some applications to fronts and rendez-vous problems
SIAM Journal on Applied Mathematics
A simple proof of convergence for an approximation scheme for computing motions by mean curvature
SIAM Journal on Numerical Analysis
Generalized geodesy via geodesic time
Pattern Recognition Letters
Sub-pixel distance maps and weighted distance transforms
Journal of Mathematical Imaging and Vision - Special issue on topology and geometry in computer vision
Chamfer metrics, the medial axis and mathematical morphology
Journal of Mathematical Imaging and Vision - Special issue on topology and geometry in computer vision
A fast level set based algorithm for topology-independent shape modeling
Journal of Mathematical Imaging and Vision - Special issue on topology and geometry in computer vision
Lattice calculus of the morphological slope transform
Signal Processing
Geometric partial differential equations and iterative filtering
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
Robot Vision
A Euclidean Distance Transform Using Grayscale Morphology Decomposition
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Morphological Structure of Images: The Differential Equations of Morphological Scale-Space
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
Evolution equations for continuous-scale morphological filtering
IEEE Transactions on Signal Processing
Differential morphology and image processing
IEEE Transactions on Image Processing
Optimum design of chamfer distance transforms
IEEE Transactions on Image Processing
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In differential morphology, multiscale dilations and erosions are modeled via nonlinear partial differential equations (PDEs) in scale-space. Curve evolution employs methods of differential geometry to study the differential equations governing the propagation of time-evolving curves, under velocities dependent on global information or on local geometric properties of the curve. The PDEs governing multiscale morphology, and most cases of curve evolution, are of the Hamilton-Jacobi type and are related to the eikonal PDE of optics. In this paper, we explore the common theoretical concepts, tools, and numerical algorithms used in differential morphology and curve evolution, by emphasizing level set methods. Morphological operator representations of various curve evolution cases are discussed, as well as evolution laws for various morphological curve operations. We also focus on distance transforms, as the major route to connect differential morphology and curve evolution to the eikonal PDE. Furthermore, we discuss applications of differential morphology and curve evolution to various multiscale and/or eikonal problems, such as distance transform computation, ray tracing in optics, eikonal image halftoning, and watershed-based image segmentation.