Level set surface editing operators
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Multiscale Morphological Segmentations Based on Watershed, Flooding, and Eikonal PDE
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
Nonlinear PDEs and Numerical Algorithms for Modeling Levelings and Reconstruction Filters
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
An Explanation for the Logarithmic Connection between Linear and Morphological System Theory
International Journal of Computer Vision
A Lattice Approach to Image Segmentation
Journal of Mathematical Imaging and Vision
Median and morphological specialized processors for a real-time image data processing
EURASIP Journal on Applied Signal Processing
An Efficient Morphological Active Surface Model for Volumetric Image Segmentation
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
An explanation for the logarithmic connection between linear and morphological systems
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Mathematical morphology in computer graphics, scientific visualization and visual exploration
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Voxel-based assessment of printability of 3D shapes
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
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Image processing via mathematical morphology has traditionally used geometry to intuitively understand morphological signal operators and set or lattice algebra to analyze them in the space domain. We provide a unified view and analytic tools for morphological image processing that is based on ideas from differential calculus and dynamical systems. This includes ideas on using partial differential or difference equations (PDEs) to model distance propagation or nonlinear multiscale processes in images. We briefly review some nonlinear difference equations that implement discrete distance transforms and relate them to numerical solutions of the eikonal equation of optics. We also review some nonlinear PDEs that model the evolution of multiscale morphological operators and use morphological derivatives. Among the new ideas presented, we develop some general 2-D max/min-sum difference equations that model the space dynamics of 2-D morphological systems (including the distance computations) and some nonlinear signal transforms, called slope transforms, that can analyze these systems in a transform domain in ways conceptually similar to the application of Fourier transforms to linear systems. Thus, distance transforms are shown to be bandpass slope filters. We view the analysis of the multiscale morphological PDEs and of the eikonal PDE solved via weighted distance transforms as a unified area in nonlinear image processing, which we call differential morphology, and briefly discuss its potential applications to image processing and computer vision