A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Idempotent one-sided approximation of median smoothers
Journal of Approximation Theory
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
An Introduction to Nonlinear Image Processing
An Introduction to Nonlinear Image Processing
Idempotent and co-idempotent stack filters and min-max operators
Theoretical Computer Science
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
A Lattice Approach to Image Segmentation
Journal of Mathematical Imaging and Vision
Exact and asymptotic distributions of LULU smoothers
Journal of Computational and Applied Mathematics - Special issue: Jef Teugels
Discrete Pulse Transform of Images
ICISP '08 Proceedings of the 3rd international conference on Image and Signal Processing
Fast digital locally monotonic regression
IEEE Transactions on Signal Processing
The Roadmaker's Algorithm for the Discrete Pulse Transform
IEEE Transactions on Image Processing
3D shape from focus using LULU operators
ACIVS'12 Proceedings of the 14th international conference on Advanced Concepts for Intelligent Vision Systems
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The LULU operators for sequences, that is Ln, Un and their compositions, are extended to multidimensional arrays in a way which preserves their essential properties, e.g., consistent separation, total variation and shape preservation. The power of the operators is demonstrated by deriving the discrete pulse transform (DPT), which is a hierarchical decomposition of the input array into pulses. Similar to its 1-D counterpart this transform satisfies a basic consistency property.