A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Algorithms for Low-Level Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimal filter for edge detection methods and results
ECCV 90 Proceedings of the first european conference on Computer vision
Recursive Regularization Filters: Design, Properties, and Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Biased anisotropic diffusion: a unified regularization and diffusion approach to edge detection
Image and Vision Computing - Special issue on the first ECCV 1990
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Regularization, Scale-Space, and Edge Detection Filters
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume II - Volume II
A Regularized Solution to Edge Detection
A Regularized Solution to Edge Detection
Relations Between Regularization and Diffusion Filtering
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
International Journal of Computer Vision - Joint special issue on image analysis
Graduated Nonconvexity by Functional Focusing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Reconstructing Surfaces by Volumetric Regularization Using Radial Basis Functions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space Properties of Regularization Methods
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
The Hausdorff Dimension and Scale-Space Normalisation of Natural Images
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
A fast multi-scale edge detection algorithm
Pattern Recognition Letters
Vector-Valued Image Regularization with PDEs: A Common Framework for Different Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Correction for the Dislocation of Curved Surfaces Caused by the PSF in 2D and 3D CT Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Anisotropic Smoothing of Multi-Valued Images using Curvature-Preserving PDE's
International Journal of Computer Vision
Splines in Higher Order TV Regularization
International Journal of Computer Vision
Algorithmic Differentiation: Application to Variational Problems in Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
On the Rate of Structural Change in Scale Spaces
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Mumford-Shah regularizer with contextual feedback
Journal of Mathematical Imaging and Vision
On the accuracy of image normalization by Zernike moments
Image and Vision Computing
Reconstructing the optical thickness from Hoffman modulation contrast images
SCIA'03 Proceedings of the 13th Scandinavian conference on Image analysis
Equivalence results for TV diffusion and TV regularisation
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
On the statistical interpretation of the piecewise smooth Mumford-Shah functional
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Review article: Edge and line oriented contour detection: State of the art
Image and Vision Computing
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part II
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Regularity and scale-space properties of fractional high order linear filtering
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Relations between higher order TV regularization and support vector regression
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Curvature-Preserving regularization of multi-valued images using PDE's
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
A unified image registration framework for ITK
WBIR'12 Proceedings of the 5th international conference on Biomedical Image Registration
Hi-index | 0.00 |
Computational vision often needs to deal with derivatives ofdigital images. Such derivatives are not intrinsic properties ofdigital data; a paradigm is required to make them well-defined.Normally, a linear filtering is applied. This can be formulated interms of scale-space, functional minimization, or edge detectionfilters. The main emphasis of this paper is to connect these theoriesin order to gain insight in their similarities and differences. We donot want, in this paper, to take part in any discussion of how edgedetection must be performed, but will only link some of the current theories. We take regularization (or functional minimization) as astarting point, and show that it boils down to Gaussian scale-space ifwe require scale invariance and a semi-group constraint to besatisfied. This regularization implies the minimization of afunctional containing terms up to infinite order of differentiation.If the functional is truncated at second order, the Canny-Deriche filter arises. It is also shown that higher dimensional regularizationboils down to a rotated version of the one dimensional case, whenCartesian invariance is imposed and the image is vanishing at theborders. This means that the results from 1D regularization can beeasily generalized to higher dimensions. Finally we show how anefficient implementation of regularization of order n can be made byrecursive filtering using 2n multiplications and additions peroutput element without introducing any approximation.