Scaling Theorems for Zero Crossings
IEEE Transactions on Pattern Analysis and Machine Intelligence
Uniqueness of the Gaussian Kernel for Scale-Space Filtering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space for Discrete Signals
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Design and Use of Steerable Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Generic Neighborhood Operators
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale and the differential structure of images
Image and Vision Computing - Special issue: information processing in medical imaging 1991
Steerable-scalable kernels for edge detection and junction analysis
Image and Vision Computing - Special issue: 2nd European Conference on Computer Vision
ECCV '94 Proceedings of the third European conference on Computer vision (vol. 1)
Recursive Filters for Optical Flow
IEEE Transactions on Pattern Analysis and Machine Intelligence
Direct computation of shape cues using scale-adapted spatial derivative operators
International Journal of Computer Vision - Special issue: machine vision research at the Royal Institute of Technology
The Intrinsic Structure of Optic Flow Incorporating Measurement Duality
International Journal of Computer Vision
Affine Invariant Texture Segmentation and Shape from Texture by Variational Methods
Journal of Mathematical Imaging and Vision
Feature Detection with Automatic Scale Selection
International Journal of Computer Vision
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Linear Scale-Space has First been Proposed in Japan
Journal of Mathematical Imaging and Vision
An Extended Class of Scale-Invariant and Recursive Scale Space Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Spatiotemporally Adaptive Estimation and Segmenation of OF-Fields
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume II - Volume II
Scale-Space with Casual Time Direction
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume I - Volume I
Time-Recursive Velocity-Adapted Spatio-Temporal Scale-Space Filters
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
On Automatic Selection of Temporal Scales in Time-Causal Scale-Space
AFPAC '97 Proceedings of the International Workshop on Algebraic Frames for the Perception-Action Cycle
Linear Spatio-Temporal Scale-Space
SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
A representation for visual information with application to machine vision
A representation for visual information with application to machine vision
Matching Widely Separated Views Based on Affine Invariant Regions
International Journal of Computer Vision
On the Axioms of Scale Space Theory
Journal of Mathematical Imaging and Vision
The Monogenic Scale-Space: A Unifying Approach to Phase-Based Image Processing in Scale-Space
Journal of Mathematical Imaging and Vision
Scale & Affine Invariant Interest Point Detectors
International Journal of Computer Vision
Galilean-Diagonalized Spatio-Temporal Interest Operators
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 1 - Volume 01
International Journal of Computer Vision
Local velocity-adapted motion events for spatio-temporal recognition
Computer Vision and Image Understanding
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
α scale spaces on a bounded domain
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
A morphological, affine, and Galilean invariant scale-space for movies
IEEE Transactions on Image Processing
Fingerprint enhancement by shape adaptation of scale-space operators with automatic scale selection
IEEE Transactions on Image Processing
Volumetric nonlinear anisotropic diffusion on GPUs
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Full length article: Singular integrals, scale-space and wavelet transforms
Journal of Approximation Theory
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This paper describes a generalized axiomatic scale-space theory that makes it possible to derive the notions of linear scale-space, affine Gaussian scale-space and linear spatio-temporal scale-space using a similar set of assumptions (scale-space axioms).The notion of non-enhancement of local extrema is generalized from previous application over discrete and rotationally symmetric kernels to continuous and more general non-isotropic kernels over both spatial and spatio-temporal image domains. It is shown how a complete classification can be given of the linear (Gaussian) scale-space concepts that satisfy these conditions on isotropic spatial, non-isotropic spatial and spatio-temporal domains, which results in a general taxonomy of Gaussian scale-spaces for continuous image data. The resulting theory allows filter shapes to be tuned from specific context information and provides a theoretical foundation for the recently exploited mechanisms of shape adaptation and velocity adaptation, with highly useful applications in computer vision.It is also shown how time-causal spatio-temporal scale-spaces can be derived from similar assumptions. The mathematical structure of these scale-spaces is analyzed in detail concerning transformation properties over space and time, the temporal cascade structure they satisfy over time as well as properties of the resulting multi-scale spatio-temporal derivative operators. It is also shown how temporal derivatives with respect to transformed time can be defined, leading to the formulation of a novel analogue of scale normalized derivatives for time-causal scale-spaces.The kernels generated from these two types of theories have interesting relations to biological vision. We show how filter kernels generated from the Gaussian spatio-temporal scale-space as well as the time-causal spatio-temporal scale-space relate to spatio-temporal receptive field profiles registered from mammalian vision. Specifically, we show that there are close analogies to space-time separable cells in the LGN as well as to both space-time separable and non-separable cells in the striate cortex. We do also present a set of plausible models for complex cells using extended quasi-quadrature measures expressed in terms of scale normalized spatio-temporal derivatives.The theories presented as well as their relations to biological vision show that it is possible to describe a general set of Gaussian and/or time-causal scale-spaces using a unified framework, which generalizes and complements previously presented scale-space formulations in this area.