Lindeberg "Temporal scale selection in time-causal scale space", Journal of Mathematical Imaging and Vision, 58 1 : From Wikipedia, the free encyclopedia. When implementing scale-space smoothing in practice there are a number of different approaches that can be taken in terms of continuous or discrete Gaussian smoothing, implementation in the Fourier domain, in terms of pyramids based on binomial filters that approximate the Gaussian or using recursive filters. Machine Intell. It should be noted, however, that not all of these non-linear scale-spaces satisfy similar "nice" theoretical requirements as the linear Gaussian scale-space concept. Namespaces Article Talk. PAMI-8, no. Ikeuchi, EditorSpringer, pages Duits, L. Ridge detection.

A genuinely discrete scale-space theory is developed and its connection to the . for Continuous-Scale B-Splinesand Affine-Invariant Progressive Smoothing. space for 1-D discrete signals comprising a continuous scale parameter, namely by The blurring is shift invariant and does not depend.

Axiomatic theories for continuous and discrete scale-space as well as foveal scale-space. Lindeberg () "Discrete approximations of the affine Gaussian derivative A scale-space theory is developed for auditory signals, showing how Feature detection, automatic scale selection and scale-invariant image features.

Generalized axiomatic scale-space theoryAdvances in Imaging and Electron Physics, Elsevier, volumepages Scale-space theory is a framework for multi-scale signal representation developed by the computer visionimage processing and signal processing communities with complementary motivations from physics and biological vision.

Bretzner "Real-time scale selection in hybrid multi-scale representations", Proc. Specifically, invariance or more appropriately covariance to local geometric transformations, such as rotations or local affine transformations, can be obtained by considering differential invariants under the appropriate class of transformations or alternatively by normalizing the Gaussian derivative operators to a locally determined coordinate frame determined from e.

Video: Affine invariant scale-space for discrete signals Continuous and Discrete Time Signals

Separability is, however, not counted as a scale-space axiom, since it is a coordinate dependent property related to issues of implementation. There exists a generalization of the Gaussian scale-space theory to more general affine and spatio-temporal scale-spaces.

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This overall framework has been applied to a large variety of problems in computer vision, including feature detectionfeature classificationimage segmentationimage matchingmotion estimationcomputation of shape cues and object recognition.
The uniqueness of the Gaussian derivative operators as local operations derived from a scale-space representation can be obtained by similar axiomatic derivations as are used for deriving the uniqueness of the Gaussian kernel for scale-space smoothing. Poggio: Scaling theorems for zero crossings. II, Generalized Gaussian scale-space axiomatics comprising linear scale-space, affine scale-space and spatio-temporal scale-space, Journal of Mathematical Imaging and Vision, Volume 40, Number 1, |

Indeed, this affine scale space can also be expressed from a non-isotropic.

Affine shape adaptation · Scale-space segmentation · Axiomatic theory of receptive fields · v · t · e. In image processing and computer vision, a scale space framework can be used to represent shift invariance.

There has also been work on discrete scale-space concepts that carry the scale-space properties over to the. first processing layer for affine covariant and affine invariant visual scale-space theory for discrete signals and images (Lindeberg [42,

Scale space Scale-space axioms Scale-space implementation Feature detection Edge detection Blob detection Corner detection Ridge detection Interest point detection Scale selection Affine shape adaptation Scale-space segmentation Axiomatic theory of receptive fields v t e.

Namespaces Article Talk. The motivation for generating a scale-space representation of a given data set originates from the basic observation that real-world objects are composed of different structures at different scales. Many scale-space operations show a high degree of similarity with receptive field profiles recorded from the mammalian retina and the first stages in the visual cortex. Furthermore, a detailed analysis of the discrete case shows that the diffusion equation provides a unifying link between continuous and discrete scale spaces, which also generalizes to nonlinear scale spaces, for example, using anisotropic diffusion.

For a computer vision system analysing an unknown scene, there is no way to know a priori what scales are appropriate for describing the interesting structures in the image data.

Baudin, and R.