Journal ArticleDOI
Implications of invariance and uncertainty for local structure analysis filter sets
Hans Knutsson,Mats Andersson +1 more
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TLDR
The evaluation supports the claim that loglets are preferable to other designs and it is demonstrated that the loglet approach outperforms a Gaussian derivative approach in resolution and robustness.Abstract:
The paper discusses which properties of filter sets used in local structure estimation that are the most important. Answers are provided via the introduction of a number of fundamental invariances. Mathematical formulations corresponding to the required invariances leads up to the introduction of a new class of filter sets termed loglets. Loglets are polar separable and have excellent uncertainty properties. The directional part uses a spherical harmonics basis. Using loglets it is shown how the concepts of quadrature and phase can be defined in n-dimensions. It is also shown how a reliable measure of the certainty of the estimate can be obtained by finding the deviation from the signal model manifold. Local structure analysis algorithms are quite complex and involve a lot more than the filters used. This makes comparisons difficult to interpret from a filter point of view. To reduce the number ‘free’ parameters and target the filter design aspects a number of simple 2D experiments have been carried out. The evaluation supports the claim that loglets are preferable to other designs. In particular it is demonstrated that the loglet approach outperforms a Gaussian derivative approach in resolution and robustness.read more
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References
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Theory of Edge Detection
David Marr,Ellen C. Hildreth +1 more
TL;DR: The theory of edge detection explains several basic psychophysical findings, and the operation of forming oriented zero-crossing segments from the output of centre-surround ∇2G filters acting on the image forms the basis for a physiological model of simple cells.
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The wavelet transform, time-frequency localization and signal analysis
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TL;DR: In this paper, the authors provide a broad overview of Fourier Transform and its relation with the FFT and the Hartley Transform, as well as the Laplace Transform and the Laplacian Transform.
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Robot Vision
TL;DR: Robot Vision as discussed by the authors is a broad overview of the field of computer vision, using a consistent notation based on a detailed understanding of the image formation process, which can provide a useful and current reference for professionals working in the fields of machine vision, image processing, and pattern recognition.