# Affine invariant scale-space

@article{Sapiro2005AffineIS, title={Affine invariant scale-space}, author={Guillermo Sapiro and Allen R. Tannenbaum}, journal={International Journal of Computer Vision}, year={2005}, volume={11}, pages={25-44} }

A newaffine invariant scale-space for planar curves is presented in this work. The scale-space is obtained from the solution of a novel nonlinear curve evolution equation which admits affine invariant solutions. This flow was proved to be the affine analogue of the well knownEuclidean shortening flow. The evolution also satisfies properties such ascausality, which makes it useful in defining a scale-space. Using an efficient numerical algorithm for curve evolution, this continuous affine flow… Expand

#### 228 Citations

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On projective plane curve evolutionOlivier

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In this paper, we investigate the evolution of curves of the projective plane according to a family of projective invariant intrinsic equations. This is motivated by previous work for the Euclidean… Expand

Affine-invariant curvature estimators for implicit surfaces

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This work proposes a geometrical reduction allowing a much simpler and more stable formulae, and compares the results by incorporating the proposed estimators for the local affine structure of an implicit surface in Marching Cubes based algorithms. Expand

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Affine Invariant Distance Using Multiscale Analysis

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- Journal of Mathematical Imaging and Vision
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This paper introduces an affine invariant distance definition from a $$2D$$2D point to the boundary of a bounded shape using morphological multiscale analysis and proves that the proposed distance is bounded in the convex hull of the shape and infinite otherwise. Expand

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- 2004

It is common to use an affine transformation to approximate the plane curve matching problem under a projective transformation. The plane curve itself can be used as an identity to solve the… Expand

Invariant image descriptors and affine morphological scale-space

- Computer Science
- 2007

This research report proposes a novel approach to build interest points and descriptors which are invariant to a subclass of affine transformations, based on the so-called Affine Morphological Scale-Space, a non-linear filtering which has been proved to be the natural equivalent of the classic linear scale-space when affine invariance is required. Expand

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Morphological Counterparts of Linear Shift-Invariant Scale-Spaces

- Mathematics, Computer Science
- Journal of Mathematical Imaging and Vision
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A simple and fairly general dictionary that allows to translate any linear shift-invariant evolution equation into its morphological counterpart and vice versa is presented, based on a scale-space representation by means of the symbol of its (pseudo)differential operator. Expand

Affine Invariant Flows in the Beltrami Framework

- Computer Science
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- 2004

The geometric Beltrami framework is shown to incorporate and explain some of the known invariant flows e.g. the equi-affine invariant flow for hypersurfaces, and it is demonstrated that the new concepts put forward enable us to suggest new invariants namely the case where the codimension is greater than one. Expand

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