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Subadditive affine-invariant transformations of convex bodies

✍ Scribed by Guy Valette

Publisher
Springer
Year
1974
Tongue
English
Weight
195 KB
Volume
2
Category
Article
ISSN
0046-5755

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✦ Synopsis

We prove two results about the continuous maps F, from the space of d-dimensional convex bodies K of R g into the space of non-empty compact sets of R ~, which are subadditive and invariant by affine permutations. The first theorem gives properties of the images F(K). In the second one, we determine the largest map (with respect to inclusion of images) in the family of all subadditive and continuous aft-me invariants F such that

where P is a given parallelotope with center P and where r is a number between d/(d + 1 ) and 1.

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✍ SΓ©bastien Roy; Daniel Lefebvre; Henri H Arsenault πŸ“‚ Article πŸ“… 2004 πŸ› Elsevier Science 🌐 English βš– 609 KB

We address the problem of image recognition in the presence of unknown uniform and nonuniform intensity transformations. Multiplicative and additive uniform intensity transformations considered are solved using a method that we recently proposed called the locally adaptive contrast-invariant filter.