2007 (English)In: Lecture Notes in Computer Science, ISSN 0302-9743, E-ISSN 1611-3349, Vol. 4485, 326-337 p.Article in journal (Refereed) Published
A family of spatio-temporal scale-spaces suitable for a moving observer is developed. The scale-spaces are required to be time causal for being usable for real time measurements, and to be velocity adapted , i.e. to have Galilean covariance to avoid favoring any particular motion. Furthermore standard scale-space axioms: linearity, positivity, continuity, translation invariance, scaling covariance in space and time, rotational invariance in space and recursivity are used. An infinitesimal criterion for scale-spaces is developed, which simplifies calculations and makes it possible to define scale spaces on bounded regions. We show that there are no temporally causal Galilean scale-spaces that are semigroups acting on space and time, but that there are such scale-spaces that are semigroups acting on space and memory (where the memory is the scale-space). The temporally causal scale-space is a time-recursive process using current input and the scale-space as state, i.e. there is no need for storing earlier input. The diffusion equation acting on the memory with the input signal as boundary condition, is a member of this family of scale spaces and is special in the sense that its generator is local.
Place, publisher, year, edition, pages
Berlin / Heidelberg: Springer , 2007. Vol. 4485, 326-337 p.
IdentifiersURN: urn:nbn:se:kth:diva-33685DOI: 10.1007/978-3-540-72823-8_28ISI: 000247066200028ScopusID: 2-s2.0-37249080358OAI: oai:DiVA.org:kth-33685DiVA: diva2:417095
1st International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2007; Ischia; 30 May 2007 through 2 June 2007
QC 201105172011-05-152011-05-152013-11-26Bibliographically approved