A comparison of the deep structure of alpha-scale spaces

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureConferentiebijdrageAcademicpeer review

2 Citaten (Scopus)

Samenvatting

We compare the topology and deep structure of alternative scale space representations, so called α-scale spaces, 1/2 ≤ α ≤ 1, which are subject to a first order pseudo partial differential equation on the upper half plane {(x,s) ∈ ℝ d ×ℝ|s > 0}. In particular, the cases α = 1 and α = 1/2, which correspond to respectively Poisson scale space and Gaussian scale space, are considered. Poisson scale space is equivalent to harmonic extension to the upper half plane, inducing potential physics, whereas Gaussian scale space is generated by the diffusion equation on the upper half plane, inducing heat physics. Despite the continuous connection (by parameter 1/2 ≤ α ≤ 1) between these scale spaces and the similarity between their convolution convolution kernels, we show both theoretically and experimentally that there is a strong difference between the topology in the deep structure of these scale spaces.
Originele taal-2Engels
TitelDeep Structure, Singularities, and Computer Vision
SubtitelFirst International Workshop, DSSCV 2005, Maastricht, The Netherlands, June 9-10, 2005, Revised Selected Papers
RedacteurenO.F. Olsen, L.M.J. Florack, A. Kuijper
Plaats van productieBerlin
UitgeverijSpringer
Hoofdstuk21
Pagina's234-248
Aantal pagina's15
ISBN van elektronische versie978-3-540-32097-5
ISBN van geprinte versie3-540-29836-3, 978-3-540-29836-6
DOI's
StatusGepubliceerd - 2005

Publicatie series

NaamLecture Notes in Computer Science (LNCS)
Volume3753
ISSN van geprinte versie0302-9743

Vingerafdruk Duik in de onderzoeksthema's van 'A comparison of the deep structure of alpha-scale spaces'. Samen vormen ze een unieke vingerafdruk.

  • Citeer dit

    Duits, R., Kanters, F. M. W., Florack, L. M. J., & Haar Romenij, ter, B. M. (2005). A comparison of the deep structure of alpha-scale spaces. In O. F. Olsen, L. M. J. Florack, & A. Kuijper (editors), Deep Structure, Singularities, and Computer Vision: First International Workshop, DSSCV 2005, Maastricht, The Netherlands, June 9-10, 2005, Revised Selected Papers (blz. 234-248). (Lecture Notes in Computer Science (LNCS); Vol. 3753). Springer. https://doi.org/10.1007/11577812_21