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Galilean differential geometry of moving images
KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
2004 (English)In: COMPUTER VISION: ECCV 2004, PT 4, BERLIN: SPRINGER , 2004, Vol. 2034, 494-506 p.Conference paper (Refereed)
Abstract [en]

In this Paper we develop a systematic theory about local structure of moving images in terms of Galilean differential invariants. We argue that Galilean invariants are useful for studying moving images as they disregard constant motion that typically depends on the motion of the observer or the observed object, and only describe relative motion that might capture surface shape and motion boundaries. The set of Galilean invariants for moving images also contains the Euclidean invariants for (still) images. Complete sets of Galilean invariants are derived for two main cases: when the spatio-temporal gradient cuts the image plane and when it is tangent to the image plane. The former case correspond to isophote curve motion and the later to creation and disappearance of image structure, a case that is not well captured by the theory of optical flow. The derived invariants are shown to be describable in terms of acceleration, divergence, rotation and deformation of image structure. The described theory is completely based on bottom up computation from local spatio-temporal image information.

Place, publisher, year, edition, pages
BERLIN: SPRINGER , 2004. Vol. 2034, 494-506 p.
Keyword [en]
motion, perception, movement, parallax, scale
National Category
Computer Science
URN: urn:nbn:se:kth:diva-43996ISI: 000221523800040ScopusID: 2-s2.0-35048870632ISBN: 3-540-21981-1OAI: diva2:449128
8th European Conference on Computer Vision. Prague, CZECH REPUBLIC. MAY 11-14, 2004
QC 20111019Available from: 2011-10-19 Created: 2011-10-19 Last updated: 2011-10-19Bibliographically approved

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Fagerström, Daniel
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