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Specular flow and Weingarten map : Technical Report IES-2015-13

Pak, Alexey

Abstract:
If a moving camera observes a specular surface in which some environment is reflected, the pixel values per se do not directly characterise the surface. However, the associated optical flow, or specular flow (SF), as it is called in this situation, is an environment-agnostic observable that depends on the surface position, orientation, and curvature. The derivation of the SF in the limit of an infinitely remote environment has been published earlier by the authors, but in a relatively opaque coordinate-dependent form. In this report, we present a simpler and a more general derivation of the SF as a function of the surface structure, where the crucial part is played by the so-called Weingarten map. This result allows us to formulate the conditions when the SF diverges, and to derive a simple formula to relate the Gaussian curvature of the surface to the SF.


Zugehörige Institution(en) am KIT Institut für Anthropomatik und Robotik (IAR)
Publikationstyp Proceedingsbeitrag
Jahr 2016
Sprache Englisch
Identifikator ISBN: 978-3-7315-0519-8
ISSN: 1863-6489
URN: urn:nbn:de:swb:90-603819
KITopen ID: 1000060381
Erschienen in Proceedings of the 2015 Joint Workshop of Fraunhofer IOSB and Institute for Anthropomatics, Vision and Fusion Laboratory. Ed.: J. Beyerer
Verlag KIT Scientific Publishing, Karlsruhe
Seiten 167-176
Serie Karlsruher Schriften zur Anthropomatik / Lehrstuhl für Interaktive Echtzeitsysteme, Karlsruher Institut für Technologie ; Fraunhofer-Inst. für Optronik, Systemtechnik und Bildauswertung IOSB Karlsruhe ; 24
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