Detection of Linear Symmetry in Multiple Dimensions for Description of Local Orientation and Optical Flow
1988 (English)Report (Other academic)
The symmetries in a neighbourhood of a gray value image are modelled by conjugate harmonic function pairs. A harmonic function pair is utilized to represent a coordinate transformation defining a symmetry type. Inthis coordinate representation the image parts, which are symmetric with respect to the chosen function pair, have iso-gray value curves which are simple lines or parallel line patterns. The detection is modelled in thespecial Fourier domain corresponding to the new variables by minimizing an error function. It is shown that the minimiza.tion process ar detection of these patterns can be carried out for the whole image entirely in the spatial domain by convolutions. The convolution kernel is complex valued, as is the the result. The magnitudes of the result are shown to correspond to a well defi.ned certainty measure, while the orientation is the lea.st square estimate of an orientation in the Fourier transform corresponding to the harmonic coordinates. Applica tions to four symmetries a.re given. These are circular, linear, hyperbolic and parabolic symmetries. Experimental results a.re presented.
Place, publisher, year, edition, pages
Linköping, Sweden: Linköping University, Department of Electrical Engineering , 1988.
LiTH-ISY-I, ISSN 8765-4321 ; 893
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-53372ISRN: LiTH-ISY-I-0893OAI: oai:DiVA.org:liu-53372DiVA: diva2:288323