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J. Bigün, G.H. Granlund, J. Wiklund, "Multidimensional Orientation Estimation with Applications to Texture Analysis and Optical Flow," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 8, pp. 775790, August, 1991.  
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@article{ 10.1109/34.85668, author = {J. Bigün and G.H. Granlund and J. Wiklund}, title = {Multidimensional Orientation Estimation with Applications to Texture Analysis and Optical Flow}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {13}, number = {8}, issn = {01628828}, year = {1991}, pages = {775790}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.85668}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Multidimensional Orientation Estimation with Applications to Texture Analysis and Optical Flow IS  8 SN  01628828 SP775 EP790 EPD  775790 A1  J. Bigün, A1  G.H. Granlund, A1  J. Wiklund, PY  1991 KW  computer vision; multidimensional orientation estimation; least squares approximations; texture analysis; optical flow; finite dimensional Euclidean spaces; Fourier transform; spatial domain; orientation estimate; certainty measure; image analysis; texture segmentation; computer vision; Fourier transforms; least squares approximations VL  13 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
The problem of detection of orientation in finite dimensional Euclidean spaces is solved in the least squares sense. The theory is developed for the case when such orientation computations are necessary at all local neighborhoods of the ndimensional Euclidean space. Detection of orientation is shown to correspond to fitting an axis or a plane to the Fourier transform of an ndimensional structure. The solution of this problem is related to the solution of a wellknown matrix eigenvalue problem. The computations can be performed in the spatial domain without actually doing a Fourier transformation. Along with the orientation estimate, a certainty measure, based on the error of the fit, is proposed. Two applications in image analysis are considered: texture segmentation and optical flow. The theory is verified by experiments which confirm accurate orientation estimates and reliable certainty measures in the presence of noise. The comparative results indicate that the theory produces algorithms computing robust texture features as well as optical flow.
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