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Direct estimation of shape from texture
Garding, J.  
Dept. of Numerical Anal. & Comput. Sci., R. Inst. of Technol., Stockholm;

This paper appears in: Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publication Date: Nov 1993
Volume: 15,  Issue: 11
On page(s): 1202-1208
ISSN: 0162-8828
References Cited: 12
CODEN: ITPIDJ
INSPEC Accession Number: 4580753
Digital Object Identifier: 10.1109/34.244682
Current Version Published: 2002-08-06

Abstract
Witkin (1981) has proposed a maximum likelihood (ML) estimator of surface orientation based on the observed directional bias of projected texture elements. However, a drawback of this procedure is that the estimate is only defined indirectly in terms of a set of nonlinear equations. An alternative method is proposed, which allows an estimate of the surface orientation to be computed directly in a single step from certain simple statistics of the image data. We also show that this direct estimate allows Witkin's ML estimate to be computed to within 0.05° in only two or three iterative steps. The performance of the new estimator is demonstrated experimentally and compared to that of the ML estimator, using both synthetic data and real gray-level images

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