|Title:|| THE TENSOR BRIGHTNESS
CONSTRAINTS: DIRECT ESTIMATION OF MOTION REVISITED.
|Authors:|| A. Shashua and K.J. Hanna
|Abstract:||We revisit the line of research known as ``direct estimation'' of 3D motion. The direct estimation paradigm seeks to combine image brightness information (in the form of spatial and temporal derivatives) with geometric constraints in order to solve for 3D motion without the need for obtaining point matches in the process (hence the term ``direct''). We derive a number of brightness constraint equations which are linear in the 3D motion parameters defined over three views. In the most general case (projective world), the brightness constraint parameters form what is known as the ``trilinear tensor'' . The paper presents two main results: (i) 3D direct motion estimation is transformed into a linear and parametric problem, (ii) we use a general motion model, and from there go through a stratification of motion models down to the Longuett-Higgins-Prazdny  equations.|
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