Abstract
This paper presents a method of normalizing an image relative to a complete group of
projective transformations on a plane, based on the iterative optimization of the
solution in space of the two parameters of the projective transformation that
distinguish it from an affine transformation. This pair of parameters is represented
by a vector. Each iteration of the normalization is preceded by a measurement of the
parameters and compensation of the affine transformation according to formulas
derived and published earlier by the author. To partially compensate the projective
transformation, the vector of a normalizing transformation is used at each iteration
along such a direction that changing its direction to the opposite corresponds to
the largest-in-modulus change of the displacement rate of the center of gravity of
the image to be transformed. The iterative process reduces to an image state that is
standard relative to the projective transformation for which a normalizing
transformation vector of any direction causes a displacement of the center of
gravity that is identical in modulus.
© 2009 Optical Society of America
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