A Linear Algorithm for Determining Plane Projective Transformations Based on Quadratic Curves

Abstract

This paper presents the study on determining a transformation between two projective planes, i.e., a plane projective transformation, based on quadratic curves. For a plane projective transformation, the parameters representing the corresponding pair of quadratic curves satisfy a linear constraint and its coefficients are expressed as the tensor product of the plane projective transformation and itself. We present a linear algorithm for uniquely determining from these coefficients the plane projective transformation up to a scale factor. Our algorithm makes full use of redundant information to determine the plane projective transformation with only linear computation. We can now handle plane projective transformations based on quadratic curves.