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Of great importance to a wide variety of computer vision and image analysis problems is the ability to represent two-(2D) and three-dimensional (3D) data or objects. Implicit polynomial curves and surfaces are two of the most useful representations available. Their representational power is evidenced by their ability to smooth noisy data and to interpolate(More)
This paper presents new approaches to two fundamental 3D vision problems: 3D surface representation, and fast extraction of geometric information from this representation, particularly 3D alignment. For surface representation by implicit algebraic surfaces, a non-iterative, robust, repeat-able and approximately least squares fitting algorithm, 3D 3L, is(More)
Combining implicit polynomials and algebraic invariants for representing and recognizing complicated objects proves to be a powerful technique. In this paper, we explore the findings of the classical theory of invariants for the calculation of algebraic invariants of implicit curves and surfaces, a theory largely disregarded in the computer vision community(More)
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