Localization and pose estimation of free-form shapes under Euclidean transformation

Implicit polynomials can be used quite effectively for describing a large variety of shapes. In most of the earlier works, the emphasis had been on the use of second degree implicit polynomials because it can be used for describing a large class of industrial parts. To describe more complex curves and surfaces, it is necessary that higher degree implicit polynomials be used. In this paper, we have proposed an approach for obtaining certain Euclidean invariants from higher degree implicit polynomials which can be used for both recognition and pose estimation. The traditional method is based on symbolic computations which is computationally intensive and it cannot be used for determination of pose. Our approach is based on tensor based representation of the implicit polynomial coefficients and has a precise algorithmic formulation. It provides a reliable shape signature in terms of a shape invariant and a rotational component, which facilitates its use for recognition and pose estimation