Introducing a Conditional Ghost Correction Into the Vector Method

Abstract

The concept of conditional ghost correction is introduced into the vector method of quantitative texture analysis. The mathematical model actually chosen here reduces the texture problem to one of quadratic programming. Thus, a well defined optimization problem has to be solved, the singular system of linear equations governing the correspondence between pole and orientation distribution being reduced to a set of equality constraints of the restated texture problem. This new mathematical approach in terms of the vector method reveals the modeling character of the solution of the texture problem provided by the vector method completely.

A novel optimization-based pole-figure inversion method: comparison with WIMV and maximum entropy methods

“…In methods where global interpolation functions are used, such as the harmonic methods, smoothness is enforced via the interpolation functions themselves, or rather through low-order expansions thereof. In discrete or 'vector' methods, which typically use many more degrees of freedom (DOF) to describe the ODF and PFs, smoothness may be enforced via the minimization of variational sums in the auxiliary problem (Schaeben, 1984;Schaeben et al, 1985). Maximum entropy methods are an extension of this concept, replacing a variational operator with the expression for Shannon's entropy (Schaeben, 1988b(Schaeben, , 1991.…”

“…One particularly suitable class of problems for this task is constrained optimization. This approach has been suggested for various PF inversion methods, both explicitly (Schaeben, 1984(Schaeben, , 1988b(Schaeben, , 1991Dahms & Bunge, 1989) and implicitly (Matthies & Vinel, 1982;Pawlik, 1986). In short, many PF inversion methods have been proposed and nearly as many enjoy practical implementation, each with its own benefits and weaknesses.…”