On the Mathematics of the Sub-pixel Efficacy Region of the Interpolation Function: Sub-pixel Efficacy Region - Couverture souple

Ciulla, Carlo; Deek, Fadi P.

Couverture souple

ISBN 10 : 1477666605 ISBN 13 : 9781477666609

Editeur : CreateSpace Independent Publishing Platform, 2012

Synopsis

This research expands on previously published works and reinforces on the use a unifying theory for the improvement of the interpolation error. Regardless of the degree or of the dimensionality, the unifying theory is applicable to interpolation functions which embed the property of second order differentiability. Bivariate linear (two-dimensional), one-dimensional quadratic and cubic B-Splines, cubic Lagrange, and the trivariate linear (three-dimensional) interpolation functions result into improved interpolation paradigms and this is presented along with the software counterpart of the engineering optimization problem being solved. The engineering problem consists of the adaptive re-sampling technique, and such technique depends on the local curvature of the model interpolation function. The unifying theory makes use of the local curvature in order to attain the improvement in the interpolation error. In this research, the interpolation error is measured through the Mean Absolute Error (MAE). This research provides a clear demonstration that the methodology employed in the unifying theory, which makes use of the following four steps: (i) the math formulation of the Intensity-Curvature terms before and after interpolation, (ii) the quantification of the Intensity-Curvature Functional, (iii) the calculation of the Sub-pixel Efficacy Region (SRE), and (iv) the calculation of the novel re-sampling locations from the SRE; makes possible to derive improved interpolation paradigms called SRE-based interpolation functions with improved approximation characteristics. The Novel Re-sampling Locations have been sized to be a fraction of the pixel size whereas in the previously works they were sized to be a fraction of the misplacement, and such difference works in favor of a wider applicability of the unifying theory.

Détails de l'édition

• Éditeur: CreateSpace Independent Publishing Platform
• Date d'édition: 2012
• Langue: anglais
• ISBN 10: 1477666605
• ISBN 13: 9781477666609
• Reliure: Broché
• Nombre de pages: 44
• Coordonnées du fabricant: Printed by Amazon on behalf of the author; https://www.amazon.fr/hz/contact-us; ; c/o Amazon Media EU S.à.r.l., 38 Avenue John F. Kennedy; Luxembourg; L-1855; Luxembourg