This paper describes a novel theoretical approach for the improvement of the bivariate linear interpolation function. The basic premise of this theory consists of quantifying the effect of the interpolation function on an image’s pixel by the product of the value of the pixel intensity times the sum of non-null second order derivatives of the function. The product is called intensity-curvature term and it is calculated at the grid node (x, y) = (0, 0) and termed E_o(x, y), and at the generic intra-pixel location (x, y) ≠ (0, 0) and termed E_IN(x, y). The ratio between the two terms E_o(x, y) and E_IN(x, y) consists of the Intensity-Curvature Functional (ΔE). First order derivatives of ΔE are computed to derive a polynomial system, with zeros at the extreme points of ΔE within the pixel and that are called Sub-pixel Efficacy Region (SRE). Given a re-sampling location (x₀, y₀), the SRE is used to project it onto a novel location (x^r0, y^r0) where the approximation properties of the interpolation function lead to error minimization. Two conceptions are thus derived from ΔE: (i) error improvement is set dependent on pixel intensity and curvature of the interpolation function and (ii) the novel re-sampling location varies locally between pixels depending on local properties of the interpolation function as expressed by the intensity-curvature distribution at the neighbourhood. Accordingly, a novel scheme of bivariate linear interpolation is determined with improved approximation properties.

Keywords:  Intensity-Curvature Functional, Sub-pixel Efficacy Region, Novel Re-sampling Location.

Biographies:

Carlo Ciulla holds a graduate degree in Management Engineering (Laurea) awarded in 1994 from the University of Palermo - Italy. In 2000 and 2002 respectively he was awarded the Master of Science in Information Systems and the Doctorate in Computer and Information Science from the New Jersey Institute of Technology - USA, where he was Teaching Assistant in Computer Science service courses. He was previously a Research Associate at the National Institute of Bioscience and Human Technology in Tsukuba - Japan, while he worked on recording and analysis of Magnetoencephalography (MEG) data from the human brain. He was also a Research Associate at Yale University and the University of Iowa, while working on recording and analysis of anatomical and functional Magnetic Resonance Imaging (MRI) data from the human brain. His research interests span in the domain of Computational Engineering from Artificial Neural Networks to Signal Processing applications to MRI and functional MRI. He has published 10 papers in Journals and Conference Proceedings, and given 20 professional presentations. 

 Fadi P. Deek received his B.S. Computer Science, 1985; M.S. Computer Science, 1986; and Ph.D. Computer and Information Science, 1997 all from New Jersey Institute of Technology (NJIT). He is Dean of the College of Science and Liberal Arts, Director of the Information Technology Program, and Professor of Information Systems and Mathematical Sciences at NJIT where he began his teaching career as a Teaching Assistant in 1985. He is also a member of the Graduate Faculty - Rutgers University PhD Program in Management. Dr. Deek maintains an active funded-research program. His research interests include Learning/Collaborative Systems, Software Engineering, Programming Environments, and Computer Science Education. Dr. Deek has published over 100 papers in journals and conference proceedings and he has given over 40 invited and professional presentations. He is also the author of eight book chapters and the co-author (with J. McHugh) of the book Computer-Supported Collaboration with Applications to Software Development (Kluwer Academic Publishers, 2003, 265 pages) and the co-author (with J. McHugh and O. Eljabiri) of Strategic Software Engineering – An Interdisciplinary Approach (Taylor & Francis Group - Auerbach Publications, 2005, 365 pages). Dr. Deek has received numerous teaching, research and service awards: The NJIT Student Senate Faculty of the Year Award, given to him in 1992 and 1993; the NJIT Honors Program Outstanding Teacher Award in 1992; the NJIT Excellence in Teaching Award in 1990 and 1999; the NJIT Master Teacher Designation in 2001 and the NJIT Robert W. Van Houten Award for Teaching Excellence in 2002. He has also been awarded the NJIT Overseers Public and Institute Service Award in 1997 and the IBM Faculty Award in 2002.