Abstract:

This paper reports on a novel methodology for improving the approximation properties of the cubic form of the Lagrange interpolation function through the use of two mathematical formulations: (i) the Intensity- Curvature Functional (∆E) and (ii) its derived Sub-pixel Efficacy Region (SRE). Equations are determined dependent on the local curvature of the interpolation function and the pixel intensity at the neighbourhood, thus making it possible to calculate the Lagrange function with improved approximation properties. Characterizations of interpolation error and interpolation error improvement bounds are also presented. Fast Fourier Transform and Root-mean-square-error analyses are used to realize and present the improvements. The significance of the results is discussed within the context of a unifying framework which uses the same methodology for the improvement of the interpolation error of diverse functions.

Keywords: Lagrange Interpolation, Intensity-Curvature Functional, Sub-pixel Efficacy Region.

Biography:

Biographical Sketch for Carlo Ciulla

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. 

Contact Information:

Carlo Ciulla, New Jersey Institute of Technology, College of Science and Liberal Arts, 323 M.L.King Blvd., University Heights, Newark, NJ 07102-1982, USA
 

Biographical Sketch for Fadi P. Deek

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.

Contact Information:

Fadi P. Deek, New Jersey Institute of Technology, College of Science and Liberal Arts, 323 M.L.King Blvd., University Heights, Newark, NJ 07102-1982, USA

Email : fadi.deek@njit.edu

URL: csla.njit.edu/fadi

BibTex:

@ARTICLE{P1120619001,

AUTHOR = {Carlo Ciulla and Fadi P. Deek},

TITLE = {Extension of the Sub-pixel Efficacy Region to the Lagrange Interpolation Function},

JOURNAL ={ICGST International Journal on Graphics, Vision and Image Processing},

}

(Full Paper 842KB)