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On the
Approximate Nature of the Bivariate Linear Interpolation
Function: A Novel Scheme Based on Intensity-Curvature
College
of Science and Liberal Arts,
New Jersey Institute of
Technology , 323
M.L.King Blvd. University Heights - Newark, NJ
07102-1982, USA
Abstract:
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 Eo(x, y), and at the generic
intra-pixel location (x, y)
≠
(0, 0) and termed EIN(x, y). The ratio
between the two terms Eo(x, y) and EIN(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 (xr0, yr0) 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. BibTex: @ARTICLE{P1150527003,
AUTHOR = {C. Ciulla and F.P.
Deek},
TITLE = {On the Approximate Nature of the Bivariate Linear Interpolation Function: A Novel Scheme Based on Intensity-Curvature}, JOURNAL = {ICGST International Journal on Graphics, Vision and Image Processing}, YEAR = {2005}, MONTH = {July}, VOLUME = {05}, ISSUE = {7}, PAGES = {9--19} }
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