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Novel Schemes of Trivariate Linear and One-Dimensional Quadratic B-Spline Interpolation Functions Based on the Sub-pixel Efficacy Region College of Science and Liberal Arts, New Jersey Institute of Technology 323 M.L.King Blvd. University Heights - Newark, NJ 07102-1982, USA ABSTRACT A practical approach for the improvement of the interpolation error is presented and is applied to trivariate linear and one-dimensional quadratic B-Spline interpolation functions. The departing point of this work is that of incorporating the intensity-curvature distribution of the given interpolation function into the mathematical formulation named Intensity-Curvature Functional (∆E). While the intensity is determined by the sequel of discrete samples and also by the values established through interpolation, the curvature is expressed by the sum of second order partial derivatives of the interpolation function. The study continues by finding the solution of the polynomial consisting of the partial derivatives of ∆E with respect to each of the dimensional variables. Such a solution reveals a spatial domain of intra-pixel points called Sub-pixel Efficacy Region (SRE), which is used to improve the approximation characteristics of the interpolator. Thus, for a given re-sampling location and also for given intensity values at the pixel to re-sample and the neighbourhood, the Sub-pixel Efficacy Region is used to determine a novel re-sampling location to calculate the interpolation function. For a signal or an image, the novel re-sampling location varies pixel by pixel depending on (i) the local distribution of pixel intensity across the neighbourhood and (ii) the local curvature of the interpolation function. Benefits and limitations of the application of the SRE are studied in space domain by analysis of root mean square errors, and in frequency domain by analysis of spectral power distributions. Novel schemes of trivariate linear and one-dimensional quadratic B-Spline functions are determined with improved approximation capabilities. Keywords: Intensity-Curvature Functional, Sub-pixel Efficacy Region, Novel Re-sampling Location.
Biography:
BibTex: @ARTICLE{P1150535004,
AUTHOR = {C.
Ciulla and F.P. Deek },
TITLE = {Novel Schemes of Trivariate Linear and One-Dimensional Quadratic B-Spline Interpolation Functions Based on the Sub-pixel Efficacy Region}, JOURNAL = {ICGST International Journal on Graphics, Vision and Image Processing}, YEAR = {2005}, MONTH={August}, ISSUE = {V8}, PAGES ={42--53} } ( |
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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.
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