Two-dimensional Chebyshev polynomials for image fusion

This report documents in detail the research carried out by the author throughout his first year. The paper presents a novel method for fusing images in a domain concerning multiple sensors and modalities. Using Chebyshev polynomials as basis functions, the image is decomposed to perform fusion at feature level. Results show favourable performance compared to previous efforts on image fusion, namely ICA and DT-CWT, in noise affected images. The work presented here aims at providing a novel framework for future studies in image analysis and may introduce innovations in the fields of surveillance, medical imaging and remote sensing.

[1]  Hassan Foroosh,et al.  Rendering Synthetic Objects in Natural Scenes , 2006, 2006 International Conference on Image Processing.

[2]  Łukasz Jan Wojakowski.  Moments of measure orthogonalizing the 2-dimensional Chebyshev polynomials , 2006 .

[3]  Tom H. Koornwinder,et al.  Orthogonal polynomials in two variables which are eigenfunctions of two algebraically independent partial differential operators. III , 1974 .

[4]  Andrew Starr,et al.  A Review of data fusion models and architectures: towards engineering guidelines , 2005, Neural Computing & Applications.

[5]  Sim Heng Ong,et al.  Image Analysis by Tchebichef Moments , 2001, IEEE Trans. Image Process..

[6]  R. Mukundan,et al.  Some computational aspects of discrete orthonormal moments , 2004, IEEE Transactions on Image Processing.

[7]  Nikolaos Mitianoudis,et al.  Pixel-based and region-based image fusion schemes using ICA bases , 2007, Inf. Fusion.

[8]  Arthur T. Benjamin,et al.  Combinatorial trigonometry with Chebyshev polynomials , 2010 .

[9]  Rudolf Lidl,et al.  Generalizations of the classical Chebyshev polynomials to polynomials in two variables , 1982 .

[10]  Anthony G. Constantinides,et al.  Data Fusion for Modern Engineering Applications: An Overview , 2005, ICANN.

[11]  Marc C. Y. Cheong,et al.  Textile Recognition Using Tchebichef Moments of Co-occurrence Matrices , 2008, ICIC.

[12]  T. J. Rivlin.  The Chebyshev polynomials , 1974 .

[13]  Tania Stathaki,et al.  Image Fusion: Algorithms and Applications , 2008 .

[14]  Aapo Hyvärinen,et al.  Emergence of Phase- and Shift-Invariant Features by Decomposition of Natural Images into Independent Feature Subspaces , 2000, Neural Computation.

[15]  J. Dicapua.  Chebyshev Polynomials , 2019, Fibonacci and Lucas Numbers With Applications.