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i |
Title of Course |
Surface Modeling (NR 802) |
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ii |
Credit Sructure |
L T P C 3 0 0 6 |
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iii |
Prerequisite, if any (for the students) |
Nil |
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iv |
Course Content |
Interpolation: Determination of the coefficients; Artifacts – Ringing, Aliasing, Blocking and Blurring; Desirable properties – Separability Symmetry and Partition of unity; Approximation theory – The Strang-fix equivalence, Reproduction of polynomials, Regularity, Decomposition theorem, Piecewise-polynomial analysis; Piecewise polynomials – Nearest neighbour, Linear, B-splines, o-Moms, Schau’s functions, Keys’ function; The Sinc and its apodizations – Dirichlet and Hanning. Approximation: Variational reconstruction from arbitrarily spaced samples, the optimal solution – Radial basis functions (RBFs). Splines, B-splines and the relation of the optimal solution to B-splines. RBFs: The thin-plate spline, Multiquadric, Gaussian and Wendland’s Compactly supported function. Surface Approximation using the non-uniform FFT.
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v |
Text / References |
1.The’venaz, P., Blu T. and Unser, M.: Interpolation Revisited, IEEE Transactions on Medical Imaging, Vol. 10 No. 7, July 2000, pp 739-758. 2.Arigovindan, M., Suhling, M., Hunziker, . and Unser, M.: Variational Reconstruction from Arbitrarily Spaced Samples – A Fast Multiresolution Spline Solution, IEEE Transactions on Image Processing, Vol. 14, No. 4, April 2005, pp. 440-450. 3.Schumaker, L.L.: Splines-Basic Theory, John Wiley and Sons, 1981. 4.Carr, J.C., Beatson, R.K., McCallum, B.C., Fright, W.R., McLellan, T.J. and Mitchell, T.J.: Smooth Surface Reconstruction from Noisy Range Data, Proceedings of the 1st International ACM conference on Computer Graphics, February 2003, pp. 119-126. 5.Liu, Q.H. and Nguyen, N.: An Accurate Algorithm fro the Non-uniform Fast Fourier Transform, IEEE Microwave Guided Wave Lett., Vol. 8, No. 1, 1988, pp. 18-20.
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vi |
Instructor(s) name |
Dr. Shyamlee Mukherji |
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vii |
Name of Other departments to whom the course is relevant |
KReSIT, CSE, Civil Engineering, Earth Sciences, CESE, Electrical Engineering |
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viii |
Justification |
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