Compression of Video Data Using Parametric Line and Natural Cubic Spline Block Level Approximation

2007 ◽  
Vol E90-D (5) ◽  
pp. 844-850 ◽  
Author(s):  
M. A. KHAN ◽  
Y. OHNO
1979 ◽  
Vol 18 (02) ◽  
pp. 84-88 ◽  
Author(s):  
H. Prestele ◽  
W. Gaus ◽  
L. Horbach

A three stop procedure is proposed for the comparison of groups, where for each individual a process is investigated on the basis of repeated measurements (e.g. 3 up to about 15 time points).1. A natural cubic spline function is fitted to the time-dependent measurements of each individual. A cubic spline is a function which is composed of piecewise polynomials, continuous up to and including second derivatives; it has a minimal »curvature«, so that a »smooth« curve is generated.2. For each individual the value of a problem-oriented parameter is estimated from the spline function.3. The values of the problem-oriented parameter are evaluated with standard, not necessarily longitudinal methods for estimating and hypothesis testing.The proposed procedure requires neither an equal number of measurements for each individual, nor the same time points of measurement for all individuals, nor equal length of the time intervals. Splines can be fitted to very different patterns of curves. They can be used for a more exact calculation of parameters adequate to the problem concerned. The procedure necessitates the use of a computer; programs are available and do not demand excessive arithmetic precision and computing time.


2008 ◽  
Vol 19 (08) ◽  
pp. 1291-1304 ◽  
Author(s):  
MONTRI THONGMOON ◽  
SUWON TANGMANEE ◽  
ROBERT MCKIBBIN

Four types of numerical methods namely: Natural Cubic Spline, Special A-D Cubic Spline, FTCS and Crank–Nicolson are applied to both advection and diffusion terms of the one-dimensional advection-diffusion equations with constant coefficients. The numerical results from two examples are tested with the known analytical solution. The errors are compared when using different Peclet numbers.


Author(s):  
Farida ◽  
Nifatamah Makaje ◽  
Phattrawan Tongkumchum ◽  
Aniruth Phon-On ◽  
Jetsada Laipaporn

2002 ◽  
Vol 6 (4) ◽  
pp. 73-80 ◽  
Author(s):  
Marco Congedo ◽  
Cem Özen ◽  
Leslie Sherlin

Author(s):  
Alasdair C. Steven ◽  
Robert Stall ◽  
Peter M. Steinert ◽  
Benes L. Trus

Powerful methods based on Fourier analysis have been devised for deducing the helical symmetries of macromolecular filaments and reconstructing their 3-dimensional density maps from electron images of negatively stained specimens. However, their applicability is restricted by the requirement that the particles be precisely straight. Only a limited number of specimens are sufficiently rigid to meet this constraint. Filamentous particles that exhibit varying degrees of flexibility constitute a much wider class of specimens, but their curvature impairs the coherence of their diffraction patterns. A solution to this problem is afforded by computational a posteriori straightening, effected by interpolating the digitized images on to a curvilinear coordinate system defined by the curve described by the particle axis. Here, we describe an algorithm for this purpose based on natural cubic spline interpolation, and illustrate its operation with model data and as applied to a flexuous biological specimen.


1992 ◽  
Vol 15 (2) ◽  
pp. 229-234 ◽  
Author(s):  
Arun Kumar ◽  
L. K. Govil

From the result in [1] it follows that there is a unique quadratic spline which bounds the same area as that of the function. The matching of the area for the cubic spline does not follow from the corresponding result proved in [2]. We obtain cubic splines which preserve the area of the function.


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