This model adapts the prior information of piecewise continuity of image to construct a nonlinear diffusion model,which is used to smooth an enlarged image by nearest interpolation to reduce the blocky effect caused by enlargement,simultaneity,and interpolation condition is added into the iterated process to avoid a too smooth image.
Moreover, the segmentation process requires to take into account well data to interpolate, which implies integrating interpolation condition in the mathematical model.
This spatial information will allow us to obtain the desired interpolation condition.
In this paper,we described a shape preserving spline function withHermite interpolation condition.A spline function of monotone perservingq(x)is constructed,and q(x)satisfies1)q(x_i)=y_i,i=0,1,…,n,n+1,2)q′(x_i)=y′_i,i=0,1,…,n,n+1.Similar spline functions have also been studied for convex sequences{y_i}_(i=0)~(n+1).
An element Ln(x) was found in linear space for Ln(x) to satisfy some given conditions. This paper proposed two kinds of interpolation condition, derived Ln(x) and error function.
The Pythagorean-hodograph (PH) curves are polynomial parametric curves {x(t). y(t)} whose hodograph components satisfy the Pythagorean condition. There are two Pythagorean-hodograph cubic which satisfy first-order hermite interpolation condition. We explain how to construct a piecewise smooth G1 Pythagorean-hodograph interpolating cubic.