newton divided difference interpolation

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image-pro 2022-4-4

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https://ww2.mathworks.cn/matlabcentral/answers/1688054-newton-divided-difference-interpolation

编辑： Jan 2022-5-5

i have dicom image and converted into jpg now i want to apply newton divided difference interpolation. please anyone suggest the answer.

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image-pro 2022-4-12

编辑：image-pro 2022-4-12

在 MATLAB Online 中打开

i have read an image using imread and apply segmentation method for detection of disease, now i want to use newton divided difference interpolation method on segmented image to find the tumor region. using newton divided interpolation to estimate value i have to specify X and Y coordinates to estimate missing value of Y. Now, my question is that how i can use image pixel values in place of X And Y coordinates. i have to pick image pixel value in place of x and y coordinates and calculate missing value using newton divided difference interpolation method.

This is my code. plz solve my problem. Thanks in advance.

%READ AN INPUT IMAGE
IMG=imread('C:\Users\DELL\OneDrive\Documents\MRI-images\Folder1\image-1.jpg');
%IMG = ind2rgb(IMG.X, IMG.map);
X=1:256;
Y=1:256;
[Dx, Dy] = meshgrid(X, Y);
x=Dx;
y=Dy;
size=length(x);
d=zeros(size,size);
xlength=length(x);
DDlim=length(x)-1;
D=zeros(xlength,xlength);
D(:,:,1)=y;
for i=1:DDlim
    for j=1:i
        D(i+1,j+1)=(D(i+1,j)-D(i,j))/(x(i+1)-x(i-j+1));
    end
end
a=diag(D)

image-pro 2022-4-12

编辑：image-pro 2022-4-12

%READ AN INPUT IMAGE

IMG=imread('C:\Users\DELL\OneDrive\Documents\MRI-images\Folder1\image-1.jpg');

%IMG = ind2rgb(IMG.X, IMG.map);

X=1:256;

Y=1:256;

[Dx, Dy] = meshgrid(X, Y);

x=Dx;

y=Dy;

size=length(x);

d=zeros(size,size);

xlength=length(x);

DDlim=length(x)-1;

D=zeros(xlength,xlength);

D(:,:,1)=y;

for i=1:DDlim

for j=1:i

D(i+1,j+1)=(D(i+1,j)-D(i,j))/(x(i+1)-x(i-j+1));

end

a=diag(D);

expr = poly2sym(a) ;% This create polynomial from the coefficient matrix

fpe = fplot(expr);

title(fpe.DisplayName)

hold on

plot(x,y,'*')

I have to apply below formula on above image. The below given formula is of newton divided difference interpolation.

Suppose f(x0), f(x1), f(x2)………f(xn) be the (n+1) values of the function y=f(x) corresponding to the arguments x=x0, x1, x2…xn, where interval differences are not same

Then the first divided difference is given by

The second divided difference is given by

and so on…

Divided differences are symmetric with respect to the arguments i.e independent of the order of arguments.

so,

f[x0, x1]=f[x1, x0]

f[x0, x1, x2]=f[x2, x1, x0]=f[x1, x2, x0]

By using first divided difference, second divided difference as so on .

image-pro 2022-5-5

SUB-PIXEL EDGE DETCTION FOR PHOTOGRAMMETRY USING LAPLACE DIFFERENCE OF GAUSSIAN AND 4TH ORDER ENO INTERPOLATION

anyone has code for this paper?

Jan 2022-5-5

编辑：Jan 2022-5-5

Please, @image-pro, provide the names of the author or even better the DOI: https://doi.org/10.1109/ICIP.2010.5652041 . Do not let the readers search your paper.

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