Combine multiple objects to create Super Sampled representation
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Hi, I have an image consisting of holes and want to create a "composite" representation by combining all of them.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1512769/image.png)
I believe the idea is that because the centroid of each on jitters (i.e. is not in exactly the same location as seen by the red dots), its possible to to use this to create a super resolved reconstruction. As far as I udnerstand, I can for example consider 1/2 pixel and hence create a 18x18 (sub pixel) image from this 9x9 pixel image. So I need to start at the centroid and step 1/2 pixel away and record the actual real pixel value and then populate this in the 18x18 array. I do this for all 3 and then I can for example take the median on a pixel basis.
The problem is, considering the 1st image, Im not sure how to get the 1/2 pixel values from the centroid to then fill in the 18x18 array.
any pointers would be appreciated.
Thanks
Jason
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Matt J
2023-10-22
编辑:Matt J
2023-10-23
Hi Matt, thanks for your thoughts. As I understand this is very similar to the slanted edge MTF where the slant gives you the ability to super resolve.
But in that scenario, people are normally curve fitting. They assume that the LSF is a Gaussian lobe or a spline or something like that. That's why I asked you to begin with whether there was a parametric surface model that the samples are supposed to follow.
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Matt J
2023-10-22
编辑:Matt J
2023-10-23
Here's an algebraic solution in which we model the blobs as circularly symmetric with a radial profile parametrized by cubic splines. The code assumes NxN image data with N odd and requires that you download func2mat from,
IM=load('CoarseImages').IM;
K=numel(IM);
N=length(IM{1});
Rad=(N-1)/2; %Lobe radius
obj=lobeFitter(Rad,Rad+1);
%Build equation matrix, A
tic;
A=cell(K,1);
c0=ones(1,obj.ncoeff);
for k=1:K
t=obj.displacement(IM{k});
A{k}=func2mat(@(c) obj.radialInterp(c,N,t),c0,'doSparse',0);
end
A=cell2mat(A); %final equation matrix
c=A\reshape([IM{:}],[],1); %compute spline coefficients, c, algebraically
toc
IMsuper = obj.getLobe(c,N,2); %Super-res image upsampled by 2
tiledlayout(1,2);
nexttile, imshow(IM{1},[]);
nexttile, imshow(IMsuper,[]);
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