Combine multiple objects to create Super Sampled representation

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Jason 2023-10-16

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2034384-combine-multiple-objects-to-create-super-sampled-representation

评论： Matt J 2023-10-23

采纳的回答： Matt J

Hi, I have an image consisting of holes and want to create a "composite" representation by combining all of them.

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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Jason 2023-10-18

编辑：Jason 2023-10-18

在 MATLAB Online 中打开

Trying out Matt's suggestion of griddata

            % Use grid data to interpolate sub pixel values but use
            %"nearest" 
            x=1:sx;
            y=1:sy;
            v=I(y,x);
            %Create query points
            [xq,yq] = meshgrid(1:0.5:sx);
            z1 = griddata(x,y,v,xq,yq,'nearest');
            figure
            plot3(x,y,v,'mo');
            hold on
            s=mesh(xq,yq,z1);
            s.FaceColor = 'flat';
            s.EdgeColor='k';
            view(0,90)
            
            

Seems to be a step forward, but still not there.

Not sure why the original image locations (magenta) are not shwoing correctly
Nor is it "referenced" to the real centroid (red spot)

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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采纳的回答

Matt J 2023-10-22

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2034384-combine-multiple-objects-to-create-super-sampled-representation#answer_1338581

编辑：Matt J 2023-10-23

在 MATLAB Online 中打开

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,

https://www.mathworks.com/matlabcentral/fileexchange/44669-convert-linear-functions-to-matrix-form

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

Elapsed time is 0.110118 seconds.

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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Matt J 2023-10-23

编辑：Matt J 2023-10-23

在 MATLAB Online 中打开

Here's a variant that uses lsqlin to constrain the estimated blob profile to be monotonically decreasing. This regularizes the estimation, allowing you to use more spline knots (and hence more flexible splines).

IM=load('CoarseImages').IM;

K=numel(IM);

N=length(IM{1});

Rad=(N-1)/2; %Lobe radius

obj=lobeFitter(Rad,2*Rad); %twice as many spline knots as before

%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

Q=diff(func2mat(@(c) obj.getProfile(c,N,20),c0,'doSparse',0)); %for monotnicity constraints

c=lsqlin(A, reshape([IM{:}],[],1) , Q, zeros(height(Q),1) ); %compute spline coefficients, c

Minimum found that satisfies the constraints. Optimization completed because the objective function is non-decreasing in feasible directions, to within the value of the optimality tolerance, and constraints are satisfied to within the value of the constraint tolerance.

toc

Elapsed time is 0.370543 seconds.

IMsuper = obj.getLobe(c,N,20); %Super-res image upsampled by 20

tiledlayout(1,3);

nexttile, imshow(IM{1},[]); title 'Measured'

nexttile, imshow(IMsuper,[]); title 'Super-resolved (20x)'

nexttile, plot(IMsuper(ceil(end/2),:)); axis square; title 'Radial Profile'