Is it possible to reconstruct an image from the number of pixel counts and bins information?

Happy New Year and I need your help!

I have the following imhist function that yields the number of pixel counts and bin locations.

[counts,binLocations] = imhist(I)

Is it possible to reconstruct a "new" image using the number of "new pixel" counts and "same" bins information? If yes - can you please suggest how?

Answer 1

[Walter Roberson]

I = imread('pout.tif');
imshow(I)

I1 = reshape(sort(I), size(I));
imshow(I1)

[c,b] = imhist(I);
[c1,b1] = imhist(I1);
all(c == c1)

ans = logical
   1

all(b == b1)

ans = logical
   1

Two different images, exactly the same counts and bin values.

It follows that knowing the counts and bin locations is not enough to recreate the image.

Answer 2

[Matt J]

As Walter has shown, it is not an invertible mapping, however, if you use histcounts() instead, there is enough information for a coarse inversion:

I = double(imread('pout.tif'));

[counts,binLocations,label]=histcounts(I(:),4); 

vals=movmean(binLocations,2);

Irecon=reshape(vals(label), size(I)); %reconstructed


montage({I/255,Irecon/255})

[Gobert]

Thanks, Matt J. I would also love to accept your answer - but I did not see the option to accept two constructive answers on this platform.