Remove pixel whose value is below given threshold

Hello, how can i remove pixels from an image whose values are below/above a given threshold value? As far as I know images in MATLAB are rectangular. So is this even possible? How most efficiently can this be achieved, or something close to this?

Say I have an image A, my threshold is 4. So i want ot remove A(i,j) <= 4 .

I looked at this post, but i think the title is a bit misleading, they are more like changing the value of the pixel. I want total removal/deletion if possible. So in the end i expect the resulting/output image to have different dimensions from the original input. So its more like customized croping.

Thank you very much.

[Catalytic]

How in your mind would common image manipulation routines even handle a non-rectangular image?

What would it mean to sum the rows of an image in which pixels are "missing"? If the missing pixels are not to be included in the sum, why not just set the pixels to zero?

What does an image with deleted pixels look like when displayed? Would the missing pixels be black? If so, why again is it insufficient simply to set the pixels to zero or NaN?

[DGM]

If your goal is to actually remove the elements (i.e. for each removed pixel, the image has one fewer element), then the question becomes how should the image be reshaped? Is it still necessary to preserve local image content? Consider the examples:

% get a basic test image
A = imread('cameraman.tif');
A = A*0.7 + 0.3*255;
s = size(A);
imshow(A)

% this image should be easy enough to deal with.  this is basically just cropping
B1 = zeros(s,'uint8');
B1(50:end-50,50:end-50) = A(50:end-50,50:end-50);
imshow(B1)

% but how would this image be reshaped?
B2 = A;
B2(100:end-100,100:end-100) = 0;
nnz(B2~=0) % pixels that are to be preserved

ans = 62287

imshow(B2)

% what about this?
B3 = A;
idx = randi([1 prod(s)],1,500);
B3(idx) = 0;
nnz(B3~=0) % pixels that are to be preserved

ans = 65038

imshow(B3)

Note the counts of the good pixels. The original image is 255x255 (65025px). Even if image content is abandoned and the output of B2 is just reshaped into a rectangle, there are only a handful of rectangles that contain 62287px.

>> factor2(62287)

ans =

1 62287

199 313

313 199

62287 1

Similarly with B3:

>> factor2(65038)

ans =

1 65038

2 32519

31 2098

62 1049

1049 62

2098 31

32519 2

65038 1

Would any of those geometries be acceptable? If the masked regions are the consequence of some random or natural process, there's nothing stopping you from having a prime number of pixels left in your image.

[MatlabEnthusiast]

@DGM, exactly. Thats the same question I have in mind. In fact its more like cropping a given region within the image. Now considering that i wish to retain remaining content (well obviously some of it will be lost). I am looking for a way that gives me the most of the remainder of the image. If that makes any sense :). Let me take a look at this tool in detail see what it offers. It might take me a while since am quite slow. Thanks

@Catalytic, I think you misunderstood me, or I did not express my self clearly enough. The gold is not to change the 'Shape' of the image form. It will obviously remain rectangular. But i want an optimal resultant rectangular image. Thats wht am looking for.

[DGM]

If some sort of best-fit box approach were implemented, would it be acceptable for some of the bad pixels to be left if it would allow for local content preservation? On the other hand, would it be acceptable to discard some good pixels?

Would it be better to keep the image rigid, or would some amount of shearing be acceptable? Using reshape() tends to progressively displace content, but a vectorwise approach may be less destructive:

% get a basic test image
A = imread('cameraman.tif');
A = A*0.7 + 0.3*255;
s = size(A);

% same noisy image
B3 = A;
idx = randi([1 prod(s)],1,1000);
B3(idx) = 0;

imshow(B3)

C = zeros(s,'uint8');
for col = 1:s(2)
    thisvec = B3(:,col);
    thisvec = thisvec(thisvec~=0); % select only good pixels
    C(1:numel(thisvec),col) = thisvec;
end

imshow(C)

At which point, you could choose to crop off as much of the bottom of the image as you need (again, the remark about whether it's okay to leave bad pixels or discard good pixels). Similar can obviously be done on rows.

[DGM]

Regarding a fit-box and preserving some bad pixels:

% get a basic test image
A = imread('cameraman.tif');
A = A*0.7 + 0.3*255;
s = size(A);

% generate a noisy image
% this uses MIMT tools, so ignore that.
BG = zeros(s,'uint8');
alph = radgrad(s,[0.5 0.5],0.5,[255;0],'cosine','uint8') + 100;
FG = cat(3,A,alph);
B = imblend(FG,BG,1,'normal',1,'dissolvezf');
B = B(:,:,1);

% obviously i can't use MIMT here, so i just attached B
% B = imread('noisyb.png');

imshow(B)

% try to find some sort of mask that describes the least-noisy region
mask = B~=0;
mask = imopen(mask,strel('disk',20,0));

imshow(mask)

% find the extents of the blob and crop the image to it
S = regionprops(mask,'boundingbox');
C = imcrop(B,S.BoundingBox);

imshow(C)

Answer 1

[Matt J]

It is possible to do, but only when the pattern that remains is a rectangular sub-image, e.g.,

A    =[1 1 1 1; 
       1 6 1 6;
       2 5 2 5;
       3 3 3 3]

A = 4×4

1 1 1 1 1 6 1 6 2 5 2 5 3 3 3 3

map=A<=4;

I=all(map,2); J=all(map,1);

A(I,:)=[]; A(:,J)=[];

A

A = 2×2

6 6 5 5

[MatlabEnthusiast]

@Matt J Indeed, I want something close to this. Can you please briefly explain whats happening here.

For instance, I tried this approach with a value greater than the threshold in the uppermost or even lowest row, say:

A = [1 1 8 1;

1 6 1 6;

2 5 9 5;

3 3 3 3]

With your approach it gives:

A =

     1     8     1
     6     1     6
     5     9     5

[Matt J]

The method deletes rows and columsn in which all pixels fall below the deletion threshold.

[MatlabEnthusiast]

@Matt J ok, fully understood now. Thanks. :).

[Matt J]

You're welcome, but if your question has been answered, please Accept-click the answer that best addressed it.

[MatlabEnthusiast]

@Matt J, yeah I will accept ofcourse but there's alot of new information for me. Am going to try them out for different cases then ofcourse i will accept an answer. Thank you guys for all these awesome suggestions.

Answer 2

[DGM]

If you're trying to automatically crop borders off an image, you might be able to use the comments from ImageAnalyst and myself on this thread:

https://www.mathworks.com/matlabcentral/answers/23921-remove-white-space-from-around-image#answer_825324

I give a comparison of a few different methods.

Answer 3

[DGM]

Alternatively, this is an extension from my comment above. If image content preservation is not important, the images can be reshaped. I'm not sure why this would be necessary though. In most cases, I assume that it would suffice to simply vectorize the image instead.

A = imread('cameraman.tif');
A = A*0.7 + 0.3*255;
s = size(A);

% central black region
B2 = A;
B2(100:end-100,100:end-100) = 0;
% find bad pixels and reshape to the most-square geometry possible
mask = B2~=0;
goodpx = nnz(mask);
npf = factor2(goodpx,'ordered',false);
B2r = reshape(B2(mask),npf(end,:));

imshow(B2r)

% random pixel locations
B3 = A;
idx = randi([1 prod(s)],1,500);
B3(idx) = 0;
% find bad pixels and reshape to the most-square geometry possible
mask = B3~=0;
goodpx = nnz(mask);
npf = factor2(goodpx,'ordered',false);
B3r = reshape(B3(mask),npf(end,:));

imshow(B3r)

Attached is the tool used for finding candidate geometries.

Answer 4

[DGM]

Here's another silly answer based on my last two comments. In this case, we're accepting minor local distortion in order to sift the pixels toward the least-noisy region in order facilitate subsequent cropping. This really would only work well in cases where the noise density is largely non-convex. In the example with a square hole in the middle of the image, the distortion would be significantly increased.

% % get a basic test image
% A = imread('cameraman.tif');
% A = A*0.7 + 0.3*255;
% s = size(A);
% 
% % generate a noisy image
% % this uses MIMT tools, so ignore that.
% BG = zeros(s,'uint8');
% alph = radgrad(s,[0.5 0.5],0.5,[255;0],'cosine','uint8') + 100;
% FG = cat(3,A,alph);
% B = imblend(FG,BG,1,'normal',1,'dissolvezf');
% B = B(:,:,1);

% obviously i can't use MIMT here, so i just attached B
B = imread('noisyb.png');
s = size(B);

imshow(B)

% create a mask that describes the least-noisy region
mask = B~=0;
mask = imopen(mask,strel('disk',20,0));
mask = bwareafilt(mask,1);

imshow(mask)

% find center
S = regionprops(mask,'centroid');
cen = round(S.Centroid); % center of good region

% sift radially toward the center
for d = 1:4
    for c = 2:s(1)-1
        linemask = logical(xwline(s,[cen(1) 1],[cen(2) c])); % create a mask
        sampvec = B(linemask); % sample B along that line
        outvec = zeros(size(sampvec),'uint8'); % allocate
        sampvec = sampvec(sampvec~=0); % only get good pixels
        outvec(end-numel(sampvec)+1:end) = sampvec;  % sift vector
        B(linemask) = outvec; % replace 
    end
    B = rot90(B);
    s = size(B);
end

imshow(B)

At this point, it's up to the user to decide whether to crop off all the bad pixels (discarding some good pixels) or do crop only bad pixels (keeping some bad pixels).

This is probably a hilariously inefficient way to do this, but consider it a proof of concept.