Resizing and Repeating an Image

Question

I've run into a problem with images. I am trying to take an image and make it 1/4th of it's original size, then have it repeated as a 2x2 matrix. Kind-of like this:

Given an input image:
           ---------------------
           |                   |
           |                   |
           |       IMG         | 
           |                   |
           |                   |
           ---------------------

   Firstly, shrink it to 1/4 of its original size:
           -----------
           |   img   | 
           |         | 
           |---------|

   Then concatenate it into a "2x2 array" of the shrunken image:
           ---------------------
           |   img   |   img   |
           |         |         |
           |---------|---------| 
           |   img   |   img   |
           |         |         |
           ---------------------

What I am struggling with is the fact that I do not know how to make it into a 2x2 array. Any suggestions? This isn't actually HW this time :) It's for studying purposes. Here's what I've tried so far:

function[newImg] = immultiply(picture)

Image = imread(picture); %// Reads in the picture
[r, c, l] = size(Image); %// Finds the images rows, columns and layers
rows = round(r ./ 2); %// Divides up the rows
columns = round(c ./ 2); %// Divides up the columns

newImg = cat(3,rows,columns,3); %// Creates my image, but just gives me a blank thing
imshow(newImg)


end

I will update as I work on it further. Thanks!

Answer 1

The previous two answers are correct, and I originally worked on this just playing around and wasn't going to post it, but with a slight modification I think it addresses part of Luis Mendo's comments on Kamtal's answer.

My original thought was, why throw away data? If you're downsampling to 1/4 size but plotting 4 of them, you have room for all of the data:

img1 = imread('myimage.png');
subplot(1,2,1),imshow(img1) 
img2 = img1([1:2:end, 2:2:end], [1:2:end, 2:2:end]); 
subplot(1,2,2),imshow(img2);

The resulting top-left quadrant of img2 will be exactly what Kamtal's answer produces: a nearest-neighbor interpolation of the pixels with odd-valued x and y coordinates. The other 3 will be (even/odd), (odd/even), (even/even). Every pixel in img1 appears in img2 and each sub-image can be slightly different.

If instead we want to combine the data from each of the 4 images into a single image without throwing away all of the data, we can change this up slightly. We just take the average of the 4 images. Note that img2 is the same here as above, I'm just breaking out the calculations to make it obvious.

img1 = imread('myimage.png');
subplot(1,3,1),imshow(img1) 
img2a = img1(1:2:end, 1:2:end);
img2b = img1(1:2:end, 2:2:end);
img2c = img1(2:2:end, 1:2:end);
img2d = img1(2:2:end, 2:2:end);
img2 = [img2a img2b; img2c img2d];
subplot(1,3,2),imshow(img2);
img3a = (img2a + img2b + img2c + img2d)/4;
img3 = [img3a img3a; img3a img3a];
subplot(1,3,3),imshow(img3);

Here img3 shows 4 identical images, all the result of downsampling the original image using mean filtering.

To do this with a filter, you would use the kernel:

[0.25 0.25]
[0.25 0.25]

This just takes the average of the 4 elements in the neighborhood. With the origin of the kernel at (1,1) your interpolated, downsampled image would be in the odd-numbered rows/columns as before:

img1 = imread('myimage.png');
subplot(1,2,1),imshow(img1) 
h = [0.25, 0.25; 0.25, 0.25]   //% define the mean filter kernel
img2a = imfilter(img1, h);     //% filter before applying Kamtal's solution
img2b = img2a(1:2:end, 1:2:end);
img2 = [img2b img2b; img2b img2b]; 
subplot(1,2,2),imshow(img2);

The resulting image should be the same as img3 above.

(Incidentally, mean filtering with a 2x2 kernel and then downsampling to 1/4 size is essentially bilinear interpolation. imresize uses bicubic interpolation by default, so its results will be slightly different.)

Answer 2

Just use the instructions imresize and repmat

i = imread('lena.png');

figure(1),subplot(1,2,1),imshow(i) 
[n,m,d] = size(i);

newI = imresize(i,0.5); 
finalI = repmat(newI,2,2); 
figure(1),subplot(1,2,2),imshow(finalI);

newI is the image resized to 1/2. This is equivalent to shrink the image to 1/4. finalI is the final image repeated 4 times. repmat is concatenating the matrix 2x2 times.

I strongly recommend you to check the documentation of these two functions: http://uk.mathworks.com/help/images/ref/imresize.html http://uk.mathworks.com/help/matlab/ref/repmat.html