为什么在传递到中值滤镜之前需要将图像转换为灰度？

Question

Why when I pass a coloured image through median filter I get an error saying that the expected input should be 2D?

what does this mean?

Answer 1

This makes sense because the way colors are described in RGB, that is a 3D array, as opposed to grayscale being these 2D.

RGB is not a linear scale, and the three channels change the color spectrum quite a lot when used independently. This will cause weird effects in color in RGB median filters.

If you think about how a median filter could be applied to a RGB there are 2 different possibilities:

1. Treat each channel independently

2. Treat each pixel as unique RGB values.

In the first case, the median filter would give strange colors. Choosing repeatedly R,G and B values without taking into account the other values will generate random colors that have nothing to do with the originals

Instead, if you chose to treat pixel values as triplets, as single RGB data, then you will never get anything out of the median filter, because the likelihood of 2 pixel values to have the exact same color in RGB bite by bite is very very low. Thus a median filter in RGB triples would be the same as doing nothing in 99.99% of the cases.

This is why the median filter is not defined/makes no sense in RGB.

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However ...

If you convert your data to HSV or L a*b* then you can do a median filter of each of its components, and transform the result back to RGB.

Answer 2

Actually it's not uncommon to apply median filter in RGB color space.

If the purpose is removing salt & pepper noise , it is working quite well in RGB color space.
Instead of passing RGB as input to medfilt2 , you need to pass each color channel separately.

Ander Biguri is right: from mathematical perspective, it's incorrect to apply median filter in RGB color space. It's probably the reason why it's not supported by Matlab implementation of medfilt2 .

Example for applying medfilt2 in RGB color space:

RGB = imread('https://i.stack.imgur.com/G2aNm.png');

figure;imshow(RGB);title('Original');

R = RGB(:, :, 1);
G = RGB(:, :, 2);
B = RGB(:, :, 3);

R = medfilt2(R);
G = medfilt2(G);
B = medfilt2(B);

RGB = cat(3, R, G, B);

figure;imshow(RGB);title('After median filter of each color channel');

Original image:

Image after median filter of each color channel:

As you can see, it's working quite well...