Apply a Local Averaging Mask

How can you apply a 3x3 local averaging mask to enhance the sharpness in an image. How can you set the mask? I'd like to get a better understanding in how this method of filtering an image works and how to compute the algorithm.

Answer 1

[Walter Roberson]

Local averaging:

conv(double(YourImage), ones(3,3)/9, 'same')

ones(3,3)/9 is not usually the mask used for sharpening. You tend to sharpen horizontally and vertically separately, using a mask such as [0, 1, 0; -1 0 -1; 0 1 0]

[Diego Espinosa]

Can you explain what you are doing with this line of code?

[Walter Roberson]

Oops should be conv2 instead of conv.

Using each pixel as the upper left corner temporarily, lay down the ones(3,3)/9 and multiply that by the pixels overlayed and add those all together. So in other words, total a 3 x 3 area and divide by 9, the number being totalled, so thereby calculating the average there. Store that. Now move the mask one pixel to the right and do the same and so calculate the local average relative to that position, store, move on...

It is a 3 by 3 moving average, effectively.

[Diego Espinosa]

Is there another way to apply a local mask without using the convolution function; I'd like to know how to do this manually by iterating though the an image's array or matrix?

[Walter Roberson]

Yes you can use loops. You could also use blockproc with a block size of 1 1 and a border size of 1 1, in which case you should be careful about the setting for trimming the border (see blockproc)

[Thulitha Theekshana]

Remember to convert the output of conv2 to uint range. ( maybe using a function such as mat2gray ) before imshow. Otherwise the image wouldn't be displayed.

[Image Analyst]

Or you can use bracket bracket and leave it as floating point:

filteredImage = conv(double(YourImage), ones(3,3)/9, 'same')
imshow(filteredImage, []);

Answer 2

[Image Analyst]

You can use imfilter() instead of convolution, but it's doing pretty much a similar thing (multiplying a sliding window by the image under the window). To sharpen edges you'd use a kernel that's 17 in the middle and -1 around the sides:

kernel = -1 * ones(3);
kernel(3,3) = 17;
output = conv2(double(intputImage), kernel, 'same');
imshow(output, []);

See my attached manual convolution, though I don't recommend it. It's mainly for students who are not allowed to use built-in functions.

The theory for the -1, 17 thing is that it's the average gradient around the 8 directions (which gives a flat, harsh, Laplacian edge detection image), plus 9 in the center to add back in the original image so that the result looks like a edge enhanced image rather than a pure edge detection image. If you need more explanation on the theory, ask.