Sharpening Using Laplacian Kernel - How to Handle the Output (Specifically Negative Values)?

Question

In order to sharpen an image using Laplacian kernel, it should be convolved with the original image.

It is evident that the result might have negative values. I am not sure what to do with these values:

1. Subtract the minimum from laplacian then map to [0, 255]
2. Clip negative values to zero and map to [0, 255]
3. Just clip negative values to zero

I know the next step is to add/subtract the laplacian to/from the original image and map to [0, 255] but I have doubts about the laplacian.

Indeed, I tested all three methods and 2, 3 got me to the right results but according to my Image Processing textbook, Laplacian should be scaled but it is not mentioned clearly that which version of laplacian is used to derive the sharpened image.

Thank you!

Answer 1

@SOFUser, Welcome to our community.

Since the High Pass Filter, such as the Laplacian Kernel, output has zero mean (As the DC Component is removed) it indeed can (Should) have negative values as the output oscillates around zero.

What to do with it depends on the objective:

1. Display Purpose
   In case on wants to display the output of the Sharpening / HPF Filter process it is very common to add 50% gray to it. In case of 8 [Bit] image it means adding 127 / 128. This is what's don in Adobe Photoshop.
2. Processing Purpose
   Usually we keep the negative values as they might be important in the next steps. For instance in Laplacian Pyramid if one won't keep the negative values the reconstruction won't be accurate. Another example would be sharpening where we add the output of the Laplacian Filter scaled by the sharpening factor to the image to have sharpened image.
3. Generating Image
   If one wants to generate image and archive it in one of the UINT based formats (JPEG, PNG, etc...) usually one would clip data into the compatible range.