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

1. How is Laplacian operator used for image sharpening?
2. What is the use of applying a Laplacian kernel and a smoothing kernel to an image in which order these operations should be applied?
3. How is sharpening done using filtering?

How is Laplacian operator used for image sharpening?

The input gray image is first subjected to a Laplacian filter, which acts as the preprocessing block and then Adaptive Histogram Equalization (AHE) is applied to the image obtained after preprocessing as shown in Fig. 3. The Laplacian filter is an edge-sharpening filter, which sharpens the edges of the image.

What is the use of applying a Laplacian kernel and a smoothing kernel to an image in which order these operations should be applied?

Because these kernels are approximating a second derivative measurement on the image, they are very sensitive to noise. To counter this, the image is often Gaussian smoothed before applying the Laplacian filter. This pre-processing step reduces the high frequency noise components prior to the differentiation step.

How is sharpening done using filtering?

The sharpening process works by first creating a slightly blurred version of the original image, the unsharp mask. This is subtracted away from the original to detect the presence of edges. Contrast is then selectively increased along these edges using this mask — leaving behind a sharper final image.