Laplacian Operator with and without Diagonal Direction Elements in the Kernel

1. What does Laplacian kernel do?
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 Laplacian operator used for image sharpening?

What does Laplacian kernel do?

A Laplacian filter is an edge detector used to compute the second derivatives of an image, measuring the rate at which the first derivatives change. This determines if a change in adjacent pixel values is from an edge or continuous progression.

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 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.