I've read few articles that Laplacian (second derivative in x + second derivative in y) is used to actually sharpen the images. Because when you apply a Laplacian kernel on an image, it essentially marks its intensities, and (after some re-scaling), if you add the result of the filter to the original image it is as if that you are intensifying the pixels that have high intensities already, and it is very clear that why this technique actually used to sharpen the intensities. (for example: http://homepages.inf.ed.ac.uk/rbf/HIPR2/log.htm)

But one thing that I don't understand is that why this operation (Laplacian operation) in some other articles and some other parts of the literature is referred to as an smoothing filter!! I don't see how Laplacian filter just by itself can be used as an smoothing tool ?!! Isn't it used to sharpen the image even more rather than smoothing it? Isn't it that the effect of this filter is to highlight edges in an image? What is it when they talk about Laplacian smoothing filter?

Thanks, --Rudy