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What is the different between LoG (Laplacian of Gaussian) filter, first and second derivative Gaussian filter?

Is it second derivative Gaussian filter equal to Laplacian Operator?

enter image description here

https://docs.opencv.org/3.4/d5/db5/tutorial_laplace_operator.html

When I search online, there are different shape said that is second derivative Gaussian filter. So which one is correct?

enter image description here http://www.me.umn.edu/courses/me5286/vision/VisionNotes/2017/ME5286-Lecture7-2017-EdgeDetection2.pdf (P.39)

enter image description here https://www.swarthmore.edu/NatSci/mzucker1/e27_s2016/filter-slides.pdf (P.31)

enter image description here http://www.cse.psu.edu/~rtc12/CSE486/lecture11_6pp.pdf (P.3)

hippietrail
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Skyline
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1 Answers1

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Yes, the Laplace is defined as the sum of second order partial derivatives. As in the equation you show.

In the first image, f is not a Gaussian, f' is. Thus f" there is the first derivative of the Gaussian. The other image shows the 2nd derivative of a Gaussian.

Cris Luengo
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