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I've recently been asked the following question:

Why are second order edge detectors better at finding edges than first order detectors?

The problem is, I cannot see why! Second order filters are always more sensitive to noise (e.g. laplacian filter), and the same and better results can be obtained when a first order (e.g. sobel filter). Not only is there less noise but the edges appear to be better.

Could anyone shed some light on the matter or give their opinion?

Juan Cruz Carrau
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    your bewilderment is to be expected. it's a stupid question/assignment and should be answered by throwing a worn out shoe in the direction of the instructor. if the instructor thinks this was a sensible question, they failed to teach something. -- first order means steps, jumps, edges. second order means **ridges**, i.e. narrow lines, or peaks in the 1-D case. the question basically asks why a ridge detector should be better at finding edges than an edge detector... both types react to the other's features somewhat but each reacts best to its own features. – Christoph Rackwitz May 24 '22 at 18:22
  • @ChristophRackwitz haha thank you! So basically, when using a second order filter I would be able to find more accurately the exact edge, although the overall result might be more noisy? – Juan Cruz Carrau May 25 '22 at 10:39
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    As @ChristophRackwitz said, second order derivatives are **not** edge detectors, they are ridge detectors. You can build an edge detector by finding zero crossings in the Laplacian, but the Laplacian by itself is not an edge detector. – Cris Luengo May 26 '22 at 00:00
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    That said, the question talks about “second order filters”, not “second order derivative filters”. A second-order filter is understood in the signal processing field to be a filter with a steeper transition between the passband and the stopband. In image processing this terminology is not used, ever, because we are not limited by capacitors and resistors to build filters. – Cris Luengo May 26 '22 at 00:05
  • The question is meaningless as long as "better" has not been defined. And there can be poor 2nd order detectors vs. good 1st order ones. –  Jun 02 '22 at 07:20

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