## Ex3 1a)

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andre_w
BASIC-Programmierer Beiträge: 125
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### Ex3 1a)

Hello,

we're still unsure how to get started calculating the 2nd order derivatives of the gauss function.
Should we calculate the derivatives by hand? Should we use the 1D or the 2D version of gauss?

Or is it enough if we use finite differences as an approximation like shown on slide 41 in the lecture about filtering?

I would be very happy about an hint leading in the correct direction Thanks,
Andre

DanielR
Mausschubser Beiträge: 83
Registriert: 19. Feb 2008 13:15

### Re: Ex3 1a)

Hi Andre.
andre_w hat geschrieben: we're still unsure how to get started calculating the 2nd order derivatives of the gauss function.
Should we calculate the derivatives by hand? Should we use the 1D or the 2D version of gauss?
We have calculated the 2nd order derivative by hand using the 1d version of the gaussian function. We have thereby observed quite plausible results, although we were not able to "reconstruct" the exact result given on the excercise sheet example - in contrast to the Harris Detector, where we obtained exactly the results given in the example.

Was anyone able to reproduce the given example using the Hessian Interest Point Detector? andre_w
BASIC-Programmierer Beiträge: 125
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### Re: Ex3 1a)

We're doing the same now. An official answer would be great diane
Windoof-User Beiträge: 25
Registriert: 21. Jun 2009 17:33

### Re: Ex3 1a)

My answer would be that in all cases you have an approximation of 1) a gaussian 2D smoothing, and 2) the computation of the second order derivative. Because everything is done in a discrete (and not continuous) space, with masks.
The most common approximation, which also allows to precompute as much as possible, is to apply the second order derivatives to the Gaussian, and then to convolute the results with the image.
For this second order, you can go for an exact analytical form of the second derivative of the Gaussian, or apply twice the first order derivative of the Gaussian. With the latter, you also get sensible results, although slightly smoother.
The different solutions make sense, and I will discuss about them on Friday. Pick the one you prefer for your submission.
Note that the threshold given in the starting kit would work better with applying twice the first order derivative, but in all cases you should adapt this threshold value to your own solution (it can be really different), in order to have enough interest points per image, and then obtain a satisfactory matching.