@Carl Love 

Please use the attached Maple file.  The objective is to do 2nd Order Gaussian Filtering/Smoothing of the x-y data with fitting of a 10th degree polynomial

_2nd_Order_Gaussian_29_yo_Smoothing_6_21_2024.mw

Thanks 

Ron

@mmcdara 

Are you able to supply the code for the 2nd Order Gaussian Smoothing of my data?

Thanks again!!

Ron

@mmcdara 

Please note Page 1738, First Column, last paragraph of the Kumar paper that describes the method I wish to apply to my data:

If the required optical performance is still not achieved with the above step, then the

D(Iteration-1) design dataset is further converted to the D(Smooth) design dataset by

implementing 2nd order Gaussian filtration. Manufacturing of freeform optics of high-order XY polynomial of 10th order with toolpath based on the D(Smooth) design dataset controls surface imperfections.

Of course I am not manufacturing just getting the best fit so then the surfaces can be best evaluated with optical analyis softeware.

Thanks again.

Ron

@mmcdara 

The units for my data for both x and y are millimeters.

@mmcdara 

Yes the data I sent is unrelated to my data it is to show that there are 2 Gaussian filters and the 2nd order gaussian filter fits best.  Please use the fit that you know is best.  However, my objective is to be able to reference the advantages of 2nd order Gassian filtration for optical surfaces that was demonstrated in the graphs to work best with smoothing and fitting a 10th order polynomial for the surfaces of a lens.  The objective is to take the measurements made of the surfaces of a human lens (my data) by a profilometer and be able to assess the surfaces optically.  I found a paper that is open access (free to anybody) that you should have no trouble opening that is based on the prior paper I sent that you were not able to access.  Hopefully this new paper by Kumar explains what I need.

https://link.springer.com/article/10.1007/s00170-023-12738-7

Kumar_Polynomial_Lens_Fit

Thanks again

Ron

@sand15 
I only have x,y coordinates.  The object is to use Gaussian Smoothing and to ensure the endpoints fit.  Therefore please use the method that will work best.  See the attached image of graphs fitted with different Gaussian orders and note that 2nd order Gaussian filter fits best.  Therefore, I need you to do the same for my data

Thanks 

Ron

@mmcdara 

Do not worry about not being able to access the published paper.  Please use the convolution of field (X, Y) by a 2D  gaussian for the data.  That should work fine.  The reason for my request for your email is that I would like to know if you would want to be a co-author on a paper that myself and co-authors are completing?

Again most appreciated!!

Ron

Ronald A Schachar, MD, PhD

Cell: (858) 784-1705

ron@2ras.com

@schachar 

Can you send me your personal email?  

Thanks

Sincerely

Ron

Ronald A Schachar, MD, PhD

Email: ron@2ras.com

Cell: (858) 784-1705

@mmcdara 

Here is the data in .mw format.
_2nd_Order_Gaussian_29_yo_Smoothing_6_21_2024.mw

I also attached another copy of the paper that should open. [deleted by moderator. see earlier note.]

@mmcdara 

I selected the green arrow but did not realize I had to insert links.  I will do it again.  Please be patience with me I am an ophthalmologist not a mathematician, but this is very important for fitting the surface of the human lens.  Yes, I am pretty certain the 2nd order Gaussian refers to convolution of field (X, Y) by a 2D  gaussian signal.  So please apply that to the data.

Data_for_2nd_Order_Gassian_Smoothing_6_21_2024.maple

[link to copyrighted material edited by moderator. See Terms of Use, Conduct: item h)]
Zeng_Fast_Robust_Gaussian_Filtration_Smoothing_XY_Polynomial_2011

Thanks

Ron

Email: ron@2ras.com

@mmcdara 

Attached is workbook. My understanding of 2nd Order Gaussian smoothing is that it is done for both x and y.  Please see Section 4.1 of the attached paper:

Thus, Aij (x, y) can be calculated separately in the x and y directions; the re-weighting function at each iteration δ(x, y) can be seen as the input signal, while the ith-order Gauss type functions xis(x) and yj s(y) can be seen as the response function or the convolution kernel in the x and y directions respectively. Then, in the same way as the normal Gaussian filter, Aij (x, y) can be calculated: first calculate the convolution of the re-weighting function δ(ξ, η) with the ithorder Gauss type kernel xis(x) in the x direction, and then calculate the convolution with the j th-order Gauss type kernel yj s(y).

   Also I have attached the Workbook.  It would be most appreciated if you can enter the code and send it back to me

Sincerely,

Ron

Email: ron@2ras.com

Cell:(858) 784-1705