How to calculate a Gaussian distance?

[thomas]

Hello,

in front of me, there is a paper. In this paper the authors write,
that they calculated a Gaussian distance for colors in CIE LUV space.
CIE LUV space is a special color space that represents the proximity
of colors also in a psychological way.

But my problem now is: What is a Gaussian distance and how to
calculate it?

Best regards,
Tom

[dkw]

I found one paper that defined Gaussian distance as:

FD_i,j = ( 1 - exp(-d_i,j /2sigma^2) ) x 255

where d_i,j is the Euclidean distance. Unfortunately neither that
paper nor the reference it cited defined sigma. It appears that sigma
may be defined over a region, and the Gaussian distance would then
yield a scaled or intensity-corrected output.

At any rate it appears that the Gaussian distance is an exponential
transform.

--
David Winsemius

[Greg Heath]

On Nov 19, 10:31 am, dkw <dwinsem...@comcast.net> wrote:
> On Nov 19, 3:45 am, thomas <tohenn...@yahoo.de> wrote:
>
> > Hello,
>
> > in front of me, there is a paper. In this paper the authors write,
> > that they calculated a Gaussian distance for colors in CIE LUV space.
> > CIE LUV space is a special color space that represents the proximity
> > of colors also in a psychological way.
>
> > But my problem now is: What is a Gaussian distance and how to
> > calculate it?
>
> I found one paper that defined Gaussian distance as:
>
>       FD_i,j = ( 1 - exp(-d_i,j /2sigma^2) ) x 255
>
> where d_i,j is the Euclidean distance.

Could it be squared distance ?

Hope this helps.

Greg

[dkw]

On Nov 20, 4:13 am, Greg Heath <he...@alumni.brown.edu> wrote:
> On Nov 19, 10:31 am, dkw <dwinsem...@comcast.net> wrote:
>
>
>
> > On Nov 19, 3:45 am, thomas <tohenn...@yahoo.de> wrote:
>
> > > Hello,
>
> > > in front of me, there is a paper. In this paper the authors write,
> > > that they calculated a Gaussian distance for colors in CIE LUV space.
> > > CIE LUV space is a special color space that represents the proximity
> > > of colors also in a psychological way.
>
> > > But my problem now is: What is a Gaussian distance and how to
> > > calculate it?
>
> > I found one paper that defined Gaussian distance as:
>
> >       FD_i,j = ( 1 - exp(-d_i,j /2sigma^2) ) x 255
>
> > where d_i,j is the Euclidean distance.
>
> Could it be squared distance ?

Generally referred to as Euclidean distance.

[hava...@gmail.com]

Hello Tom
I am wondering if you got any solution for your Gaussian result, because I am facing the same problem I want to get the value for the the below equation,

X=argmin(-sum(log f(ai)) +sum(dj^2)/(2*sigma^2));

The paper says to get the result I have to minimize the X, for your information I have the function f(a)for a group of (a) and also I have d, but my question how start to calculate the value of X, so I can decide the result.?
Best regards
Haval

[Rich Ulrich]

Do you know that you are Replying to a post that is 5 years old?
I remember neither the post nor the person.

Googling and Advanced Googling in groups for < Gaussian distance >
both come up with barely more than the note that you post from.
There is another one in an image processing group, which leads to a
confusing home page. Images "e" and "f" are missing (as I see it with
Firefox); they are the ones that are supposed to show something
about the Gaussian distance transformation.

The form of the equation in the post that you reply to rather looks
like the Gaussian or normal equation. So it is possibly something
that resembles a normal z-score, or some function of it.

My final take-away is that the term has almost never been used,
and it might belong to a proprietory property that you will never be
able to use unless you buy the software.

--
Rich Ulrich