RE: Minimum spanning circles and Voronoi diagrams

["Creager, Robert S" <CreagRS@LOUISVILLE.STORTEK.COM>]

You're stretching my brain here Chris :-)

> -----Original Message-----
> From: Chris Albertson [mailto:chrisalbertson90278@yahoo.com]
> 
> Why would the error in RA and DEC not be equal?  The only
> thing I can think of is that at non-equatorial areas an
> RA degree is not the same as a DEC degree.  I'll bet the
> one sigma error angle as seen from the earth's center is
> the same both ways.  After all our pixels are square.

I would never expect the error to be equal (I think).  If you have an offset
in ra, but not dec, then the dec error will be 0, while the ra will be
something.  Maybe the scope is jittery in ra during tracking?  Maybe in
reality, the error is very close.  I guess if you have data with random
sample errors, then the errors would be equal.

> 
> I think the error is constant if you use great circle
> angles.
> 
> In the most general case you are right.  we may want to use
> more parameters like brightness and color to help
> match.  Now you have four dimensional "hyper blob" (or
> whatever they call it.)

I really love this idea, but would not even know where to start.

> 
> Try this:  If you know the one sigma error in both directions
> then you can compute the sigma value for any point on the
> plain.  The funtion would look like a little hill centered on
> the star.
> 
> I was thinking that if you had two stars you could superimpose
> the two hills.  You'd have a double peaked hill.  Now look
> at the hieght of the saddle between the two peaks if > N
> (with N about 2) then you have one star not two.
> Finding the minima of a line connecting the two stars is
> not to hard to compute 

Let me try to restate this, as I understand what you're saying, but am not
sure how to get the data to apply.  You choose some radius to match stars
to.  If that radius is too small, you may end up with two stars (the same)
very close.  You plot the sigma's addictively (where they intersect), and
based on some saddle height criteria, you know only one star exists.
Correct?

> 
> Still, I'd just compute the angle between the stars and
> apply a threshold.

But, like I said, this is computing the angle between all the observed stars
which went into making one star, right?

> 
> In the real world the problem is that in some images double
> stars resolve and in others they do not.  When they do resolve
> they are both inside each other's one sigma error bound.  Now
> when the double does not resolve which of the pair is it asigned
> to?   None of the above address this problem and it is the
> one we will see.  If not for this my simple thresholding
> would work
>