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PostPosted: Fri, 04-12-09, 16:38 GMT 
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Hi all,

let me continue by discussing first for completeness the effects of galactic & internal extinction as well as that of redshift on the above B-V color versus Hubble stage correlation. Guillermo has already been asking about the effects of the redshift on the galaxy colors that we expect to be small.

Then -- towards the end-- I'll start with the very task of galaxy coloration via B-V information!

Fortunately, the RC3 catalog offers already a column (B-V)oT with the total (B-V) values corrected for redshift as well as galactic & internal extinction. The latter effects could well be more significant.

Let's see what the RC3 data say!

So, in analogy to my first post in this thread, let us first compare the correlation of (B-V) with the Hubble Stage (T) without and with the mentioned corrections:

1) Without these corrections (as above)
=============================
Image

Quadratic least-square-fit relation
Code:
(B-V)T_th = 0.865 - 0.0334 * T - 0.000974 * T^2


2) With these corrections
===================
Image

Quadratic least-square-fit relation
Code:
(B-V)oT_th = 0.738 - 0.0397 * T + 0.000560 * T^2


What do we observe? Firstly, the general trend and also the range of the correlation remains identical. But upon a closer look, one can notice some interesting differences:
The shape of the black best-fit curve has slightly changed from convex to concave, while the initial and final (T, B-V) values have remained almost identical. Moreover, we observe a markedly smaller fluctuation of B-V values notably for negative T (i.e. on the left)

This latter feature is also evident upon comparing the two B-V distributions for the three fixed values of the Hubble Stage T:

1) Without these corrections (as above)
=============================

Image

2) With these corrections
========================

Image


In the latter case we clearly note the sharper peaked B-V distribution notably for T = -5 (more reddish galaxies, elliptics, lenticulars).

++++++++++++++++++++++
That's nice, since the better corrected case also gives a sharper correlation of B-V with the galaxy morphology!
++++++++++++++++++++++


++++++++++++++++++++++
The next step is to implement a B-V dependence into our generic color profile, such that the colors of a set of reference galaxies with small B-V ~ 0.4-0.5 (blueish) and with large B-V ~ 0.8-1 (orange/reddish) are perfectly matched within Celestia.Sci !
++++++++++++++++++++++

As to selecting reference galaxies, one has to be VERY careful, since all too often available color photographs are artificially modified/enhanced (for PR reasons ;-) ) and color biases differ strongly among different imaging sources ! So we need to use a set of blue and orange/reddish reference galaxies that are all from the SAME source. Then the relative color effects are much more trustworthy, while absolute color rescalings are relatively harmless and rather a matter of taste and monitor display ;-)

Therefore, I mainly chose as a reference, some galaxies from SDSS-DR7, the seventh major data release of the Sloan Digital Sky Survey.

http://cas.sdss.org/dr7/en/tools/places/
http://cosmo.nyu.edu/hogg/rc3/

Another big advantage of SDSS-DR7 is that the relevant galaxy spectra are available and may be directly inspected! Many further useful tools are available on that site as well.

Let me just display some of the reference galaxies that are all catalogued in RC3 , to give you a flavor how well the bluish and reddish colors are distinguishable:


1) low B-V ~ 0.4-0.5 (blue reference galaxies)
=======================================
Image

Image

Image


2) high B-V ~ 0.8-1.0 (orange reference galaxies)
==========================================

Image

Image

Image


++++++++++++++++++++++++++++++++
You can clearly observe from these nice SDSS-DR7 photographs (using a universal photographic color bias) the striking B-V and T dependent coloration!
++++++++++++++++++++++++++++++++


Currently, I am still tuning and checking the colors ... stay tuned ;-) there will be concrete examples within Celestia.Sci in the near future.

Fridger


Last edited by t00fri on Sat, 05-12-09, 19:30 GMT, edited 1 time in total.

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PostPosted: Sat, 05-12-09, 13:45 GMT 
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I was just going to say that... all that you said there... you beat me to it! :D


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PostPosted: Sat, 05-12-09, 19:33 GMT 
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bh wrote:
I was just going to say that... all that you said there... you beat me to it! :D


;-) He he!

Next time, just try to be a LITTLE bit faster :lol:

Cheers,
Fridger


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PostPosted: Sat, 19-12-09, 14:09 GMT 
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Hi all,

before showing you next time the final result of this galaxy coloration project in form of representative, individually colored galaxies, let me tell you a bit more about the strategy and custom tools that I have used.

Custom tools (Maple) were essential for trying out various color profiles quickly, notably in comparison to my reference SDSS set that is matched to the RC3 galaxy catalog:

http://cosmo.nyu.edu/hogg/rc3/

+++++++++++++++++++++++++++++
First of all, how can we parametrize complex RGB color profiles for individual galaxies most easily and intuitively, i.e matched to the actual requirements of the project?
+++++++++++++++++++++++++++++

The trick is to compose the galaxy color profiles NOT in R,G,B color space but rather in the so-called H,S,V space. Here H=Hue, S=Saturation ("color intensity") and V=Value ("brightness").

The transformation between RGB and HSV is a standard task in image manipulation. I have also written a corresponding C++ method in Celestia long ago.

Why is color matching in the HSV basis so much simpler?

Well in first approximation, during the coloration process, one may set the Value (<=> brightness) and the Saturation (<=> "color intensity") equal to some convenient, constant value across a galaxy! Then the coloration task reduces to just parametrizing the desired Hue profile (instead of THREE profiles for the individual R,G,B colors!). After the color transition (Hue) is settled correctly, one then proceeds to tune both the two intensities (S and V) in a second step. The latter does interfere very little with the Hue settings, which makes the coloration task so much simpler and more intuitive.

The Hue is usually given in degrees within the range 0 <= H <= 360 degrees. Here is a nice circular Hue display (from The GIMP):
Image

In this example, the Hue is located along the circle, increasing counter-clockwise. Presently we have set H=0 (white bar on circle). The actual color with V=100% and S=20% is displayed as well at the bottom.

++++++++++++++++++++++++++++
For Celestia (.Sci), we need to map the Hue values across a galaxy to a field, the so-called colorindex, with 256 (r,g,b) - triplet entries (i = 0..255). These triplets denote the sprite color starting from the galaxy center (i=0) and increasing towards its periphery (i = 255).
++++++++++++++++++++++++++++

What I needed next was a mathematical function that allows to implement intuitively -- yet precisely-- the transition of the Hue from a desired starting value (hue0) to a final one (hue1), at a particular location of the colorindex (i=i0) with a certain "transition speed" = slope.

Hence I determined a very flexible and intuitive hue-transfer function from the ansatz
Code:
hue = a - b * tanh(-i /c+slope)

involving the 4 parameters a, b, c, slope besides the colorindex i.
The three parameters a, b, c were fixed in terms of hue0, hue1, i0 and slope with Maple from the 3 conditions:
  • at i -> 255 ~ 'infinity': hue = hue1;
  • at i = 0 : hue = hue0;
  • at i = i0 : hue = (hue0 + hue1) / 2;
    i.e. i0 = hue transition point in i

The result then reads:
Code:
hue = hue1 + (hue1 - hue0)/sl * ( -1 + tanh( i * (slope - arctanh(sl / 2 - 1))/i0 - slope)));
with hue-transition "engine"
sl = tanh(slope) + 1;

As desired, the transition hue0 -> hue1 gets much sharper for increasing slope parameter. Remember that the hyperbolic tangens, tanh(x), varies between -1 and +1.

For Saturation and Value profiles in the second step, I also chose some flexible, intuitive forms. As a last convenience, I implemented the option of skipping a certain band of colors (green!) during the hue transition.

The resulting tool and the ImageTools package of Maple 13 then allowed quickly AND intuitively to try out any desired H, (and S,V) profiles in terms of a realistic RGB test image.

++++++++++++++++++++++
Notably after these considerations, I can just measure the initial and final H,S,V values of any SDSS galaxies with the GIMP "pipette" tool and Maple/C++ code do the rest.
++++++++++++++++++++++

Here are some actual example plots generated with my corresponding Maple code:

Look e.g. at this SDSS galaxy, NGC 3344 with a measured value B-V = 0.57 according to the RC3 galaxy catalog. As you can see, it's indeed quite blue but still with an ochre/orange center ... So a "visual blueness" B-V=0.57 seems adequate.

Image

According to the GIMP "pipette tool", the colorindex profile should start around Hue = ochre/orange ~ 37 in the galaxy center, transiting quickly (slope = 5.0, say) to Hue=blue ~ 208 in the outer regions. In addition the green band of hue (50<H<180) must be skipped during the transition!

Here is what my Maple tools display for such a configuration:

First the corresponding plots of Hue, Saturation and Value
(Click for Big!)

Image

Note that a more realistic behaviour of S,V than a constant has also been implemented. Again the "pipette tool" provides central and peripheral values for the galaxy under consideration...

Then, after my Maple code combined quickly the H,S,V layers and transformed them to RGB color space, here is the image content of the colorindex (i=0..255)
top: combined layers in RGB space,
bottom: R,G,B layers displayed separately as grayscale images.

Image

Since my modified C++ code in galaxy.cpp has all these considerations implemented as well, Here is the color result of Celestia.Sci for this configuration.

Image

Suppose, I now wanted to see what the galaxy would look like with a somewhat redder central region (and everything else the same) I just enter hue0=17, say (instead of 37) and Maple instantaneously gives this:

Image

A Celestia.Sci run indeed confirms the redder center:

Image

I hope this was kind of instructive? However, the actual procedure was considerably more involved ;-) ...

Fridger


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PostPosted: Sat, 19-12-09, 20:09 GMT 
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:shock:


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PostPosted: Sat, 19-12-09, 20:22 GMT 
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fenerit wrote:
:shock:


That "face" is hard to interpret ;-)

Fridger


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PostPosted: Sat, 19-12-09, 20:38 GMT 
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t00fri wrote:
fenerit wrote:
:shock:


That "face" is hard to interpret ;-)

Fridger


I'm shocked! Practically you have solved the problem.


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PostPosted: Sat, 19-12-09, 20:41 GMT 
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fenerit wrote:
t00fri wrote:
fenerit wrote:
:shock:


That "face" is hard to interpret ;-)

Fridger


I'm shocked! Practically you have solved the problem.


Yes ;-)

Fridger


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PostPosted: Sat, 19-12-09, 21:35 GMT 
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Just curious, then I no longer escape out the topic: such Celestia.sci does is mind as "complement pack" for official distributions or is an "abarth" version by you? For instance, the galaxy render c++ code needs to be changed for accomplishing that beautiful behaviour: will these changes belong to all the next Celestia's versions or just to .sci?


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PostPosted: Sat, 19-12-09, 21:50 GMT 
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fenerit wrote:
Just curious, then I no longer escape out the topic: such Celestia.sci does is mind as "complement pack" for official distributions or is an "abarth" version by you? For instance, the galaxy render c++ code needs to be changed for accomplishing that beautiful behaviour: will these changes belong by all the next Celestia's versions or just to .sci?


For now, Celestia.Sci is merely a "name" to the outside ;-) . Precise definitions, modalities and more will follow when things are getting ready. This may still take a while, since so far, I am working just by myself. Also, I don't want to spend all my spare time in front of a computer;-) ...

Unfortunately, Celestia.Sci developments are not available for download before a first release of the project has taken place. I continue to develop also for the official Celestia distribution, just like ChrisL is involved BOTH in Celestia and Celestia.STA.

Fridger


Last edited by t00fri on Sat, 19-12-09, 21:56 GMT, edited 1 time in total.

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PostPosted: Sat, 19-12-09, 21:53 GMT 
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Ok.

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Never at rest.
Massimo


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