Hi all,

since the possiblility of using PCA (Principal Components Analysis) in analyzing multi band
MER pancam data has been mentioned before in the forum (among others by slinted, tedstryk)
I'd like to share the results of my experiments using my suite of C implementations of
various multivariate analysis algorithms applied to multi-band MER pancam data.

(short recap: the goal of this analysis is to reduce the dimensionality of the multi-filter remote sensing
input or feature space (e.g. 6 dimensional for 6-filter frame sequences) in a low dimensional
"representation space", e.g. 1-dimensional for greyscale or 3-dimensional for RGB color images)

In my experiments I'vebeen using a combination of Principal Components Analysis and Self Organizing
Neural Network Feature Maps as follows:



In this example, the neural network was used to project the original six dimensional feature space
of the L234567 sequence to a 2-dimensional neural grid which in turn was used to
project feature points to the LAB color space and finally transformed to RGB space used to false
color the original image on the left hand side.
The right hand side window illustrates the feature space with the white dots representing
PCA projections of samples 6 dimensional input pixels and the blue grid is a projection of the
neural network after a training phase to adapt to the structure of the feature space as close as possible.

In the feature space representation, on can see an obvious grouping of pixels into distinct clusters
possibly each representing different surface compositions.

Remarkably, the "intrinsic dimension" of the six dimensional feature space is just 2, with the most
prominent component of course being the "brightness" channel which confirms the observation that
color variation in the Martian environment in general is not very complex ...

Here are some other examples with L234567 sequences:




Unfortunately, other than a general interest in implementing, experiencing and playing with the
algorithms (and using them for aesthetic purposes in my color image processing) I am by no means
an expert enough to geologically/chemically judge the value and implications of such analysis and I am sure that JPL must have implemented something similar ... would be interesting to know their results

You've been reading some interesting Pancam papers havent you - They do JUST that - it's very interesting stuff

Doug

I've been reading general papers like this one

www2.in.tu-clausthal.de/ ~hammer/papers/postscripts/NN_sat.pdf

but not specific for the MER pancam yet (although I knew that they must be doing something like this)

Do you have a link/URL to the MER specific stuff you mentioned ?

Amazing study, Nirgal!
How did you trained the neural network? or it is self organized? (In the PCA projection I see more some secondary clusters in addition to main ones you highlight...).
The URL you put above doesn't function, can you repost it?
Ciao!

I'll have a look around for it - but I have a lot of them around - I'll have a hunt.

( JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111, E02S14, doi:10.1029/2005JE002494, 2006 )
Doug

Hi dilo, the Network is self organized (the difficulty lies in tuning the parameters for the self organizing
process, though
However, if the intrinsic diemension is really only "two" and all clusters are roughly located on
a two-dimensional hyper plane, as indicated by the results so far, then one wuld not even need a
neural network but could use the "ordinary" PCA only (which just projects all the points to the
two-dimensional hyper plane that captures most of the variation within the data)

here is the corrected link:
click here for the correct link to the paper



here is another highly recommended paper:

http://webhost.ua.ac.be/visielab/papers/scheun/icpr2000.pdf

Thanks!

Timothy Leary would have loved this, including the pictures.

Check out this paper: I think something similar underlies it and your work, and it won an award!

http://www.cs.indiana.edu/event/maics96/Pr...ef/shareef.html

Nirgal:

This is most interesting and sophisitcated work. I am a bit familiar with simpler forms of cluster analysis, which can be powerful tools for some types of geological problems. If you have other examples it would be interesting to see them. I don't know how much work it is for you to do an analysis on a set of images, but if you take requests, I think I could find a few images that might be interesting experiments.

Yes, surely someone at JPL or one of the universities is doing similar work. It would probably be an interesting question to ask Jim Bell in the next interview. Have you tried this with any of the images from the right filter? The right filter bandwith is almost twice a wide as that of the left.

*head explodes*


super neato work though.

just post/send the Sol/PDS-ID of the image sequence...
and I'll try to do the analysis of it ...

P.S.:

> Timothy Leary would have loved this, including the pictures.

A friend of mine is doing PCA work with VIMS data of Titan

Finding the principle components is the easy part. Figuring out what they all mean is hard.

Volcanopele: "A friend of mine is doing PCA work with VIMS data of Titan. Finding the principle components is the easy part. Figuring out what they all mean is hard."

When I did principal components work with some Viking data, it was only with 3-channel data. I was working with Orbiter images (Violet/Green/Orange bands) and was trying to see what additional information was present in the green band that was different from a weighted average of orange and violet.

There was a little, but not much. Single-pixel signal-to-noise ratio was significantly less than one, and digitization color contours put color banding through the data. But you could see that the "redder" surface materials were all essentially the same "red" and had essentially no +green or -green color variations. They did vary a lot in reflectance, but not in color.

"Less red" ("bluer") areas had considerable color variations, the darkest were had relatively low reflectance in the green band while intermediate brightness areas tended to have higher than average green band data. I was inclined and still am to interpret this in much the same way as the high reflectance and "yellowish" colors of many (otherwise dark gray) rock surfaces that are thinly dust coated at the Viking and Rover sites.

A basic rule in presenting color or color-coded data: The brain is both hard and softwired to interpret shading and color in specific ways. Brightness, coupled with perceived illumination, primarily tells shape. Hue, with the brain correcting for lighting dependent color variations, primarily tells something about composition. Saturation tells degree of composition or mixing between different hued compositions.

Something to try with principle components analysis: Put the first component in a recombined image as "brightness". Use the second and third components as red-blue and green-purple color directions, respectively. Back off on color saturation (contrast stretch of second and third components) if it's over-strong on color. If there are more components, and you want to see what higher components contribute to geological interpretation, try throwing away the second component, substituting third as second and forth as third, etc. You may want to smooth noisy higher components before trying to use them in a composite.

I'll try to see if I can scan some of my old slides of 25 year old data to see what I can post as examples.

Thank you, Nirgal. When I first asked if you could do some others I was thinking of Voltaire and some of the other rocks in that vicinity, but I have not yet found what I think would be the best one imaged with all filters.

Another location that I have found a full set for, and which might be interesting, is the view of the soil churned up by Spirit and imaged in the sol 721 pancams. The color variations in that were quite distinct, though subtle. What do you think about these? http://marsrovers.jpl.nasa.gov/gallery/all/spirit_p721.html

Edit: It just occurred to me that there may not yet be a PDS release of those soil images.