The color map I chose when doing Victoria does a poor job of showing the Anatolia features - they all ended up green. Maybe I was too optimistic. But they are there in the data, and can be clearly seen in the grayscale image, for example image3a.png.

Yes, I remember a description of a conversation between the scientists and the drivers when they discussed the original Anatolia:

Drivers - "Wait a minute, explain again what you said about 'falling in'".

In any case I think they are difficult to cross and so the rover will have to weave around them.

I have finally completed my analysis of the new Endeavor image. I used exactly the same parameters as for my Victoria analysis. Apparently the Victoria image was near the limits of a couple of the tools I used because the new image broke them. But I persevered and found different ways to get it into the processing tool (the actual analysis tool didn't have a problem with the size, although I think it was getting close!). And of course the outputs are larger as well. I did my 64x64 2dfft on every fifth pixel in each direction, and filled the result in all 25 pixels (even so it took 10 hours!). So I can decimate by 5x each way without losing any information at all. That png file is 5961x17628 pixels and 130MB, and I don't know how to post it. The jpgs are of postable size. So I further decimated by 4x each way, and now the files are small enough to be posted to speedyshare, as I did earlier. The links are here (jpgs are on 5x decimated from original, pngs are 20x):

blended image:
http://www.speedyshare.com/714664859.html
(image1a.png)
http://www.speedyshare.com/793846195.html
(image1.jpg)

analysis only in RGB:
http://www.speedyshare.com/725624573.html
(image2a.png)
http://www.speedyshare.com/714399661.html
(image2.jpg)

analysis only as grayscale:
http://www.speedyshare.com/978793399.html
(image3a.png)
http://www.speedyshare.com/604469177.html
(image3.jpg)

original image at same scale:
http://www.speedyshare.com/591706186.html
(image4a.png)
http://www.speedyshare.com/338648594.html
(image4.jpg)

I attach here some previews at yet another 2x decimation and conversion to jpg. I originally used a somewhat more optimistic choice of color scale than James did (which I stuck with for this one), and it makes the Endurance section look like a cakewalk, at least as far as ripples go. I also saw lots of 'Anatolia' features that could be a whole different kind of drivability hazard. Looking forward to the journey!

If anyone wants the larger files and has a place for me to send them, just let me know!

Bill Butler

I have uploaded my png files to speedyshare - thanks to Juramike for the suggestion. The links are:

http://www.speedyshare.com/217480217.html - final blended result of diagnostic and terrain
http://www.speedyshare.com/119902873.html - diagnostic only as green/blue/red
http://www.speedyshare.com/473996607.html - diagnostic only as greyscale

Let me know if I screwed something up and you can't access for any reason. Thanks!

Bill

And finally I post the actual values of the 2dfft attribute as a greyscale image. I post it along side the original photographic image at the same scale. To my eye, it does appear that I can see things in the processed image that I cannot in the original. I agree with CosmicRocker that the main lobed features are present in both, but the processed image really does look to me to contain rays, more so than the original. I suspect it has to do with slight topographic highs along the rays, where the sand tends not to accumulate, hence smaller dunes. I would expect such a topographic pattern shortly after imact, but it is surprising it has perisisted to present, if that is the cause.

Bill

In this post I will attach just the raw color classification. Artifacts from jpg compression are evident, but of course aren't on the original png file.

Bill

Well, better late than never! I tried many different plans of attack, but in the end could find no combination of attributes that did any better than the single attribute of mean spacing of the ripples as derived from my 2dfft filter. The texture classifier I played with for a while will only give improved results if there are several attributes that together segment the image, but in this case I could not find such suitable attributes. They either weren't very diagnostic or were highly correlated with the spacing attribute. Even the 2dfft is probably overkill, since all the ripples are all in virtually the same direction. So I think my result is very similar to James' result, although I colored it somewhat more optimistically. I also did some work on attempting to pick the ripples to identify the highly curved segments, but nothing worked as well as the very elegant and simple method of SteveM's!

A side note - you will see in my images that the sides of the image appear different than the center. It appears that several images were combined to form the image I started from, and while there is no visual difference (at least to my eye), the difference stands out clearly in many of my computed attributes. For example, the standard deviation of the pixel values is quite different. Did others find this problem, and how did you get around it? Did you start with PSP_005423_1780_RED.QLOOK.JP2 as I think I did, or from a different source?

I have several results to show, and I will spread them out over several posts. All the images here are jpgs, which I needed to use for size reasons. They are also chopped down to some degree. Because of time, I did my analysis only on every 5th pixel in each direction, and put the result in the surrounding 25 pixels in the original image. So I could shrink the result by this factor with no loss of information. All but the main result I shrunk again just to save space. I have all the png files at the 5x5 shrunk scale, which are of the order 20MB, but I don't have any place of my own to post them, and I don't have any experience with sites out there that will host it for me. I'll be happy to provide them if anyone can give me some instructions.

Now that I've put you to sleep with my rambling - here is my result!

Bill

Steve M.,

I think that filtering in the 2dfft domain is a nice idea. I think it will be important to not just cut out some components, but smoothly suppress them with some sort of dampening field. Sharp edges in one domain makes ringing in the other. I've got a couple of other ideas to work on first, but I'll keep it in mind. Thanks!

Bill

Hi Paolo,

Could you give us some guidance on what you mean by large ripples? Are they what is in the eastern half of Erebus, or do you mean even larger than that? Approximately what percentage of the full Erebus image we have been playing with would you consider large ripples? Thanks!

Bill

Hi Geert,

I may not have been as clear as I wanted about the attributes I was computing. The only attribute I posted earlier today that was computed in the image domain (eg actual pixel values of the image) was the one I called stddev, which was the standard deviation of the pixel values. All the others were computed in the frequency domain. I took a 2dfft of a 64x64 square of pixels, keeping the lowest 32x32 amplitudes of the frequency components, and take their absolute value. So I think your comment:

"What I hope will give you an indication of 'cross-ripples' is taking the standard deviation in the frequency range of the ripples..."

is what I'm already doing. That is, to compute wdist I find the centroid of the frequency samples, or the amplitude weighted mean of all of them: mean_fx=sum(amp*fx)/sum(amp), and mean_fy=sum(amp*fy)/sum(amp) over all the samples. This gives me a coordinate (mean_fx,mean_fy). The radial distance to this point is the mean frequency of the ripples, and its reciprocal is the mean wavelength, which is what I call wdist. I started out just using the maximal amplitude sample for that coordinate, but I thought this might be too influenced by noise (I called this dist earlier). Interestingly, I found that dist was significantly more than wdist (like 2x-3x), for reasons I still don't understand, but the trend of the two quantities is similar. wstddev is the standard deviation of this distribution, or the width in frequency space of the ripple distribution. I don't take the reciprocal here, because a large frequency distribution width should correspond to a large wavelength distribution width. There is probably a more accurate way to do it, but I think to just get the trend right this is fine.
Similarly, wangstddev is computed in the frequency domain. Each cell in the 32x32 fxy space is assigned its polar angular value, and then I compute mean angle wang=sum(amp*angle)/sum(amp) over all the cells. wangstddev is computed similarly, but using the standard deviation equation rather than the mean. Since a single angle in frequency space also maps to a single angle in image space, I expect that wangstddev should measure the spread of angles present in the actual image. I haven't played with different sized ffts, and this may be helpful, but I feel like most of my pictures are rather splotchy, and I don't have a good enough feel for the ground truth to know which ones are the most helpful.
I also think a fingerprint algorithm may be helpful here, but I don't have one handy

If I have completely misunderstood your post, I apologize. Carry on and have fun!

Bill

I have played around with some more attributes. Previously, I was doing a 64x64 2dfft and finding the maximal sample in frequency space. From the full amplitude distribution in the 2d frequency space, I have computed several statistical quantities, and these are the most interesting ones:

wdist - the radial distance of the amplitude weighted average of the position, ie the centroid of the amplitude distribution (then converted to a physical distance by taking the reciprocal)
wstdev - the standard deviation of the amplitude distribution, which should be related to the width of the distribution - bigger values should mean more frequencies and thus more variation in ripple size within the window (no reciprocal here)
wangstddev - the standard deviation of the amplitude weighted angle distribution - bigger values should mean more angles in the window, which was my attempt to find the curvy ripples. This didn't seem to be successful.

I also replot the simple standard deviation of the values in the 64x64 window (no fft) in a color map consistent with the other three. I have scaled the color map in each case so that the data pretty well covers the whole color range.

I have also tried some classifications, with mixed results. The small ripples (eg in the center of erebus) are easily distinguishable, and the medium sized ripples on the east side of the crater are reasonably distinguishable. But I have not been able to highlight the curvy ripples, or reliably segment out the bedrock areas yet.

I think that Juramike's idea of looking to the ground truth to choose clasification examples is the right way to go, but of course Paolo is right that that job is best done by the guys with the most data. I would be happy to incorporate such guidance in the classifier.

I think I've done about all I can at this point without knowing more about what is helpful and what is not. But it has been a very interesting exercise. I was not optimistic at all in the beginning about the 2dffts, but they turned out to do a very nice job of distinguishing ripple spacing! Looking forward to the trip!

Bill

I have applied my tools to the erebus image to make comparisons easier. I have five new images.
Three of them (amp, dist, ang) are based on a 64x64 fft. I find the sample in the 2d fft plane with the maximal absolute value, then convert to radial coordinates and invert the distance to get a real distance. I do the calculation on every third sample in both directions, and put the result in all 9 pixels around the target sample.

They are:

amp - the absolute value of the largest fft sample.
ang - the angular component in degrees of the largest fft sample. Correlates well with ripple direction
dist - ripple spacing, in arbitrary units, from the radial component fft space
mean, stddev - computed on the same 64x64 moving panel as the ffts.

In my opinion, the dist attribute is very useful, as is the mean and stddev (although these appear well correlated with each other). The ang attribute should not be useful for traversability, except when you only want to consider traverses in a particular direction. Even so, the ripples are so uniformly oriented I don't think we need this one.

Ultimately, I will try the texture classifier with these attributes and possibly some others, attempting something along the lines of Juramike's suggestion. You can see my nominated regions, which I call bedrock, small, large, huge ripples. There is no parking lot texture in this image. Any suggestions about the location of these nominations are welcome.

Bill

And the last image:

And my last post for the moment - The three 2DFFT attributes. I look for the maximal fft value, other than at the origin, and convert to radial coordinates to compute a distance and angle in frequency space. I take the reciprocal of the frequency distance to get a real distance, and I wasn't sure what to do with the angle - I think I can pretty much leave it alone (is there a rotation or something?). I also plot the absolute value of that maximal fft value. This should be related to the strength of the ripples, but will also be related to their regularity. Strong ripples with varying periodicity will spread out the energy over several frequencies, so the maximum will be lower. I think the standard deviation attribute does a better job of this. On the other hand, if both attributes are given to a classifier, maybe it could distinguish strong regular ripples from more chaotic ones.

The titles of the images are in the upper left hand legend in the picture. Their meanings are:

rippledist - reciprocal of the frequency distance. Should be correlated with ripple spacing regardless of orientation. Not calibrated to any units.
ripplearg - angle of ripple (in frequency space, but should be something very close to physical space)
rippleamp - the absolute value of the maximal FFT sample

BTW for these images I did compte every pixel, as the subimage I was using was 2000x1100. WIth a 64x64 fft, this took about 5-10 minutes. Doing every third pixel goes 9x faster and I think give virtually as good information. For the full image, it may even require decimating further, but I could also imagine focusing on the likely rover paths and doing more detail.

I see I've run out of space for images for this post. I'll put the last one in the next post. If there is a better way to post these images, let me know. Thanks!

Bill

Followup to last post. These images are the raw image I started with, and the standard deviation attribute, similar to what some others were playing with. I think this attribute is a good indication of ripple height/width, which seem to me pretty well correlated with each other.

Bill

Long time lurker, first time poster.

I played around with a texture classifier I have access to at work. I picked a few image attributes I thought might be relevant, and nominated a few regions of example textures into which I wanted the image classified. The two attached images are from a place near the destination, with the classification in color. I thought it nicely segmented out the difficult ripple terrain from the rest. The polygons you see in the images are some of the nominated regions. Lots of things can be tweaked, like the choice of attributes, the example polygons, and the colors. I think I picked too many example areas, since the good areas are a mixture of colors, but the rippled areas area clearly segmented out.
The area is near the destination of Edurance, and the image has been rotated - just an artifact of my importation to the processing system that I forgot to undo.

I have also tried doing 2d FFTs to extract ripple spacing, orientation, and strength, from the maxima of the spectra. This seems successful, and I'll post some of those images shortly.
With these FFT attributes available to the texture classifier, it might be possible to nominate even the different ripple styles and have them individually classified. I have not tried this yet.

PS Since this is my first post, I'm not sure if the images will come through OK. If it doesn't, I'll try again!

Bill Butler