High-Res DEMs from single HiRISE images, First results of new "Shape from Shading" algorithm Options

[Nirgal]

Hi all,

Here the long overdue continuation of the "Alien Landscapes" series. This time based on 3D
DEMs generated with "Shape from Shading" from single HiRISE images.
Enjoy

Click on Images for larger version.

Detail views from PSP_002172_1410 (large gully system)





Detail view of Gullies from PSP_001376_1675





Detail of gully system in PSP_002022_1455



Dune Views from PSP_004339_1890





Detail from PSP_001834_1605





Here is some background info on the making of the images:

"Shape from Shading" (SFS) i.e. the possibility to extract shape information from a single image has always been a fascinating topic for me.
Now I found the time to implement a prototype for a new SFS algorithm based on some ideas that I've been thinking about for a long time.
The problem with existing SFS approaches (see here for a survey is that they either tend to over-smooth the details (due to the regularization constraint) or suffer from excessive noise in the high-frequency components of the reconstructed surface. Another problem is the large demand on CPU ressources which would make them very challenging to apply to large scale input data, such as HiRISE orbiter images.

So for a long time I was rather sceptical as to the potential of SFS and it was my impression that Methods based on multiple images (stereo) must be far superior to single-image SFS.

However, after a long time of experimenting, combining existing approaches with some new ideas, I got the following quite promising first results that I'd like to share:

All of the images were generated from a single HiRISE image (no depth information was used from stereo or laser altimeter data).
Also, no texturing or additional coloring/shading was applied when rendering the surface.
Every detail visible is real 3D down to the pixel-level...
For rendering I used a very simple model based on lambertian reflection with gouraud shading.

The resolution of the images is still moderate: that is downsampled details crops in the order of 0.5-1 Megapixels.
However, despite the heavy math machinery that drives the core of the algoritm (several systems of equations with millions of unknowns)
the processing time is still moderate (about 15 Minutes per med-res image, using about 2 Gigs main mem) such that the application to full-res HiRISE images should be possible

The following image shows an example to illustrate the general principle (click to enlarge).


On the left hand side the 2D input image (simple noisy JPEG from the Web with unknwon light source direction). On the right hand side shows the recovered 3D surface re-lighted under a different light source direction.
Note that one problem of the current implementation of the algorithm is it's vulnerability to notable distortions in the low frequency components (i.e. large scale variations) of the generated surface. However I'm confident that this can be overcome by an improved version or by adding the large-scale depth information from stereo-based DEMs or altimeter data (MOLA) where available.

[Nirgal]

Upon a request posed over at the "Dust Avalanche" thread I did a small 3D DEM study of an area near Endeavour Crater based on a single image cropped from PSP_010341_1775.



Click image to see the whole gallery. The first image shows the DEM rendered from above with the same lighting conditions as the original image so as to give an idea of the accuracy of the 3D reconstruction (note, however, that the accuracy decreases somewhat when the DEM is lit from other than the original lighting direction).

The generated DEM consists of 8192x4096 = 32 million polygons with true 3D (means no texturing) post spacing at full HiRISE resolution (28.6 cm/pixel ).

Here is my usual Disclaimer: the rendered DEMs are intended for visualization only. The absolute heights are not calibrated and there may be distortions due to albedo variations.

[tdemko]

This area has fascinated me for a while and Nirgal's renders have crystallized some of my thoughts. Since I'm a sequence stratigrapher by trade and training (and some say religion...), I look at strata in terms of their geometry (shape and topology of the boundaries) and where and how they terminate. The method of tracking stratal terminations originally comes from interpreting seismic profiles (seismic stratigraphy) where one traces the continuity and termination of reflections. Through this, relative ages, directions of transport, subsidence patterns patterns and other cool things can be determined. Among other types, some of the most obvious stratal terminations include onlap, downlap, and truncation. These little schematic cross sections show the geometry of onlapping and downlapping strata:



In the image from Nirgal below, I've highlighted several areas of stratal terminations in one of my (in)famous 5 minute speed interpretations:

red: onlap
blue: downlap
white: truncation by channels

The slightly sinuous channel on the right side of the image does some really cool things, including exiting the terrace region at the top of the image through a v-notched canyon. It suggests the channel is a subsequent geomorphic feature that has incised into previously buried strata as the landscape has been regionally degraded (think Colorado Plateau, Canyonlands, Grand Canyon, etc.). The raised lip of the terrace on the right is also intriguing (due to channel incising?, differential erosion?, etc.)

In general, the hill looks like it was a preexisting topographic feature that was onlapped by several periods of deposition, including the terrace unit which seems to have formed as an apron of downlapping strata that prograded away from the hill (like a shoreline). Subsequent regional landscape degradation has exposed various levels in the stratigraphy which allows us to examine the relative timing and geometry. The degradation has included a channel-incisement phase that has cut through most of the units and has been guided by the differential erodibility of the strata.

Ground truthing these interpretations when Opportunity get here, especially examining the depositional nature of the units and the relative timing of deposition and erosion, is going to be very interesting!

[ngunn]

The raised lip of the terrace on the right is also intriguing

Fascinating interpretation there, thanks for sharing. There is one note of caution I'd like to sound in relation to small details of these images - it may be wrong and if so I hope Nirgal will correct me. He himself pointed out that albedo differences could affect his results here. In particular the 'beach terrace' is lighter toned than most of the rest of the scene. I think this might account for its edge looking different on each side of the hill, depending on the original direction of illumination. Funnily enough this difference was the first thing my daughter remarked upon when I showed her the images. Is it real or not? I'm not sure.

I have another question. What is the elevation of the 'beach terrace' and how does it compare with the lowest elevation on the perimeter of Endeavour? I think they're fairly close.