Presentation given atthe Fall AGU Meeting

San Francisco, December 2006

Robust System for Identification of Martian Impact Craters

Tomasz F. StepinskiLunar and Planetary Institute

Michael P. MendenhallWashington Univ.in St. Louis

Brian D. BueJPL

Young, Amazonian surface, MDIM 2.1 image

The Catalog of Large MartianImpact Craters

(Barlow, Icarus 75, p285, 1988)

> 42,000 craters

Mars has variety of different kind of craters

Old, Noachian surface, MDIM 2.1 image

Hesperian surface, MDIM 2.1 image

Identification of craters from topographic dataADVANTAGES:• DEM provides a direct, three-dimensional representation of Martian surface.

• No problems associated with “visibility.”

• Possibility of calculating more parameters, such as crater depth.

DISADVANTAGES:• Low resolution of available data (MOLA).

THEMIS image, 100 meters/pixel

Rendering of MOLA topography, ~500 meters/pixel

Identification of craters from topographic dataSecond generation approach

Design criteria:• Robust, works well on all types of Martian surfaces.

• Fast, permitting generating a catalog of craters over the entire Martian surface.

• Scale-independent, can be applied to dataset other than MOLA.

• Simple, can be offered as a download.

“Crater finding” transform: an example

Tisia Valles, 383 X 422 pixels transform, r = 5 pixels transform, r = 10 pixels

transform, r = 20 pixels

• The C-Transform smoothes out features smaller than the characteristic size r.

• The C-Transform suppresses low-frequency components in topography, leveling out any slowly changing background gradients.

• A crater of the characteristic size creates a smooth, pronounced basin in the transform surface.

Process of finding craters for layer r = 5 pixels

(1) transform, r = 5 pixels (2) Identified depressions (3) After shape selection

Process of finding craters for layer r = 20 pixels

Final results: Tisia Valles

31 craters identified

No false positives

Some false negatives

Catalog contains:

1) Coordinates2) Radius3) Shape descriptors4) Depth

• New amazing CRATERMATC software.

• Performs C-Transform, crater cores identification, expansion, shape-based selection, all in one easy-to-use package.

• Fast, written in C++

• Produces catalog of crater candidates and images.

• Results can be used as an input to the machine learning-based selection algorithm

• Free!

• Available at cratermatic.sourceforge.net

Technical details on final selectionusing machine learning

• We use WEKA – an open source collection of machine learning algorithms for data mining tasks.• Different (Yes/No) classifier is constructed for each layer using 5 features: radius, depth, radius/depth ratio, two shape coefficients.

• Initial training set was labeled by human expert.

• Accuracy of the classifier for layer 1 is 95%, for other layer it is >85%.

• Obtained classifier is used for all unlabeled crater candidates.

Example: Terra Cimmeria #1, 1269 candidates, 734 craters

Example: Terra Cimmeria #1, details

Example: Terra Cimmeria #1, details

Example: Hesperia Planum, 554 candidates, 305 craters

Example: Hesperia Planum, details

Example: Hesperia Planum, details

Name Coordinates (lower left, long., lat.) (upper right, long., lat.)

Area (millions square km.)

# of craters(our code)

# of craters(Barlow)

Terra Cimmeria #1

(114.0, -18.42)(141.4, -7.58)

1.0 734 499

Terra Cimmeria #2

(117.4, -28.4)(145.4, -17.0)

0.98 748 571

Terra Cimmeria #3

(117.4, -38.6)(145.4, -26.6)

0.92 662 508

Terra Cimmeria #4

(117.4, -47.5)(145.4, -36.5)

0.73 300 409

Hesperia Planum

(107.1, -29.6)(118.5, -17.0)

0.44 305 136

Sinai Planum

(261.5, -29.7)(278.6, -10.3)

1.0 468 124

Identification of craters: automatic vs. manual

Automatic vs. manual: comparison of crater counts

Red - craters present in the Barlow catalogand identified by our algorithm.

Green - craters identified by our algorithmbut absent from the Barlow catalog.

Blue - craters present in the Barlow catalogbut not identified by our algorithm.

Automatic vs. manual: comparison of craters’ diameters

Comparison between:Our dataset (automatic)Barlow catalog (manual)

1370 craters in:Hesperia PlanumSinai PlanumTerra Cimmeria

Our values of diameterare systematically largerby about 15%.

Automatic vs. manual: comparison of craters’ depths

Comparison between:Our dataset (automatic)Joe Boyce dataset (manual)

144 craters inHesperia PlanumSinai Planum

Our values of depth aresystematically larger by about 30%.

Main reason for observeddiscrepancy:Difference in how craterdepth is defined.

Diameter – depth statistics: Terra Cimmeria

Diameter – depth statistics: Terra Cimmeria

Conclusions• Our DEM-based system for identification and characterization of Martian craters is robust and practical.

• We are finding 43% more craters than in the Barlow catalog. These are mostly small craters.

• There are almost no false positives.

• We have established a large training set to be used for identification of craters over the entire Martian surface.

• Our estimate of craters’ radii and depths compare well with results of manual measurements.

Future• Compile catalog of craters over the entire Mars surface.

• Apply our system to Martian datasets other than MOLA.

• Apply our system to datasets from other planets.