Transcript Computing the Sphericity and Roundness of Rocks

Computing the Sphericity
and Roundness of Rocks
Heather Dunlop
Robotics-811
Dec. 1, 2005
Data Set
Images of rocks and their sphericity and
roundness as determined by geologists.
 Assume segmentation problem is
solved.

Sphericity

3-D definition (Wadell):
dI ds
W  3
2
dL

2-D definition (Riley):
di
R 
dc
– Scale of 0 to 1
– Use edge points to compute dc, di
Sphericity

Approximate with eccentricity:
– Fit edge points to an ellipse
Roundness

Definition (Wadell):
r
N
Rw 
i 1
i
NR
– Scale of 0 to 1
Roundness

Requires detection of corners:
1. Assume all edge points are corners.
2. Assume edge points with largest radius of
curvature are corners.
Roundness
3. Use a corner detector (Tomasi-Kanade)
to pick out the corners.
Corner strength
Radius of curvature of corners
Experiments

Geologists
often use a
chart such as
this for quick
estimation of
sphericity and
roundness
 Problem:
different scale
Crofts, 1974
Experiments

Scale is given for roundness
– convert 0 to 1 into 1 to 6: logarithmic scale

Not given scale for sphericity
– Photocopy and scan chart and compute
sphericity using both methods to obtain
conversion
Results


Sphericity:
Method
Sum Squared Error
Mean Error
Std. Dev. of Error
Riley sphericity
0.89
-0.81
0.49
Eccentricity
1.01
-0.71
0.71
Method
Sum Squared Error
Mean Error
Std. Dev. of Error
All edge points
1.17
0.77
0.76
Largest corners
2.56
1.46
0.65
Strongest corners
0.91
0.13
0.94
Roundness
Future Work

Need to test with whole data set
– Only 10 rocks have been used so far

Segmentation
– Images were segmented by hand
– For testing with all 195 rocks to be
practical, need segmentation
References

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
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Cheel, R.J., “Introduction to Clastic Sedimentology,” ERSC 2P10 course notes, Brock
University, Ontario, 2005.
Crofts, R.S., “A Visual Measure of Shingle Particle Form for use in the Field,” Journal
of Sedimentary Petrology, vol. 44, pp. 931-934, 1974.
Fox, J., Castano, R., Anderson, R.C., “Onboard autonomous rock shape analysis for
Mars rovers,” IEEE Aerospace Conference, Big Sky, Montana, Mar. 2002.
Pettijohn, F. J., Sedimentary Rocks 2nd Ed., Harper, New York, 1957, pp. 54-68.
Powers, M. C., “A new roundness scale for sedimentary particles,” Journal of
Sedimentary Petrology, vol. 23, pp. 117-119, 1953.
Sozer, Z.B., “Two-Dimensional Characterization of Topographies of Geomaterial
Particles and Surfaces,” Ph.D. Dissertation, Georgia Institute of Technology, Atlanta,
Georgia, Mar. 2005.
Trucco, E., Verri, A., Introductory techniques for 3-D computer vision. Prentice Hall
Inc., New Jersey, 1998. pp. 82-85, 101-107.
Wagner, J., Thomas, G., Glasgow, J., Cabrol, N., Grin, E., and Anderson, R.C., “The
Accuracy of Sediment Size, Shape, and Distribution Measurements from Robotic
Geological Images,” IEEE Transactions on Systems, Man and Cybernetics, Part A
(submitted in January 2004).
Acknowledgements
The rock images and geologist’s measures of sphericity and roundness of these
rocks were provided by Geb Thomas at the University of Iowa.