Computing the Sphericity and Roundness of Rocks

Heather DunlopRobotics-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):

2-D definition (Riley):

– Scale of 0 to 1– Use edge points to compute dc, di

3 2L

sIW

d

dd

c

iR d

d

Sphericity

Approximate with eccentricity:– Fit edge points to an ellipse

Roundness

Definition (Wadell):

– Scale of 0 to 1

NR

rR

N

ii

w

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:

Roundness

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

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 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).

The rock images and geologist’s measures of sphericity and roundness of these rocks were provided by Geb Thomas at the University of Iowa.

Acknowledgements