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): 2-D definition (Riley): –Scale of 0 to 1 –Use edge points to compute d c, d i

Sphericity Approximate with eccentricity: –Fit edge points to an ellipse

Roundness Definition (Wadell): –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 strengthRadius 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

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, Crofts, R.S., “A Visual Measure of Shingle Particle Form for use in the Field,” Journal of Sedimentary Petrology, vol. 44, pp , Fox, J., Castano, R., Anderson, R.C., “Onboard autonomous rock shape analysis for Mars rovers,” IEEE Aerospace Conference, Big Sky, Montana, Mar Pettijohn, F. J., Sedimentary Rocks 2 nd Ed., Harper, New York, 1957, pp Powers, M. C., “A new roundness scale for sedimentary particles,” Journal of Sedimentary Petrology, vol. 23, pp , Sozer, Z.B., “Two-Dimensional Characterization of Topographies of Geomaterial Particles and Surfaces,” Ph.D. Dissertation, Georgia Institute of Technology, Atlanta, Georgia, Mar Trucco, E., Verri, A., Introductory techniques for 3-D computer vision. Prentice Hall Inc., New Jersey, pp , 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