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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): 2-D definition (Riley):

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Computing the Sphericity and Roundness of Rocks

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  1. Computing the Sphericity and Roundness of Rocks Heather Dunlop Robotics-811 Dec. 1, 2005

  2. Data Set • Images of rocks and their sphericity and roundness as determined by geologists. • Assume segmentation problem is solved.

  3. Sphericity • 3-D definition (Wadell): • 2-D definition (Riley): • Scale of 0 to 1 • Use edge points to compute dc, di

  4. Sphericity • Approximate with eccentricity: • Fit edge points to an ellipse

  5. Roundness • Definition (Wadell): • Scale of 0 to 1

  6. Roundness • Requires detection of corners: • Assume all edge points are corners. • Assume edge points with largest radius of curvature are corners.

  7. Roundness • Use a corner detector (Tomasi-Kanade) to pick out the corners. Corner strength Radius of curvature of corners

  8. Experiments • Geologists often use a chart such as this for quick estimation of sphericity and roundness • Problem: different scale Crofts, 1974

  9. 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

  10. Results • Sphericity: • Roundness

  11. 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

  12. 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). 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.

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