Post on 03-Jan-2016
description
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