This Article 
 Bibliographic References 
 Add to: 
Analysis of Spatially and Temporally Overlapping Events with Application to Image Sequences
October 2006 (vol. 28 no. 10)
pp. 1707-1712
Counting spatially and temporally overlapping events in image sequences and estimating their shape-size and duration features are important issues in some applications. We propose a stochastic model, a particular case of the nonisotropic 3D Boolean model, for performing this analysis: the temporal Boolean model. Some probabilistic properties are derived and a methodology for parameter estimation from time-lapse image sequences is proposed using an explicit treatment of the temporal dimension. We estimate the mean number of germs per unit area and time, the mean grain size and the duration distribution. A wide simulation study in order to assess the proposed estimators showed promising results. The model was applied on biological image sequences of in-vivo cells in order to estimate new parameters such as the mean number and duration distribution of endocytic events. Our results show that the proposed temporal Boolean model is effective for obtaining information about dynamic processes which exhibit short-lived, but spatially and temporally overlapping events.

[1] I. Molchanov, Statistics of the Boolean Model for Practitioners and Mathematicians. Chichester: John Wiley and Sons, 1997.
[2] D. Stoyan, W. Kendall, and J. Mecke, Stochastic Geometry and Its Applications, second ed. Berlin: Wiley, 1995.
[3] I. Molchanov, Theory of Random Sets (Probability and Its Applications). Springer, 2005.
[4] G. Matheron, Random Sets and Integral Geometry. London: Wiley, 1975.
[5] G. Matheron, Eléments pour une Théorie des Milieux Poreux. Paris: Masson 1967.
[6] Random Sets. Theory and Applications, The IMA Volumes in Mathematics and Its Applications, J. Goutsias, R. Mahler, and H. Nguyen, eds., vol. 97, 1997.
[7] J. Serra, Image Analysis and Mathematical Morphology, vol. 1, Academic Press, 1982.
[8] J. van den Berg, R. Meester, and D. White, “Dynamic Boolean Models,” Stochastic Processes and Their Applications, vol. 69, pp. 247-257, 1997.
[9] O. Dousse, P. Mannersalo, and P. Thiran, “Latency of Wireless Sensor Networks with Uncoordinated Power Saving Mechanisms,” Proc. Fifth ACM Int'l Symp. Mobile Ad Hoc Networking and Computing, 2004.
[10] E. Dougherty and A. Grigoryan, “Automatic Counting of Illuminated Spheres in a Random Boolean Model,” Image Processing: Algorithms and Systems, vol. 4667, no. 4667,Int'l Soc. for Optical Eng., pp. 170-180, 2003.
[11] K. Schladitz, S. Peters, D. Reinel-Bitzer, A. Wiegmann, and J. Ohser, “Design of Acoustic Trim Based on Geometric Modelling and Flow Simulation for Nin-Woven,” Technical Report 72, Fraunhofer ITWM, Feb. 2005.
[12] M. Kaksonen, C. Toret, and D. Drubin, “A Modullar Design for the Clathrin- and Actin-Mediated Endocytosis Machinery,” Cell, vol. 123, pp. 305-320, 2005.
[13] M. Ehrlich, W. Boll, A. van Oijen, R. Hariharan, K. Chandran, M. Nibert, and T. Kirchhausen, “Endocytosis by Random Initiation and Stabilization of Clathrin-Coated Pits,” Cell, vol. 118, pp. 591-605, 2004.
[14] N. Cressie, Statistics for Spatial Data. Revised Edition. New York: John Wiley and Sons, 1993.
[15] P. Diggle, Statistical Analysis of Spatial Point Patterns, second ed. London: Ar nold, 2003.
[16] D. Stoyan and H. Stoyan, Fractals, Random Shapes and Point Fields. Methods of Geometrical Statistics. Wiley, 1994.
[17] A. Law and W. Kelton, Simulation Modeling and Analysis, third ed. McGraw Hill, 2000.
[18] J. Ramsay and B. Silverman, Functional Data Analysis, first ed. Springer Series in Statistics, Springer, 1997.
[19] D. Toomre and D. Manstein, “Lighting Up the Cell Surface with Evanescent Wave Microscopy,” Trends Cell Biology, vol. 11, pp. 298-303, 2001.
[20] I. Molchanov, “Statistics of the Boolean Model: From the Estimation of Means to the Estimation of Distributions,” Advances in Applied Probability, vol. 27, pp. 63-86, 1995.
[21] J. Quenec'h, M. Coster, J. Chermant, and D. Jeulin, “Study of the Liquid-Phase Sintering Process by Probabilistic Models: Application to the Coarsening of wc-co Cermets,” J. Microscopy, vol. 168, pp. 3-14, 1992.

Index Terms:
Temporal Boolean model, 3D Boolean models, germ-grain models, coverage processes, functional data analysis, endocytosis, total internal reflection fluorescence microscopy.
Guillermo Ayala, Rafael Sebastian, Mar?a Elena D?az, Ester D?az, Roberto Zoncu, Derek Toomre, "Analysis of Spatially and Temporally Overlapping Events with Application to Image Sequences," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 28, no. 10, pp. 1707-1712, Oct. 2006, doi:10.1109/TPAMI.2006.199
Usage of this product signifies your acceptance of the Terms of Use.