Abstract
Recent advances in microscopy jointly to the development of fluorescent probes have enabled to image dynamic processes with very high spatial-temporal resolution, for instance in Cell Biology. In some applications, the segmented areas associated with different events overlap spatially and temporally forming random clumps. In order to study the shape-size features and durations of the events, it is a usual practice to analyze only isolated episodes. However, this sample is biased, because faster and smaller events tend to be isolated. We model the images as a realization of a cylindrical temporal Boolean model. We evaluate the bias introduced when ruling out non-isolated episodes. We propose an estimator of the duration distribution and perform a simulation study to assess its accuracy. The method is applied to fluorescent-tagged proteins image sequences. Results show that this procedure is effective for analyzing dynamic processes where spatial and temporal overlapping occurs.
Similar content being viewed by others
References
Ayala, G., Sebastian, R., Diaz, M.E., Diaz, E., Zoncu, R., Toomre, D.: Analysis of spatially and temporally overlapping events with application to image sequences. IEEE Trans. Pattern Anal. Mach. Intell. 28(10), 1707–1712 (2006)
Diggle, P.: Binary mosaics and the spatial pattern of heather. Biometrics 37, 531–539 (1981)
Dupač, V.: Parameter estimation in Poisson field of discs. Biometrika 67, 187–190 (1980)
Epifanio, I., Ayala, G.: A random set view of texture classification. IEEE Trans. Image Process. 11(8), 859–867 (2002)
García, P., Petrou, M., Kamata, S.: The use of boolean model for texture analysis of grey images. Comput. Vis. Image Underst. 74(3), 227–235 (1999)
Matheron, G.: Eléments Pour une Théorie des Milieux Poreux. Masson, Paris (1967)
Matheron, G.: Random Sets and Integral Geometry. Wiley, London (1975)
Molchanov, I.: Theory of Random Sets (Probability and its Applications). Springer, Berlin (2005)
R Development Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2008). http://www.R-project.org. ISBN 3-900051-07-0
Ramsay, J., Silverman, B.: Functional Data Analysis, 1st edn. Springer Series in Statistics. Springer, Berlin (1997)
Ramsay, J.O., Wickham, H., Graves, S.: FDA: Functional Data Analysis (2007). http://www.functionaldata.org. R package version 1.2.3
Sebastian, R., Diaz, E., Ayala, G., Diaz, M.E., Zoncu, R., Toomre, D.: Studying endocytosis in space and time by means of temporal boolean models. Pattern Recognit. 39(11), 2775–2785 (2006)
Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, New York (1982)
Stoyan, D., Kendall, W., Mecke, J.: Stochastic Geometry and Its Applications, 2nd edn. Wiley, Berlin (1995)
Toomre, D., Manstein, D.: Lighting up the cell surface with evanescent wave microscopy. Trends Cell Biol. 11, 298–303 (2001)
Author information
Authors and Affiliations
Corresponding author
Additional information
This paper has been supported by Human Frontier Science Organization Program (RGY40/2003-first author) and Spanish Ministry of Science and Education (TIN2007-67587-first author and TIN2006-10143-second author). The authors thank one of the referees, who also reviewed our paper [1], for his/her suggestions which contributed to the genesis of this paper. We would like to thank the anonymous reviewer who made a substantial contribution to the revision of our paper.
Rights and permissions
About this article
Cite this article
Díaz, M.E., Ayala, G. & Díaz, E. Estimating the Duration of Overlapping Events from Image Sequences Using Cylindrical Temporal Boolean Models. J Math Imaging Vis 38, 83–94 (2010). https://doi.org/10.1007/s10851-010-0214-6
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10851-010-0214-6