Scale space analysis of images and signals
IBSiZer can be used for example to detect differences in a pair of images taken from the same object. MRBSiZer resolves an image into additive, scale-dependent components. Here is a tutorial web site that explains the methodology and gives many examples. Downloadable preprints and software can also be found there. On-going work considers also scale space analysis of change detection from multispectral satellite images. A recent paper adapts the MRBSiZer method to time series.
Scale space analysis of a simulated difference image. The original image and its noisy version are on the left. The three rightmost panels show iBSiZer analysis of the features that are credible with posterior probability at least 0.95 in three different spatial resolutions. Negative and positive differences are shown in black and white, respectively, and gray indicates no credible change.
Multiresolution MRBSiZer analysis of an image of John Lennon. Upper row: four additive image components corresponding to four spatial scales. Lower panel: analysis of credible features in the component images. Credible negative and positive features are shown in black and white, respectively.
Selected papers:
- L. Holmström and L. Pasanen. Bayesian analysis of image differences in multiple scales. In Matti Niskanen and Janne Heikkilä, editors, Proceedings, Finnish Signal Processing Symposium 2007, August 30, Oulu, Finland. University of Oulu, Department of Electrical and Information Engineering, 2007. CD-ROM, ISBN 978-951-42-8546-2.
- L. Holmström, L. Pasanen, R. Furrer, and S. R. Sain. Scale space multiresolution analysis of random signals. Computational Statistics & Data Analysis, 55(10):2840 - 2855, 2011. Available on-line at http://dx.doi.org/10.1016/j.csda.2011.04.011 .
- L. Holmström and L. Pasanen. Bayesian scale space analysis of differences in images. Technometrics, 54(1), 2012. Available on-line at http://dx.doi.org/10.1080/00401706.2012.648862.
- L. Pasanen and L. Holmstrom. Bayesian scale space analysis of images. In Image and Signal Processing and Analysis (ISPA), 2013 8th International Symposium on, pages 96-100, 2013.
- L. Pasanen, I. Launonen, and L. Holmström. A scale space multiresolution method for extraction of time series features. Stat, 2(1):273-291, 2013. Available on-line at http://dx.doi.org/10.1002/sta4.35.
- L. Pasanen and L. Holmström. Bayesian scale space analysis of temporal changes in satellite images. Journal of Applied Statistics, 42(1):50-70, 2015. Available on-line at http://dx.doi.org/10.1080/02664763.2014.932761.
- L. Pasanen, L. Holmström, and M. J. Sillanpää. Bayesian LASSO, Scale Space and Decision Making in Association Genetics. PLoS ONE, 10(4):e0120017, 04 2015. Available on-line at url http://dx.doi.org/10.1371/journal.pone.0120017.
- L. Pasanen and L. Holmström. Scale space multiresolution correlation analysis for time series data. Computational Statistics, 32(1):197-218, 2017. Available on-line at url http://dx.doi.org/10.1007/s00180-016-0670-6.
- L. Pasanen, P. Laukkanen-Nevala, I. Launonen, Sergey Prusov, L. Holmström, E. Niemelä, and J. Erkinaro. The extraction of sea temperature in the Barents sea by a scale space multiresolution method - prospects for Atlantic salmon. Journal of Applied Statistics, 44(13):2317 - 2336, 2017. Available on-line at http://dx.doi.org/10.1080/02664763.2016.1252731
- L. Holmström and L. Pasanen. Statistical scale space methods. International Statistical Review, 85(1):1 - 30, 2017. Available on-line at http://dx.doi.org/10.1111/insr.12155.
- L. Holmström and L. Pasanen. Rejoinder. International Statistical Review, 85(1):43 - 45, 2017. Rejoinder to discussion of "Statistical Scale Space Methods". Available on-line at http://dx.doi.org/10.1111/insr.12179.
- L. Pasanen, T. Aakala, and L. Holmström. A scale space approach for estimating the characteristic feature sizes in hierarchical signals. Stat, 7(1):e195, 2018. Available on-line at https://onlinelibrary.wiley.com/ doi/abs/10.1002/sta4.195.
- L. Pasanen, T. Aakala, N. Kulha, and L. Holmström. Identifying the char- acteristic scales in hierarchical signals. In International Statistical Ecology Conference (ISEC 2018), Conference book, page 254, St. Andrews, Scotland, 2018.
- V. Vuollo and L. Holmström. A scale space approach for exploring structure in spherical data. Computational Statistics & Data Analysis, 125:57 - 69, 2018. Available on-line at https://doi.org/10.1016/j.csda.2018.03.014.
- S. Uteng, T. H. Johansen, J. I. Zaballos, S. Ortega, L. Holmström, G. M. Callico, H. Fabelo, and F. Godtliebsen. Early detection of change by applying scale-space methodology to hyperspectral images. Applied Sciences, 10(7):2298, 2020. Available on-line at http://dx.doi.org/10.3390/app10072298