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28 May 2003 Estimation of the distribution type and parameters based on multimodal histograms
Jari Niemi, Kalle Marjanen, Heimo Ihalainen, Olli P. Yli-Harja
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Proceedings Volume 5014, Image Processing: Algorithms and Systems II; (2003) https://doi.org/10.1117/12.477713
Event: Electronic Imaging 2003, 2003, Santa Clara, CA, United States
Abstract
In many applications involving measuring a physical phenomenon, the output data contains a mixture of different type of distributions. The data set consists often of unimodal distributions, which overlap, i.e. the ranges of the corresponding random variables have a significant intersection. After observing a multimodal histogram that has several partially overlapping distributions the aim is to separate them by inferring the correct types of the probability density functions (PDFs) and their parameters. The method is based on the non-linear least squares estimation, where several types of PDFs are fitted to the region mostly affected by a single distribution. The possible candidate PDFs are those of the Pearson system, Weibull, Fisher, chi-squared and Rayleigh distributions. This method can be extended to multidimensional cases in certain situations. The methods developed earlier for this task are based for example on the QQ-plot technique and on order statistic filter banks. The found distribution types and their parameters can be applied to different tasks in image processing and system analysis. This algorithm can be used e.g. to the estimation of PDFs of certain phenomena and to global thresholding of images. The method is applied to real two-dimensional data sets having values coming from several distributions.
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Jari Niemi, Kalle Marjanen, Heimo Ihalainen, and Olli P. Yli-Harja "Estimation of the distribution type and parameters based on multimodal histograms", Proc. SPIE 5014, Image Processing: Algorithms and Systems II, (28 May 2003); https://doi.org/10.1117/12.477713
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KEYWORDS
Error analysis
Image processing
Statistical analysis
Image segmentation
Imaging systems
Computing systems
Digital filtering
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