An average of surfaces as functions in the two-parameter Wiener space for a probabilistic 3D shape model
Bull. Korean Math. Soc. 2020 Vol. 57, No. 3, 751-762
https://doi.org/10.4134/BKMS.b190467
Published online July 23, 2019
Printed May 31, 2020
Jeong-Gyoo Kim
Hongik University
Abstract : We define the average of a set of continuous functions of two variables (surfaces) using the structure of the two-parameter Wiener space that constitutes a probability space. The average of a sample set in the two-parameter Wiener space is defined employing the two-parameter Wiener process, which provides the concept of distribution over the two-parameter Wiener space. The average defined in our work, called an average function, also turns out to be a continuous function which is very desirable. It is proved that the average function also lies within the range of the sample set. ~The average function can be applied to model 3D shapes, which are regarded as their boundaries (surfaces), and serve as the average shape of them.
Keywords : Average of the set of two-variable functions, two-parameter Wiener space, two-parameter Wiener process, average of surfaces
MSC numbers : 28C20, 46G12, 60G15
Supported by : This work was supported by the Hongik University new faculty research support fund.
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