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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.
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참고문헌 (19)
참고문헌 신청
R. G. Bartle / 1976 / The Elements of Real Analysis / John Wiley & Sons
R. Cameron / 1976 / An operator valued Yeh-Wiener integral, and a Wiener integral equation / Indiana University Mathematics Journal 25(3):235~258
Arthur H. C. Chan / 1975 / Some lower bounds for the distribution of the supremum of the Yeh-Wiener process over a rectangular region / Journal of Applied Probability 12(04):824~830
K. S. Chang / 1981 / Converse measurability theorems for Yeh-Wiener space / Pacific J. Math 97(1):59~63
Loïc Devilliers / 2017 / Template Estimation in Computational Anatomy: Fréchet Means Top and Quotient Spaces Are Not Consistent / SIAM Journal on Imaging Sciences 10(3):1139~1169
R. Cameron / 1976 / An operator valued Yeh-Wiener integral, and a Wiener integral equation / Indiana University Mathematics Journal 25(3):235~258
Arthur H. C. Chan / 1975 / Some lower bounds for the distribution of the supremum of the Yeh-Wiener process over a rectangular region / Journal of Applied Probability 12(04):824~830
K. S. Chang / 1981 / Converse measurability theorems for Yeh-Wiener space / Pacific J. Math 97(1):59~63
Loïc Devilliers / 2017 / Template Estimation in Computational Anatomy: Fréchet Means Top and Quotient Spaces Are Not Consistent / SIAM Journal on Imaging Sciences 10(3):1139~1169
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