演講訊息 TALKS

Abstract：

In integral geometry, Hadwiger's theorem characterizes the valuations on convex bodies in the n-dimensional Euclidean spaces. Because of the recent development of artificial neural network, several applications of the related theorems to the geometric measurement of convex bodies in Image Processing has drawn attention. In this talk, I will introduce our recent works, showing the similar results of Hadwiger’s in the pseudo-hermitian manifolds. Those results support the role of the Heisenberg groups as the model case of pseudo-hermitian manifolds, and this, in the sense of Klein geometry, also provides an analogy of the Heisenberg groups to pseudo-hermitian manifolds as the Euclidean spaces to the Riemannian manifolds. Some applications to Image Processing in practice will also be introduced.

20211216演講_黃彥彰教授 (國立臺南大學應用數學系)