An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group

We show the fundamental theorems of curves and surfaces in the 3-dimensional Heisenberg group and find a complete set of invariants for curves and surfaces respectively. The proofs are based on Cartan's method of moving frames and Lie group theory. As an application of the main theorems, a Crofton-type formula is proved in terms of p-area which naturally arises from the variation of volume. The application makes a connection between CR geometry and integral geometry

Shallow Triple Stream Three-dimensional CNN (STSTNet) for Micro-expression Recognition

In the recent year, state-of-the-art for facial micro-expression recognition have been significantly advanced by deep neural networks. The robustness of deep learning has yielded promising performance beyond that of traditional handcrafted approaches. Most works in literature emphasized on increasing the depth of networks and employing highly complex objective functions to learn more features. In this paper, we design a Shallow Triple Stream Three-dimensional CNN (STSTNet) that is computationally light whilst capable of extracting discriminative high level features and details of micro-expressions. The network learns from three optical flow features (i.e., optical strain, horizontal and vertical optical flow fields) computed based on the onset and apex frames of each video. Our experimental results demonstrate the effectiveness of the proposed STSTNet, which obtained an unweighted average recall rate of 0.7605 and unweighted F1-score of 0.7353 on the composite database consisting of 442 samples from the SMIC, CASME II and SAMM databases.Comment: 5 pages, 1 figure, Accepted and published in IEEE FG 201