Department of Mathematics
Mathematical design of a novel gesture-based instruction/input device using wave detection
In this paper, we present a conceptual design of a novel gesture-based instruction/input device using wave detection. The device recogonizes/detects gestures from a person and based on which gives the specific orders/inputs to the computing machine that is connected to it. The gestures are modeled as the shapes of some impenetrable or penetrable scatterers from a certain admissible class, called a dictionary. The device generates time-harmonic point signals for the gesture recognition/detection. It then collects the scattered wave in a relatively small backscattering aperture on a bounded surface containing the point sources. The recognition algorithm consists of two steps and requires only two incident waves of different wavenumbers. The approximate location of the scatterer is first determined by using the measured data at a small wavenumber and the shape of the scatterer is then identified using the computed location of the scatterer and the measured data at a regular wavenumber. We provide the mathematical principle with rigorous justifications underlying the design. Numerical experiments show that the proposed device works effectively and efficiently in some practical scenarios.
gesture recognition, instruction/input device, wave propagation, inverse scattering
Source Publication Title
SIAM Journal on Imaging Sciences
Society for Industrial and Applied Mathematics
Copyright © 2016, Society for Industrial and Applied Mathematics
The research of the authors was supported by the Startup and FRG grants from Hong Kong Baptist University, Hong Kong RGC General Research Funds, 12302415 and 22302815, and NSFC grants under 11371115 and 61501389.
Link to Publisher's Edition
Liu, Hongyu, Yuliang Wang, and Can Yang. "Mathematical design of a novel gesture-based instruction/input device using wave detection." SIAM Journal on Imaging Sciences 9.2 (2016): 822-841.