Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Mathematical design of a novel gesture-based instruction/input device using wave detection

Abstract

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.

Publication Year

2016

Journal Title

SIAM Journal on Imaging Sciences

Volume number

9

Issue number

2

Publisher

Society for Industrial and Applied Mathematics

First Page (page number)

822

Last Page (page number)

841

Referreed

1

Funder

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.

DOI

10.1137/16M1063551

ISSN (print)

19364954

Link to Publisher’s Edition

http://dx.doi.org/10.1137/16M1063551

Copyright

Copyright © 2016, Society for Industrial and Applied Mathematics

Keywords

gesture recognition, instruction/input device, wave propagation, inverse scattering

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