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

TL;DR

This paper introduces a mathematically designed gesture recognition device that uses wave detection and scattering theory to identify gestures modeled as scatterers, enabling accurate and efficient input recognition.

Contribution

It presents a novel wave-based gesture recognition method with a rigorous mathematical foundation and a two-step detection algorithm requiring only two incident waves.

Findings

Effective gesture recognition demonstrated in numerical experiments

Requires only two incident waves for detection

Accurate shape and location identification of gestures

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 to give the specific orders/inputs to the computing machine that is connected to it. The gestures are modelled 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.