Mathematical design of a novel input/instruction device using a moving emitter

TL;DR

This paper presents a mathematical framework for designing a novel input device using a moving emitter, capable of recognizing human gestures through wave field data, even in complex media and with limited data collection.

Contribution

It introduces a direct, medium-independent reconstruction method for tracking a moving emitter in inhomogeneous media, enhancing robustness and efficiency over existing techniques.

Findings

Effective trajectory reconstruction in inhomogeneous media.

Robustness against measurement noise demonstrated.

Method works with limited aperture data.

Abstract

This paper is concerned with the mathematical design of a novel input/instruction device using a moving emitter. The emitter generates a point source and can be installed on a digit pen or worn on the finger of the human being who wants to interact/communicate with the computer. The input/instruction can be recognized by identifying the motion trajectory of the emitter performed by the human being from the collected wave field data. The identification process is modelled as an in- verse source problem where one intends to identify the trajectory of a moving point source. There are several salient features of our study which distinguish our result from the existing ones in the literature. First, the point source is moving in an inhomogeneous background medium, which models the human body. Second, the dynamical wave field data are collected in a limited aperture. Third, the recon- struction method is independent of the background medium, and it is totally direct without any matrix inversion. Hence, it is efficient and robust with respect to the measurement noise. Both theoretical justifications and computational experiments are presented to verify our novel findings.