Adjacency-hopping de Bruijn Sequences for Non-repetitive Coding

TL;DR

This paper introduces adjacency-hopping de Bruijn sequences that ensure all neighboring codes differ while maintaining subsequence uniqueness, with proven existence, derived counts, and applications in structured light coding demonstrating their advantages.

Contribution

The paper defines a new class of de Bruijn sequences with adjacency-hopping properties, proves their existence, derives their count, and applies them to structured light coding.

Findings

Sequences guarantee different neighboring codes.

Sequences retain subsequence uniqueness.

Application to structured light coding shows advantages.

Abstract

A special type of cyclic sequences named adjacency-hopping de Bruijn sequences is introduced in this paper. It is theoretically proved the existence of such sequences, and the number of such sequences is derived. These sequences guarantee that all neighboring codes are different while retaining the uniqueness of subsequences, which is a significant characteristic of original de Bruijn sequences in coding and matching. At last, the adjacency-hopping de Bruijn sequences are applied to structured light coding, and a color fringe pattern coded by such a sequence is presented. In summary, the proposed sequences demonstrate significant advantages in structured light coding by virtue of the uniqueness of subsequences and the adjacency-hopping characteristic, and show potential for extension to other fields with similar requirements of non-repetitive coding and efficient matching.