A note on the structured light of three-dimensional imaging systems
Introduction
Three-dimensional (3-D) range data are spatial coordinates for surface points of an object and they are useful for 3-D object matching, object recognition, and dimensional measurement (Yee and Griffin, 1994). Griffin et al. (1992) introduced a special encoded light pattern which may be used for a structured lighting system to acquire 3-D range data with the use of a single camera. Since only a single camera is required, unlike the approaches of Altschuler et al. (1981) and Posdamer and Altschuler (1981), their approach can be used in a dynamic environment (i.e., a scene with moving objects) for 3-D imaging systems. We refer the interested readers to Griffin et al. (1992) and Yee and Griffin (1994) for details of the use of the encoded light pattern.
In this note we concern the generation of encoded light pattern for a structured lighting system used by Griffin et al. (1992) in 3-D imaging systems. The aim of this note is twofold. Firstly, we point out that the sequences used by Griffin et al. to generate the encoded light pattern are indeed special cases of de Bruijn sequences. Secondly, we present a simple algorithm for the generation of various de Bruijn sequences. As shown, the new algorithm has several computational advantages over other typical approaches. Note that, except for the generation of encoded light pattern, there are several practical applications of de Bruijn sequences, e.g., telecommunications problems (Chartrand and Oellermann, 1993) and reaction-time experiment problems (Emerson and Tobias, 1995; Sohn et al., 1996), etc.
Section snippets
De Bruijn sequences
Given m symbols which, without loss of generality, it is assumed that 1,2,...,m−1,m, with the nature order 1<···<m−1<m. An m-symbol n-tuple de Bruijn sequence ((m,n) de Bruijn sequence) is a string of mn symbols, s0s1...smn−1, such that each substring of length n,is unique with subscripts in (1) taken modulo mn. For example, sequence 123133221 is a valid (3,2) de Bruijn sequence over the symbol set {1,2,3}, since each substring of length 2, namely, 12, 23, 31, 13, 33, 32, 22,
The new algorithm
Given m and n, finding an (m,n) de Bruijn sequence is equivalent to finding an Eulerian circuit in its corresponding digraph Dm,n, in which the vertex set of Dm,n is the set of all distinct mn−1 words of length n−1 over the symbol set {1,2,...,m} (Chartrand and Oellermann, 1993). Based upon the set of vertices and the set of arcs, one may represent the de Bruijn digraph Dm,n by an mn−1×mn−1 adjacency matrix A (Emerson and Tobias, 1995), where
Acknowledgements
This research is partially supported by National Science Council, Taiwan, under grant NSC 87-2213-C-150-002.
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