On chain code probabilities and length estimators for digitized three dimensional curves

Length estimation of three dimensional digitized curves is considered. The three dimensional chain code representation is assumed. It is shown that previously suggested length estimators are biased, and alternative simple estimators that possess desired optimality properties are developed. To support optimal design of three dimensional length estimators, useful statistical properties of three dimensional chain encoded digital straight lines are derived. Although this paper focuses on simple estimators, the suggested approach can be used to design more complicated three dimensional length estimators