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In this paper we present an approach to the problem of modelling long, flexible instruments, such as endoscopes or catheters. The idea is to recursively enumerate all possible shapes and subsequently filter them according to given mechanical and physical constraints. Although this brute-force approach has an exponential worst-case complexity, we show with a typical example that in case of tubular structures the empirical complexity is polynomial. We present two approximation methods that reduce this bound to a linear complexity. We have performed accuracy, runtime and robustness tests in preparation for first clinical studies.

A Real-Time Deformable Model for Flexible Instruments Inserted into Tubular Structures