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Homotopy-based surface reconstruction with application to acoustic signals

Abstract:

This work introduces a new algorithm for surface reconstruction in ℝ3 from spatially arranged one-dimensional cross sections embedded in ℝ3. This is generally the case with acoustic signals that pierce an object non-destructively. Continuous deformations (homotopies) that smoothly reconstruct information between any pair of successive cross sections are derived. The zero level set of the resulting homotopy field generates the desired surface. Four types of homotopies are suggested that are well suited to generate a smooth surface. We also provide derivation of necessary higher order homotopies that can generate a C 2 surface. An algorithm to generate surface from acoustic sonar signals is presented with results. Reconstruction accuracies of the homotopies are compared by means of simulations performed on basic geometric primitives. © 2011 Springer-Verlag.