A NEW ALGORITHM FOR 3D SURFACE MATCHING

A new algorithm for least squares matching of overlapping 3D surfaces, digitized/sampled point by point using a laser scanner device, the photogrammetric method or other techniques, is proposed. In photogrammetry, the problem statement of surface patch matching and its solution method was first addressed by Gruen (1985a) as a straight application of Least Squares Matching. There have been some studies on the absolute orientation of stereo models using DEMs as control information. These works have been known as DEM matching. Furthermore, techniques for 2.5D DEM surface matching have been developed, which correspond mathematically with least squares image matching. 2.5D surfaces have limited value, especially in close range applications. Our proposed method estimates the transformation parameters between two or more fully 3D surface patches, minimizing the Euclidean distances instead of Z-differences between the surfaces by least squares. This formulation gives the opportunity of matching arbitrarily oriented surface patches. An observation equation is written for each surface element on the template surface patch, i.e. for each sampled point. The geometric relationship between the conjugate surface patches is defined as a 7-parameter 3D similarity transformation. The Least Squares observations of the adjustment are defined by the observation vector whose elements are Euclidean distances between the template and search surface elements. The unknown transformation parameters are treated as stochastic quantities using proper weights. This extension of the functional model gives control over the estimation parameters. The details of the mathematical modelling of the proposed method, the convergence behavior, and statistical analysis of the theoretical precision of the estimated parameters are explained. Furthermore, some experimental results based on registration of close-range laser scanner and photogrammetric point clouds are presented. This new surface matching technique derives its mathematical strength from the least squares image matching concept and offers high level flexibility for any kind of 3D surface correspondence problem, as well as statistical tools for the analysis of the quality of the final results.

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