Local Matching of Surfaces Using Critical Points (original) (raw)

Matching surfaces with characteristic points

We study approximation algorithms for a matching problem that is motivated by medical applications. Given a small set of points P ⊂ R3 and a surface S, the optimal matching of P with S is represented by a rigid transformation which maps P as 'close as possi- ble' to S. Previous solutions either require polynomial runtime of high degree (2) or they make use of heuris- tic techniques which could be trapped in some local minimum. We propose a modification of the problem setting by introducing subsets of characteristic points Pc ⊆ P and Sc ⊆ S, and assuming that points from Pc must be matched with points from Sc. We will show that especially in the case |Pc |≥ 2 this restric- tion results in new fast and reliable algorithms for the matching problem.

Least squares 3D surface and curve matching

Isprs Journal of Photogrammetry and Remote Sensing, 2005

The automatic co-registration of point clouds, representing 3D surfaces, is a relevant problem in 3D modeling. This multiple registration problem can be defined as a surface matching task. We treat it as least squares matching of overlapping surfaces. The surface may have been digitized/sampled point by point using a laser scanner device, a photogrammetric method or other surface measurement techniques. Our proposed method estimates the transformation parameters of one or more 3D search surfaces with respect to a 3D template surface, using the Generalized Gauss–Markoff model, minimizing the sum of squares of the Euclidean distances between the surfaces. This formulation gives the opportunity of matching arbitrarily oriented 3D surface patches. It fully considers 3D geometry. Besides the mathematical model and execution aspects we address the further extensions of the basic model. We also show how this method can be used for curve matching in 3D space and matching of curves to surfaces. Some practical examples based on the registration of close-range laser scanner and photogrammetric point clouds are presented for the demonstration of the method. This surface matching technique is a generalization of the least squares image matching concept and offers high flexibility for any kind of 3D surface correspondence problem, as well as statistical tools for the analysis of the quality of final matching results.

Matching of 3D surfaces and their intensities

Isprs Journal of Photogrammetry and Remote Sensing, 2007

3D surface matching would be an ill conditioned problem when the curvature of the object surface is either homogenous or isotropic, e.g. for plane or spherical types of objects. A reliable solution can only be achieved if supplementary information or functional constraints are introduced. In a previous paper, an algorithm for the least squares matching of overlapping 3D surfaces, which were digitized/sampled point by point using a laser scanner device, by the photogrammetric method or other techniques, was proposed [Gruen, A., and Akca, D., 2005. Least squares 3D surface and curve matching. ISPRS Journal of Photogrammetry and Remote Sensing 59 (3), 151–174.]. That method estimates the transformation parameters between two or more fully 3D surfaces, minimizing the Euclidean distances instead of z-differences between the surfaces by least squares. In this paper, an extension to the basic algorithm is given, which can simultaneously match surface geometry and its attribute information, e.g. intensity, colour, temperature, etc. under a combined estimation model. Three experimental results based on terrestrial laser scanner point clouds are presented. The experiments show that the basic algorithm can solve the surface matching problem provided that the object surface has at least the minimal information. If not, the laser scanner derived intensities are used as supplementary information to find a reliable solution. The method derives its mathematical strength from the least squares image matching concept and offers a high level of flexibility for many kinds of 3D surface correspondence problem.

Geodesic Distance Evolution of Surfaces: A New Method for Matching Surfaces

2000

The general problem of surface matching is considered in this study. The process described in this work hinges on a geodesic distance equation for a family of surfaces embedded in the graph of a cost function. The cost function represents the geometrical matching criterion between the two 3D surfaces. This graph is a hypersurface in 4-dimensional space, and the theory presented herein is a generalization of the geodesic curve evolution method introduced by R. Kimmel et al. (1995). It also generalizes the 2D matching process developed in Cohen and Herlin (1998). An Eulerian level-set formulation of the geodesic surface evolution is also used, leading to a numerical scheme for solving partial differential equations originating from hyperbolic conservation laws, which has proven to be very robust and stable. The method is applied on examples showing both small and large deformations, and arbitrary topological changes

LEAST SQUARES MATCHING OF 3D SURFACES

4th Symposium of Turkish Society for Photogrammetry and Remote Sensing, Istanbul, Turkey, June 5-7, (only on CD-ROM)., 2007

ABSTRACT: An algorithm for the least squares matching of overlapping 3D surfaces is presented. It estimates the transformation parameters of one or more fully 3D surfaces with respect to a template one, using the Generalized Gauss-Markoff model, minimizing the sum of squares of the Euclidean distances between the surfaces. This formulation gives the opportunity of matching arbitrarily oriented 3D surfaces simultaneously, without using explicit tie points. Besides the mathematical model of the procedure, we discuss the computational aspects. We give practical examples to demonstrate the method. KEYWORDS: Least Squares matching, surface matching, pointcloud, laser scanning