Least Squares 3D Surface Matching (original) (raw)

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

GENERALIZED LEAST SQUARES MULTIPLE 3D SURFACE MATCHING

ISPRS Workshop on Laser Scanning 2007 and SilviLaser 2007, Espoo, Finland, September 12-14. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, vol. XXXVI, part 3 / W52, pp. 1-7., 2007

ABSTRACT: A method for the simultaneous co-registration and georeferencing of multiple 3D pointclouds and associated intensity information is proposed. It is a generalization of the 3D surface matching problem. The simultaneous co-registration provides for a strict solution to the problem, as opposed to sequential pairwise registration. The problem is formulated as the Least Squares matching of overlapping 3D surfaces. The parameters of 3D transformations of multiple surfaces are simultaneously estimated, using the Generalized GaussMarkoff model, minimizing the sum of squares of the Euclidean distances among the surfaces. An observation equation is written for each surface-to-surface correspondence. Each overlapping surface pair contributes a group of observation equations to the design matrix. The parameters are introduced into the system as stochastic variables, as a second type of (fictitious) observations. This extension allows to control the estimated parameters. Intensity information is introduced into the system in the form of quasisurfaces as the third type of observations. Reference points, defining an external (object) coordinate system, which are imaged in additional intensity images, or can be located in the pointcloud, serve as the fourth type of observations. They transform the whole block of “models” to a unique reference system. Furthermore, the given coordinate values of the control points are treated as observations. This gives the fifth type of observations. The total system is solved by applying the Least Squares technique, provided that sufficiently good initial values for the transformation parameters are given. This method can be applied to data sets generated from aerial as well as terrestrial laser scanning or other pointcloud generating methods. KEY WORDS: Surface matching, co-registration, multiple surfaces, 3D surface, pointcloud, georeferencing.

Total Least Squares Registration of 3D Surfaces

ISPRS Workshop Laser Scanning 2013, Antalya, Turkey, November 11-13. The ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences, vol. II-5/W2, pp. 25-30., 2013

KEY WORDS: Laser scanning, Point Cloud, Registration, Matching, Total Least Squares ABSTRACT: Co-registration of point clouds of partially scanned objects is the first step of the 3D modeling workflow. The aim of coregistration is to merge the overlapping point clouds by estimating the spatial transformation parameters. In computer vision and photogrammetry domain one of the most popular methods is the ICP (Iterative Closest Point) algorithm and its variants. There exist the 3D Least Squares (LS) matching methods as well (Gruen and Akca, 2005). The co-registration methods commonly use the least squares (LS) estimation method in which the unknown transformation parameters of the (floating) search surface is functionally related to the observation of the (fixed) template surface. Here, the stochastic properties of the search surfaces are usually omitted. This omission is expected to be minor and does not disturb the solution vector significantly. However, the a posteriori covariance matrix will be affected by the neglected uncertainty of the function values of the search surface. . This causes deterioration in the realistic precision estimates. In order to overcome this limitation, we propose a method where the stochastic properties of both the observations and the parameters are considered under an errors-in-variables (EIV) model. The experiments have been carried out using diverse laser scanning data sets and the results of EIV with the ICP and the conventional LS matching methods have been compared.

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.

RECENT ADVANCES IN LEAST SQUARES 3D SURFACE MATCHING

In: Gruen, A., Kahmen, H. (Eds.), Optical 3-D Measurement Techniques VII, Vienna, Austria, October 3-5, vol. II, pp. 197-206., 2005

Abstract: We present an algorithm for the least squares matching of overlapping 3D surfaces. It estimates the transformation parameters between two or more fully 3D surfaces, 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.

A NEW ALGORITHM FOR 3D SURFACE MATCHING

0th ISPRS Congress, Istanbul, Turkey, July 12-23. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, vol. XXXV, part B7, pp. 960-965., 2004

ABSTRACT: 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. KEY WORDS: Surface matching, Least Squares Matching, Point clouds, Registration, Laser scanning.

Co-registration of Surfaces by 3D Least Squares Matching

Photogrammetric Engineering & Remote Sensing, 2010

A method for the automatic co-registration of 3D surfaces is presented. The method utilizes the mathematical model of Least Squares 2D image matching and extends it for solving the 3D surface matching problem. The transformation parameters of the search surfaces are estimated with respect to a template surface. The solution is achieved when the sum of the squares of the 3D spatial (Euclidean) distances between the surfaces are minimized. The parameter estimation is achieved using the Generalized Gauss-Markov model. Execution level implementation details are given. Apart from the co-registration of the point clouds generated from spaceborne, airborne and terrestrial sensors and techniques, the proposed method is also useful for change detection, 3D comparison, and quality assessment tasks. Experiments using terrain data examples show the capabilities of the method.

Co-registration of pointclouds by 3D Least Squares matching

The International LIDAR Mapping Forum, Denver, Colorado, US, February 21-22 (only on CD-ROM). , 2008

ABSTRACT The automatic co-registration of point clouds, representing 3D surfaces, is a relevant problem in 3D modeling. We treat the problem 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 surfaces. It fully considers 3D geometry. The method derives its mathematical strength from the Least Squares matching concept and offers a high level of flexibility for many kinds of 3D surface correspondence problems. The experiments demonstrate the capabilities of the basic method and the extensions. Examples on the terrain/object modeling, cultural heritage applications, accuracy assessment and change detection are presented.

Co-Registration of 3D Point Clouds by Using an Errors-In-Variables Model

The 22th ISPRS Congress, Melbourne, Australia, August 25 – September 1. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, vol. XXXIX, part B5, pp. 151-155. , 2012

KEY WORDS: Laser scanning, point cloud, registration, matching, estimation ABSTRACT: Co-registration of point clouds of partially scanned objects is the first step of the 3D modeling workflow. The aim of coregistration is to merge the overlapping point clouds by estimating the spatial transformation parameters. In the literature, one of the most popular methods is the ICP (Iterative Closest Point) algorithm and its variants. There exist the 3D least squares (LS) matching methods as well. In most of the co-registration methods, the stochastic properties of the search surfaces are usually omitted. This omission is expected to be minor and does not disturb the solution vector significantly. However, the a posteriori covariance matrix will be affected by the neglected uncertainty of the function values. This causes deterioration in the realistic precision estimates. In order to overcome this limitation, we propose a new method where the stochastic properties of both (template and search) surfaces are considered under an errors-in-variables (EIV) model. The experiments have been carried out using a close range laser scanning data set and the results of the conventional and EIV types of the ICP matching methods have been compared.

A flexible mathematical model for matching of 3D surfaces and attributes

Videometrics VIII, Proc. of SPIE-IS&T Electronic Imaging, San Jose (California), USA, January 18-20, SPIE vol. 5665, pp.184-195., 2005

An algorithm for the least squares matching of overlapping 3D surfaces is presented. It estimates the transformation parameters between two or more fully 3D surfaces, 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 and execution aspects we give further extension of the basic model. The first extension is the simultaneous matching of sub-surface patches, which are selected in cooperative surface areas. It provides a computationally effective solution, since it matches only relevant multi-subpatches rather than the whole overlapping areas. The second extension is the matching of surface geometry and its attribute information, e.g. reflectance, color, temperature, etc., under a combined estimation model. We give practical examples for the demonstration of the basic method and the extensions. Keywords: Least squares 3D surface matching, point clouds, registration, laser scanning, intensity matching.