Wolfgang Rauh

Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola

The least-squares fitting minimizes the squares sum of error-of-fit in predefined measures. By the geometric fitting, the error distances are defined with the orthogonal, or shortest, distances from the given points to the geometric feature to be fitted. For the geometric fitting of circle/sphere/ellipse/hyperbola/parabola, simple and robust nonparametric algorithms are proposed. These are based on the coordinate description of the corresponding point on the geometric feature for the given point, where the connecting line of the two points is the shortest path from the given point to the geometric feature to be fitted.

Orthogonal distance fitting of implicit curves and surfaces

Dimensional model fitting finds its applications in various fields of science and engineering and is a relevant subject in computer/machine vision and coordinate metrology. In this paper, we present two new fitting algorithms, distance-based and coordinate-based algorithm, for implicit surfaces and plane curves, which minimize the square sum of the orthogonal error distances between the model feature and the given data points. Each of the two algorithms has its own advantages and is to be purposefully applied to a specific fitting task, considering the implementation and memory space cost, and possibilities of observation weighting. By the new algorithms, the model feature parameters are grouped and simultaneously estimated in terms of form, position, and rotation parameters. The form parameters determine the shape of the model feature and the position/rotation parameters describe the rigid body motion of the model feature. The proposed algorithms are applicable to any kind of implicit surface and plane curve. In this paper, we also describe algorithm implementation and show various examples of orthogonal distance fit.

Circular coded landmark for optical 3D-measurement and robot vision

One of the primary but tedious tasks for the user and developer of an optical 3D-measurement system is to find the homologous image points in multiple images-a task that is frequently referred to as the correspondence problem. With the solution, the error-free correspondence and accurate measurement of image points are of great importance, on which the qualitative results of the succeeding 3D-measurement are immediately dependent. In fact, the automation of measurement processes is getting more important with developments in production and hence, of increasing topical interest. We present a circular coded target for automatic image point measurement and identification, its data processing, and its application to the optical 3D-measurement method.

Ellipse fitting and parameter assessment of circular object targets for robot vision

The least squares fitting minimizes the squares sum of error-of-fit in predefined measures. By the geometric fitting, the error distances are defined with the shortest distances from the given points to the geometric feature to be fitted. For the geometric fitting of ellipse, a robust algorithm is proposed. This is based on the coordinate description of the corresponding point on the ellipse for the given point, where the connecting line of the two points is the shortest path from the given point to the ellipse. As a practical application example, we show the geometric ellipse fitting to the image of circular point targets, where the contour points are weighted with their image gradient across the boundary of the image ellipse.

Least Squares Orthogonal Distance Fitting of Implicit Curves and Surfaces

Curve and surface fitting is a relevant subject in computer vision and coordinate metrology. In this paper, we present a new fitting algorithm for implicit surfaces and plane curves which minimizes the square sum of the orthogonal error distances between the model feature and the given data points. By the new algorithm, the model feature parameters are grouped and simultaneously estimated in terms of form, position, and rotation parameters. The form parameters determine the shape of the model feature, and the position/rotation parameters describe the rigid body motion of the model feature. The proposed algorithm is applicable to any kind of implicit surface and plane curve.

Automatic segmentation and model identification in unordered 3D point cloud

Segmentation and object recognition in point cloud are of topical interest for computer and machine vision. In this paper, we present a very robust and computationally efficient interactive procedure between segmentation, outlier detection, and model fitting in 3D-point cloud. For an accurate and reliable estimation of the model parameters, we apply the orthogonal distance fitting algorithms for implicit curves and surfaces, which minimize the square sum of the geometric (Euclidean) error distances. The model parameters are grouped and simultaneously estimated in terms of form, position, and rotation parameters, hence, providing a very advantageous algorithmic feature for applications, e.g., robot vision, motion analysis, and coordinate metrology. To achieve a high automation degree of the overall procedures of the segmentation and object recognition in point cloud, we utilize the properties of implicit features. We give an application example of the proposed procedure to a point cloud containing multiple objects taken by a laser radar.

Least Squares Fitting of Circle and Ellipse

The least squares fitting of geometric features to given points minimizes the squares sum of error-of-fit in predefined measures. By the geometric fitting, the error distances are defined with the orthogonal, or shortest, distances from the given points to the geometric feature to be fitted. For the geometric fitting of circle and ellipse, robust algorithms are proposed which are based on the coordinate description of the corresponding point on the circle/ellipse for the given point, where the connecting line of the two points is the shortest path from the given point to the circle/ellipse.

Circular Coded Target and Its Application to Optical 3D-Measurement Techniques

One of the primary but tedious tasks for the user and developer of an optical 3D- measurement system is to find the homologous image points in multiple images - a task that is frequently referred to as the correspondence problem. With the solution, the error-free correspondence and accurate measurement of image points are of great importance, on which the qualitative results of the succeeding 3D-measurement are immediately dependent. In fact, the automation of measurement processes is getting more important with developments in production and hence of increasing topical interest. In this paper, we present a circular coded target for automatic image point measurement and identification, its data processing and application to some optical 3D-measurement methods.

Fitting of Parametric Space Curves and Surfaces by Using the Geometric Error Measure

For pattern recognition and computer vision, fitting of curves and surfaces to a set of given data points in space is a relevant subject. In this paper, we review the current orthogonal distance fitting algorithms for parametric model features, and, present two new algorithms in a well organized and easily understandable manner. Each of these algorithms estimates the model parameters which minimize the square sum of the shortest error distances between the model feature and the given data points. The model parameters are grouped and simultaneously estimated in terms of form, position, and rotation parameters. We give various examples of fitting curves and surfaces to a point set in space.