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.

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. Along with the solution, error-free correspondence and accurate measurement of image points are of great importance, on which the qualitative results of succeeding camera calibration and 3D-measurements are immediately dependent. In fact, the automation of measurement processes is getting more important with progresses in production, and hence, is of increasing topical interest. In this paper, we present a circular coded target for automatic image point measurement and identification. The applied image processing method will be described in detail, and we will show some application examples of the circular coded target to optical 3D-measurement techniques.

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.

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.

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 descriptions 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.