Sung Joon Ahn

• Dr.-Ing.
• Founder & CEO at CurvSurf, Inc.

The use of circular object targets is very common in spatial photogrammetric object reconstruction. An object circle is projected on to the image plane as an ellipse if the object plane and the image plane are not parallel to each other. The image co-ordinates of the centre of the ellipse are usually determined automatically by means of digital ima...

This book presents in detail a complete set of best-fit algorithms for general curves and surfaces in space. Such best-fit algorithms approximate and estimate curve and surface parameters by minimizing the shortest distances between the curve or surface and the measurement point. After reviewing the basics for representing curves and surfaces in sp...

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 nonpar...

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...

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...

In this paper, we present a new method for fitting of implicit curves, with which the fitting results are invariant to the coordinate transformation of data points. The original idea of the new method is that we define the least squares cost function within the local model coordinate system instead of the global reference coordinate system. The new...

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...

Automatic object recognition in 3D measuring data is of great interest in many application fields e.g. computer vision, reverse engineering and digital factory. In this paper we present a software tool for a fully automatic object detection and parameter estimation in unordered and noisy point clouds with a large number of data points. The software...

This paper deals with the geometric fitting algorithms for parametric curves and surfaces in 2-D/3-D space, which estimate the curve/surface parameters by minimizing the square sum of the shortest distances between the curve/surface and the given points. We identify three algorithmic approaches for solving the nonlinear problem of geometric fitting...

Object detection and parameter estimation in point cloud data is a relevant subject to robotics, reverse engineering, computer vision, and sport mechanics. In this paper a software is presented for fully-automatic object detection and parameter estimation in unordered, incomplete and error-contaminated point cloud with a large number of data points...

The orthogonal distance fitting (ODF) of general curves and surfaces is by nature an analytically and computationally difficult problem. In order to start with a soft example, this chapter begins by reviewing the moment method (linear ODF) for line/plane fitting which K. Pearson [61] solved in closed form a century ago. The general aim of ODF is th...

The goal of object reconstruction is to generate the list of objects in a real environment, together with the object model parameters and the geometric interrelations between the objects. A successful object reconstruction presupposes the general information about the objects (such as object data base) and a large amount of raw data directly obtain...

In Chap. 3, the distance-based algorithm (2.28) and the coordinate-based algorithm (2.32) are generally implemented for implicit features F(X, a) = 0 according to the variable-separation method (Algorithms II and III, respectively). This chapter describes in detail the general implementation of the three ODF Algorithms I–III (Table 2.3, Sect. 2.3,...

The parametric model description of real objects is a subject relevant to coordinate metrology, reverse engineering, and computer/machine vision, with which objects are represented by their model parameters estimated from the measurement data (object reconstruction, Fig. 1.1). The parametric model description has a wide range of application fields,...

This chapter describes in detail the general implementation of the two ODF Algorithms II and III (variable-separation method, see Table 2.3 and Sect. 2.3) on implicit curves and surfaces F(a,X) = 0 in space.

Orthogonal distance fitting (ODF) estimates the parameters of a model feature by minimizing the square sum of the shortest distances (geometric distances) between the model feature and the given points. Due to the applied error measure, the ODF is a substantial mathematical tool for many scientific and engineering disciplines in which coordinate da...

In applications of optical 3D-measurement techniques segmentation and outlier elimination in point clouds is a tedious and time-consuming task. In this paper, we present a very robust and efficient procedure of segmentation, outlier elimination, and model fitting in point clouds. For an accurate and reliable estimation of the model parameters, we a...

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 appl...

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 algor...

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...

Fitting of parametric curves and surfaces to a set of given data points is a relevant subject in various fields of science and engineering. In this paper, we review the current orthogonal distance fitting algorithms for parametric models in a well organized and easily understandable manner, and present a new algorithm. Each of these algorithms esti...

Dimensional model fitting to a set of given points is a relevant subject in various disciplines of science and engineering. In this paper, we present a universal, and very efficient, best-fit algorithm for implicit surfaces and plane curves, by which the square sum of the orthogonal error distances of the given points to the model feature will be r...

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 a...

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 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 descripti...

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 a...

The element has a disc-shaped recognition mark (2) with a circular contour and a number of circular code elements (4), positioned on the outside of the recognition mark along concentric lines. The code elements are smaller in diameter than the recognition mark.They are positioned in accordance with a ring code relative to the centre of the recognit...

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 wh...

Contrary to the strong theoretical background of photogrammetry, the automation of photogrammetric principles for the efficient use of photogrammetry as a means for industrial measurement is rather poorly investigated. The automation of measurement processes is getting more important with the future development of production and hence of topical in...

The use of circular object targets is very common for a spatial photogrammetric object reconstruction. An object circle is projected on the image plane as an ellipse, if the object plane and the image plane are not parallel. The image coordinates of the center of the ellipse and the true coordinates of the projected center of the circular target ar...

Key Word : digital photogrammetry, 3D measurement, active vision, coded light approach, bundle adjustment, camera-projector calibration, coded target, ellipse adjustment, circular object points, systematic error, correction methods, point determination, edge detection.