Ivo Tchoukanov

Three-dimensional location estimation of circular features for machine vision

A closed-form analytical solution to the problem of 3D estimation of circular-feature location is presented. Two different cases are considered: 3D orientation and position estimation when the radius is known and when it is not known. Extension of the method to general 3D quadratic features is also addressed. Simulated experimental results obtained for all three cases verified the analytical method. In the case of real experiments, a set of circles located on a calibration plate, whose locations were known with respect to a reference frame, were used for camera calibration as well as for the application of the method. A sequential compensation procedure was applied to the input gray-level image to compensate for distortion. These results also showed the validity of the process and the applicability of the analytical method. >

Accurate parameter estimation of quadratic curves from grey-level images

Abstract Accurate estimation of the parameters of a curve present in a grey-level image is required in various machine-vision and computer-vision problems. Quadratic curves are more common than other curve types in these fields. The accuracy of the estimated parameters depends not only on the global interpolation technique used, but, as well, on compensation of major sources of error. In this paper, first, as a preliminary step in accurate parameter estimation of quadratic curves, a sequential distortion-compensation procedure is formulated. This procedure addresses the major distortion factors involved in the transformation of a curve from the object space to the image space. Subsequently, as a means for accurate estimation of the coordinates of edge points, a new subpixel edge detector based on the principle of the sample-moment-preserving transform (SMPT) is developed. A circular-arc geometry is assumed for the boundary inside the detection area. The new arc-edge detector is designed as a cascade process using a linear-edge detector and a look-up table. Its performance is compared with that of a linear subpixel edge detector. Then, as a part of the main theme of the paper, the estimation of the five basic parameters of an elliptical shape based on its edge-point data is addressed. To achieve the desired degree of accuracy, a new error function is introduced and as the basis for a comparative study, an objective and independent measure for “goodness” of fit is derived. The proposed new error function and two other error functions previously developed are applied to six different situations. The comparative performance of these error functions is discussed. Finally, as the basis for evaluation of the total process, a 3D location estimation problem is considered. The objective is to accurately estimate the orientation and position in 3D of a set of circular features. The experimental results obtained are significant in two separate ways: in general, they show the validity of the overall process introduced here in the accurate estimation of 3D location; in particular, they demonstrate the effectiveness of the sub-pixel edge detector and the global interpolation technique, both developed here.

Application of moment and Fourier descriptors to the accurate estimation of elliptical-shape parameters

Abstract Accurate estimation of the parameters of an elliptical shape is required in various machine-vision and computer-vision problems. In our previous work, we have addressed this problem by proposing to optimize a weighted minimum-squares-error (MSE) function. As a continuation of this work, we have studied other techniques for elliptical-parameter estimation, ones applying elliptical-Fourier descriptors, moments of area, and moments of perimeter. A study, to be reported here, was carried out to evaluate the comparative performance of the above-mentioned three techniques and the one based on the weighted MSE function. The limitation and degree of accuracy of each technique was determined. It was found that different elliptical-parameter-estimation techniques must be applied depending on acceptable computational cost, number of parameters to be estimated, the required degree of accuracy, and the specific conditions under which the estimation must be performed.

Application of moment and Fourier descriptors to the accurate estimation of elliptical shape parameters

The problem of accurate parameter estimation of elliptical shapes is addressed. Three methods based on elliptical Fourier descriptors, area moments, and perimeter moments of 2-D elliptical shapes are presented. The mathematics of these methods is discussed and, for area moments, a set of new formulas based on Gausss theorem is given. To implement a comparative performance study, a method developed by R. Safaee-Rad et al. (1990), the weighted minimum-square-error (MSE) function, is included, and an objective and independent measure of goodness of fit is used. The performance of these methods is compared for two different cases, that of a perfect simulated ellipse and an imperfect imaged ellipse.<<ETX>>

3D-pose estimation from a quadratic-curved feature in two perspective views

Estimation of 3D information from 2D-image coordinates is a fundamental problem in both machine vision and computer vision. A closed-form analytical solution is presented to the problem of 3D-location estimation of quadratic-curved features based on two images. Compared to previous solution methods, the proposed method has the advantages that it is a closed-form solution method, it is mathematically simpler, and a priori knowledge of the size and shape of the feature is not required. The method is demonstrated for an elliptical feature, using a simulated experimental set-up.<<ETX>>

An analytical method for the 3D-location estimation of circular features for an active-vision system

A closed-form analytical solution to the circular-feature problem, which arose in the context of a 3-D object recognition system, is presented. Compared to previous methods, it is mathematically simpler, provides a solution for the case in which there does not exist a priori knowledge concerning the radius of a marker, and can be extended and applied to general quadratic surfaces. In addition, the method is clearer from a geometrical viewpoint. The method was applied to a set of circles, located on a calibration plate, whose locations were known with respect to a reference frame. The camera was calibrated prior to the application of the method. Since various distortion factors had to be compensated in order to obtain accurate estimates of the parameters of the imaged circle, an ellipse, with respect to the cameras image frame, a sequential compensation procedure was applied to the input grey-level image. Experimental results showing the validity of the method are reported.<<ETX>>

The angle-of-sight signature for two-dimensional shape analysis of manufactured objects

Abstract A new two-dimensional (2D) shape-encoding scheme is introduced which is based on the idea of the angle-of-sight (AOS). Using this scheme, a shape can be efficiently transformed into a one-dimensional (1D) signature by recording the AOS vs. distance of each boundary point with respect to a shape-specific chord-of-sight (COS). The COS is selected by using an extension of the notion of shape boundary, to the idea of shape-specific points and the characteristic ellipse (CE). The AOS signature has many important properties including: it is information-preserving and thus unique, it does not require boundary smoothing; it has its own selectable smoothing property; it can provide a set of multi-scale representations by means of a simple operation; it is transformation-invariant; it is defined at all points; it preserves symmetries. As well, for matching purposes, a two-level matching process is proposed using a global measure (the eccentricity of the CE of a shape) and a dissimilarity measure based on the AOS signature. The encoding and matching techniques developed have been tested with 35 manufactured objects. The results obtained show that the AOS signature and the two-level-matching technique are quite effective and reliable for the recognition of 2D shapes of typical manufactured objects.

An active-vision system for recognition of pre-marked objects in robotic assembly workcells

A new 3-D object recognition method for robotic assembly workcells is presented. The proposed method is focused on two basic concepts, i.e., active vision and object preconditioning. The main aspects of the proposed system are presented.<<ETX>>

Constraints on quadratic curves under perspective projection

The authors address the problem of three-dimensional (3-D) location estimation based on quadratic-curved features. They derive the mathematical relations or constraints on the 3-D position and orientation of quadratic-curved features using the standard rotation and the standard transformation concepts introduced by K.I. Kanatani, (1988), and assuming that the true size and shape of a given quadratic feature are known a priori, with its projection image given. In this context, an analytical method is introduced for estimation of the standard rotation and determination of the shape of a quadratic-curved feature at its canonical position. It is shown that, in general, knowledge of the true shape and size of a quadratic-curved feature does not yield a sufficient number of constraints to determine the 3-D position and orientation uniquely. As a result, extra constraints must be acquired from various sources of information and fused with these constraints to obtain unique 3-D position and orientation estimates.<<ETX>>

The angle-of-sight signature for 2D shape analysis

A new 2D shape-encoding scheme is introduced which is based on the idea of the angle-of-sight. The shape can be efficiently transformed into a 1D signature by recording the angle-of-sight vs. distance of each boundary point with respect to a shape-specific chord-of-sight. The chord-of-sight is selected by using an extension of the motion of shape to geometrical entities, which are not part of the shape boundary-to the idea of shape-specific points and the characteristic ellipse. The angle-of-sight signature is a unique, information-preserving, transformation-invariant shape representation. It is demonstrated that the angle-of-sight shape-encoding scheme is capable of deriving well-behaved noise-tolerant signals, convenient for shape matching through alignment of signatures.<<ETX>>