A new one-parametric fitting method for planar objects

This paper is an extension of the already published paper by Voss and Suesse (1997). We developed a new region-based fitting method using the method of normalization. There we demonstrated the zero-parametric fitting of lines, triangles, parallelograms, circles, and ellipses. We discuss this normalization idea for fitting of closed regions using circular segments, elliptical segments, and super-ellipses. As features, we use the area-based low order moments. We show that we have to solve only one-dimensional optimization problems in these cases     

Hierarchical mesh segmentation based on fitting primitives

In this paper, we describe a hierarchical face clustering algorithm for triangle meshes based on fitting primitives belonging to an arbitrary set. The method proposed is completely automatic, and generates a binary tree of clusters, each of which is fitted by one of the primitives employed. Initially, each triangle represents a single cluster; at every iteration, all the pairs of adjacent clusters are considered, and the one that can be better approximated by one of the primitives forms a new single cluster. The approximation error is evaluated using the same metric for all the primitives, so that it makes sense to choose which is the most suitable primitive to approximate the set of triangles in a cluster. Based on this approach, we have implemented a prototype that uses planes, spheres and cylinders, and have experimented that for meshes made of 100 K faces, the whole binary tree of clusters can be built in about 8 s on a standard PC. The framework described here has natural application in reverse engineering processes, but it has also been tested for surface denoising, feature recovery and character skinning.     

Least-squares fitting of analytic primitives on a GPU

Metrology systems take coordinate information directly from the surface of a manufactured part and generate millions of (x$x$, y$y$, z$z$) data points. The inspection process often involves fitting analytic primitives such as sphere, cone, torus, cylinder, and plane to these points, which represent an object with the corresponding shape. Typically, a least-squares fit of the parameters of the shape to the point set is performed. The least-squares fit attempts to minimize the sum of the squares of the distances between the points and the primitive. The objective function, however, cannot be solved in the closed form, and numerical minimization techniques are required to obtain the solution. These techniques as applied to primitive fitting entail iteratively solving large systems of linear equations generally involving arithmetic-intensive operations. The current problem faced in in-process metrology is the large computational time for the analysis of these millions of streaming data points. This paper presents a framework to address the bottleneck using a graphical processing unit (GPU) to optimize operations and obtain significant gain in computation time.     

Invariant fitting of two view geometry

This paper describes an extension of Bookstein's and Sampson's methods, for fitting conics, to the determination of epipolar geometry, both in the calibrated case, where the Essential matrix E is to be determined or in the uncalibrated case, where we seek the fundamental matrix F. We desire that the fitting of the relation be invariant to Euclidean transformations of the image, and show that there is only one suitable normalization of the coefficients and that this normalization gives rise to a quadratic form allowing eigenvector methods to be used to find E or F, or an arbitrary homography H. The resulting method has the advantage that it exhibits the improved stability of previous methods for estimating the epipolar geometry, such as the preconditioning method of Hartley, while also being invariant to equiform transformations.     

Normalization of discrete planar objects

The case is made for normalization of discrete planar objects prior to comparison with test objects and an expression for normalization is derived using a Euclidean distance function based on the underlying continuous boundaries of the objects and their prototypes. The results are given in both the spatial and the frequency domain; an analysis of errors due to the quantization introduced by using a discrete grid is also given.     

Grasp synthesis for planar and solid objects

This article presents an analysis of the mechanics for multifingered grasps of planar and solid objects. We present a method that is intuitive and computationally efficient. We combine the search for finger grasp positions with finger (manipulation and squeezing) force calculations into a single method. Physically, the squeezing and frictional effects between the fingers and the grasped objects are fully visualized through our approach. Mathematically, we reduced the complexity of finger force calculations when comparing our scheme with previously available schemes. Examples are used to illustrate the effectiveness and efficiency of our scheme. Based upon the analysis of grasp mechanics, an algorithm for quantatively choosing the grasp points is proposed to ensure stable grasps.     

Analysis of the digitized boundaries of planar objects

The digitized boundary of an object can be expressed as a chain of points or of directions or of curvatures, all of which, however, are subject to contamination by spatial noise. The curvature chain is used to detect indentations in the boundary and it can be freed of noise (smoothed) by convolving it with a rectangular filter, once (the Freeman operation), twice (the Gallus operation) or more times. An analysis is made of the spatial frequencies passed by these operations. The analysis provides criteria for determining the optimal values of the width of the filter and the number of times it should be applied.The smoothing procedure is applied to the boundaries of conjugated objects consisting of two or more juxtaposed elementary objects (muscle fibres seen in transverse section). It is then possible to pick out indentations (nodes) in a boundary. The nodes are classified and matched and lines of segmentation are drawn between matched pairs. Criteria of acceptable matching of node pairs are described and examples of segmentation are illustrated.     

Reconstruction of piecewise planar objects from point clouds

This article discusses the reverse engineering problem of reconstructing objects with planar faces. We will present the main geometric features of a modeling system which are the detection of planar faces and the generation of a cad model. The algorithms are applied to the problem of reconstruction of buildings from airborne laser scanner data.     

On the consistency of line-drawings, obtained by projections of piecewise planar objects

This paper deals with line-drawings, obtained from images of piecewise planar objects after edge detection. Such images are used, e.g., for navigation and recognition. In order to be a possible image of a three dimensional piecewise planar object, it has to obey some projective conditions. Criteria for a line-drawing to be correct is given in this paper, along with methods to find possible interpretations. In real life situations, due to digitization errors and noise, a line-drawing in general does not obey the geometric conditions imposed by the projective imaging process. Under various optimality conditions, algorithms are presented for the correction of such distorted line-drawings.This work has been done within the ESPRIT-BRA project VIVA.     

Recognition of 3D planar objects in canonical frames

An algorithm for recognizing 3D planar objects by their boundaries is presented. Extreme points on a shape are extracted for constructing canonical frames, under which signatures are then generated for determining the similarity between shapes. The method is efficient and yields a high recognition rate.     

A few-shot learning framework for planar pushing of unknown objects

Intelligent Service Robotics - Robot planar pushing is one of the primitive elements of non-prehensile manipulation skills and has been widely studied as an alternative solution to complex...     

Invariant object recognition in the visual system with novel views of 3D objects

To form view-invariant representations of objects, neurons in the inferior temporal cortex may associate together different views of an object, which tend to occur close together in time under natural viewing conditions. This can be achieved in neuronal network models of this process by using an associative learning rule with a short-term temporal memory trace. It is postulated that within a view, neurons learn representations that enable them to generalize within variations of that view. When three-dimensional (3D) objects are rotated within small angles (up to, e.g., 30 degrees), their surface features undergo geometric distortion due to the change of perspective. In this article, we show how trace learning could solve the problem of in-depth rotation-invariant object recognition by developing representations of the transforms that features undergo when they are on the surfaces of 3D objects. Moreover, we show that having learned how features on 3D objects transform geometrically as the object is rotated in depth, the network can correctly recognize novel 3D variations within a generic view of an object composed of a new combination of previously learned features. These results are demonstrated in simulations of a hierarchical network model (VisNet) of the visual system that show that it can develop representations useful for the recognition of 3D objects by forming perspective-invariant representations to allow generalization within a generic view.     

A curve fitting problem and its application in modeling objects inmonocular image sequences

Presents a solution to a particular curve (surface) fitting problem and demonstrate its application in modeling objects from monocular image sequences. The curve-fitting algorithm is based on a modified nonparametric regression method, which forms the core contribution of this work. This method is far more effective compared to standard estimation techniques, such as the maximum likelihood estimation method, and can take into account the discontinuities present in the curve. Next, the theoretical results of this 1D curve estimation technique ate extended significantly for an object modeling problem. The input to the algorithm is a monocular image sequence of an object undergoing rigid motion. By using the affine camera projection geometry and a given choice of an image frame pair in the sequence, we adopt the KvD (Koenderink and van Doorn, 1991) model to express the depth at each point on the object as a function of the unknown out-of-plane rotation, and some measurable quantities computed directly from the optical flow. This is repeated for multiple image pairs (keeping one fixed image frame which we formally call the base image and choosing another frame from the sequence). The depth map is next estimated from these equations using the modified nonparametric regression analysis. We conducted experiments on various image sequences to verify the effectiveness of the technique. The results obtained using our curve-fitting technique can be refined further by hierarchical techniques, as well as by nonlinear optimization techniques in structure from motion     

OCOG: A common grasp computation algorithm for a set of planar objects

This paper addresses the problem of defining a simple End-Effector design for a robotic arm that is able to grasp a given set of planar objects. The OCOG (Objects COmmon Grasp search) algorithm proposed in this paper searches for a common grasp over the set of objects mapping all possible grasps for each object that satisfy force closure and quality criteria by taking into account the external wrenches (forces and torque) applied to the object. The mapped grasps are represented by feature vectors in a high-dimensional space. This feature vector describes the design of the gripper. A database is generated for all possible grasps for each object in the feature vector space. A search algorithm is then used for intersecting all possible grasps over all parts and finding a common grasp suitable for all objects. The search algorithm utilizes the kd-tree index structure for representing the database of the sets of feature vectors. The kd-tree structure enables an efficient and low cost nearest-neighbor search for common vectors between the sets. Each common vector found (feature vector) is the grasp configuration for a group of objects, which implies the future end-effector design. The final step classifies the grasps found to subsets of the objects, according to the common vectors found. Simulations and experiments are presented for four objects to validate the feasibility of the proposed algorithm. The algorithm will be useful for standardization of end-effector design and reducing its engineering time.     

Least-squares fitting by circles

In reflectometry and in the aircraft industry the problem of fitting data points by a circle is relevant. In contrast with other authors we realize a very special iterative method to determine such a circle. Former approximations for the parameters are used as starting values and are improved. Numerical examples are given.     

The caging configuration design and optimization for planar moving objects using multi-fingered mechanism

Due to the larger number of fingers, and the relative motion between object and fingers, the moving object caging using multi-fingered mechanism is complicated and difficulty. In this paper, a novel algorithm for planar moving objects caging configuration design and optimization using multi-fingered mechanism is proposed. In the proposed algorithm: (1) the lead finger is chosen and controlled to track the caging point nearby the moving object; (2) possible configurations of following fingers are determined according to interconnections of the multi-fingered mechanism; (3) the caging condition is applied to choose effective caging configurations. Compared to existing methods, advantages of the proposed method lie on the simple task mode – ‘leader-follower mode’ and low calculation burden. In addition, considering caging is a loose closure strategy with a certain margin, the caging margin, which is the space between the multi-fingered mechanism and the moving target, is introduced and quantified. Moreover, the caging configurations are optimized to maximize the caging margin to provide maximum local freedom for the object. For verifying the efficiency of the proposed method, it is applied in the rectangular and regular pentagonal shaped moving objects caging problems, and the simulation results illustrate the validity of the proposed algorithm.     

Pose estimation for objects with planar surfaces using eigenimage and range data analysis

In this paper we present a novel method for estimating the object pose for 3D objects with well-defined planar surfaces. Specifically, we investigate the feasibility of estimating the object pose using an approach that combines the standard eigenspace analysis technique with range data analysis. In this sense, eigenspace analysis was employed to constrain one object rotation and reject surfaces that are not compatible with a model object. The remaining two object rotations are estimated by computing the normal to the surface from the range data. The proposed pose estimation scheme has been successfully applied to scenes defined by polyhedral objects and experimental results are reported.