Commodity Trade Stabilization Through International Agreements

We introduce a simple and efficient procedure for the segmentation of rigidly moving objects, imaged under an affine camera model. For this purpose we revisit the theory of "linear combination of views" (LCV), proposed by Ullman and Basri [20], which states that the set of 2d views of an object undergoing 3d rigid transformations, is embedded in a low-dimensional linear subspace that is spanned by a small number of basis views. Our work shows, that one may use this theory for motion segmentation, and cluster the trajectories of 3d objects using only two 2d basis views. We therefore propose a practical motion segmentation method, built around LCV, that is very simple to implement and use, and in addition is very fast, meaning it is well suited for real-time SfM and tracking applications. We have experimented on real image sequences, where we show good segmentation results, comparable to the state-of-the-art in literature. If we also consider computational complexity, our proposed method is one of the best performers in combined speed and accuracy. © 2011. The copyright of this document resides with its authors

Fairplay or Greed: Mandating University Responsibility Toward Student Inventors

Over twenty years have passed since the enactment of The Patent and Trademark Law Amendments Act (Bayh-Dole Act) and universities continue to struggle with their technology transfer infrastructures. Lost in that struggle are those who could be considered the backbone of university research: the students. Graduate and undergraduate students remain baffled by the patent assignment and technology transfer processes within their various institutions. Efforts should be undertaken by universities to clarify the student\u27s position in the creative process

Signal Representation and Signal Processing using Operators

The topic of this report is signal representation in the context of hierarchical image processing. An overview of hierarchical processing systems is included as well as a presentation of various approaches to signal representation, feature representation and feature extraction. It is claimed that image hierarchies based on feature extraction, so called feature hierarchies, demand a signal representation other than the standard spatial or linear representation used today. A new representation, the operator representation is developed. It is based on an interpretation of features in terms of signal transformations. This representation has no references to any spatial ordering of the signal element and also gives an explicit representation of signal features. Using the operator representation, a generalization of the standard phase concept in image processing is introduced. Based on the operator representation, two algorithms for extraction of feature values are presented. Both have the c..

Efficient three-view triangulation based on 3d optimization

Triangulation of a 3D point from two or more views can be solved in several ways depending on how perturbations in the image coordinates are dealt with. A common approach is optimal triangulation which minimizes the total L2 reprojection error in the images, corresponding to finding a maximum likelihood estimate of the 3D point assuming independent Gaussian noise in the image spaces. Computational approaches for optimal triangulation have been published for the stereo case and, recently, also for the three-view case. In short, they solve an independent optimization problem for each 3D point, using relatively complex computations such as finding roots of high order polynomials or matrix decompositions. This paper discuss three-view triangulation and reports the following results: (1) the 3D point can be computed as multi-linear mapping (tensor) applied on the homogeneous image coordinates, (2) the set of triangulation tensors forms a 7-dimensional space determined by the camera matrices, (3) given a set of corresponding 3D/2D calibration points, the 3D residual L1 errors can be optimized over the elements in the 7-dimensional space, (4) using the resulting tensor as initial value, the error can be further reduced by tuning the tensor in a two-step iterative process, (5) the 3D residual L1 error for a set of evaluation points which lie close to the calibration set is comparable to the three-view optimal method. In summary, three-view triangulation can be done by first performing an optimization of the triangulation tensor and once this is done, triangulation can be made with 3D residual error at the same level as the optimal method, but at a much lower computational cost. This makes the proposed method attractive for real-time three-view triangulation of large data sets provided that the necessary calibration process can be performed.

The structure tensor in projective spaces

The structure tensor has been used mainly for representation of local orientation in spaces of arbitrary dimensions, where the eigenvectors represent the orientation and the corresponding eigenvalues indicate the type of structure which is represented. Apart from being local, the structure tensor may be referred to as "object centered" since it describes the corresponding structure relative to a local reference system. This paper proposes that the basic properties of the structure tensor can be extended to a tensor defined in a projective space rather than in a local Euclidean space. The result, the "projective tensor", is symmetric in the same way as the structure tensor, and also uses the eigensystem to carry the relevant information. However, instead of orientation, the projective tensor represents geometrical primitives such as points, lines, and planes (depending on dimensionality of the underlying space). Furthermore, this representation has the useful property of mapping the operation of forming the affine hull of points and lines to tensor summation, e.g., the sum of two projective tensors which represent two points amounts to a projective tensor that represent the line which passes through the two points, etc. The projective tensor may be referred to as "view centered" since each tensor, which still may be defined on a local scale, represents a geometric primitive relative to a global image based reference system. This implies that two such tensors may be combined, e.g., using summation, in a meaningful way over large regions

Signal Representation and Processing using Operator Groups

This thesis presents a signal representation in terms of operators. The signal is assumed to be an element of a vector space and subject to transformations of operators. The operators form continuous groups, so-called Lie groups. The representation can be used for signals in general, in particular if spatial relations are undefined, and it does not require a basis of the signal space to be useful. Special attention is given to orthogonal operator groups which are generated by antiHermitian operators by means of the exponential mapping. It is shown that the eigensystem of the group generator is strongly related to properties of the corresponding operator group. For one-parameter orthogonal operator groups, a phase concept is introduced. This phase can for instance be used to distinguish between spatially even and odd signals and, therefore, corresponds to the usual phase for multi-dimensional signals. Given one operator group that represents the variation of the signal and one operator ..

Introduction to Representations and Estimation in Geometry

This book contains material for an introductory course on homogeneous representations for geometry in 2 and 3 dimensions, camera projections, representations of 3D rotations, epipolar geometry, and estimation of various type of geometric objects. Based on these results, a set of applications are presented.  It also contains a toolbox of general results that are useful for the presented material.  The book is intended for undergraduate studies at advanced level in master programs, or in PhD-courses at introductory level

A fourth order tensor for representation of orientation and position of oriented segments

This report describes a fourth order tensor defined on projective spaces which can be used for the representation of medium-level features, e.g., one or more oriented segments. The tensor has one part which describes what type of local structures are present in a region, and one part which describes where they are located. This information can be used, e.g., to represent multiple orientations, corners, and line-endings. The tensor can be defined for arbitrary signal dimension, but the presentation focuses on the properties of the fourth order tensor for the case of 2D and 3D image data. A method for estimating the proposed tensor representation by means of simple computations directly from the structure tensor is presented. Given a simple matrix representation of the tensor, it can be shown that there is a direct correspondence between the number of oriented segments and the rank of the matrix provided that the number of segments is three or less. The \publication also presents techniques for extracting information about the oriented segments which the tensor represent. Finally, it shown that a small set of coefficients can be computed from the proposed tensor which are invariant to changes of the coordinate system