Quantum MDS codes induced by the projective linear transformation

Image matching is an important problem in image processing and arises in such diverse fields as video compression, optical character recognition, medical imaging, watermarking etc. Given two images, image matching determines a transformation that changes the first image such that it most closely resembles the second. Common approaches require either exponential time, or find only an approximate solution, even when only rotations and scalings are allowed. This paper provides the first general polynomial time algorithm to find the exact solution to the image matching problem under projective, affine or linear transformations. Subsequently, nontrivial lower bounds on the number of different transformed images are given which roughly induce the complexity of image matching under the three classes of transformations.

Precast concrete (PC) members are currently being employed for general construction or partial replacement to reduce construction period. As assembly work in PC construction requires connecting PC members accurately, measuring the 6-DOF (degree of freedom) relative displacement is essential. Multiple planar markers and camera-based displacement measurement systems can monitor the 6-DOF relative displacement of PC members. Conventional methods, such as direct linear transformation (DLT) for homography estimation, which are applied to calculate the 6-DOF relative displacement between the camera and marker, have several major problems. One of the problems is that when the marker is partially hidden, the DLT method cannot be applied to calculate the 6-DOF relative displacement. In addition, when the images of markers are blurred, error increases with the DLT method which is employed for its estimation. To solve these problems, a hybrid method, which combines the advantages of the DLT and MCL (Monte Carlo localization) methods, is proposed. The method evaluates the 6-DOF relative displacement more accurately compared to when either the DLT or MCL is used alone. Each subsystem captures an image of a marker and extracts its subpixel coordinates, and then the data are transferred to a main system via a wireless communication network. In the main system, the data from each subsystem are used for 3D visualization. Thereafter, the real-time movements of the PC members are displayed on a tablet PC. To prove the feasibility, the hybrid method is compared with the DLT method and MCL in real experiments.

4 - SPECIAL TRANSFORMATIONS AND THEIR MATRICES

Because of rapidness and easy to update, raster map is important in GIS and digital mapping. In many circumstances, the projection that users demand is not according with the original projection of the raster map, thus the projection transformation of raster map is necessary, Raster map projection transformation, which is essentially image transformation, involves transformation among four coordinate systems: original image coordinate system, original projection coordinate system, new projection coordinate system, new image coordinate system. In this paper, compared with the vast computation and the slow speed of traditional transform method, a rapid algorithm of raster map projection transformation based on dual transformation is researched. In this algorithm, first of all, transform rectangle control grid strictly according to the formula of projection transformation; and then, aiming at each rectangle, using the four corners to construct dual linear transformation polynomial between rectangle image and corresponding quadrilateral image in original raster map; finally, the direct transformation between image coordinates of two maps is realized. The experiment has proved that this algorithm not only satisfies precision demand, but also greatly improves transformation speed.

III.2 - DECOMPOSING PROJECTIVE TRANSFORMATIONS

11 - The homogeneous model

I - Matrix theory

This text explains the methods used in solving linear and integer programming models, using simplified numerical examples. It also describes less common methods such as Farrier's method for linear inequalities, projective transformations and Booleau algebra applied to 0-1 integer models.

It is well known that homogeneous linear matrix transformations of the projective space may be efficiently used for the representation and the execution of common geometrical transformations but the general class of such transformations include also matrices which may cause numerical problems by transforming certain finite geometrical objects to infinity Different methods have been developed for handling such cases and this paper presents a new one called‘UW clipping’which is based on some interesting properties of projective transformations. Furthermore the paper introduces die concept of ‘conic sectors’ as a generalisation to half‐planes and halfspaces respectively, with the invariance property that such sectors are mapped onto other such sectors by projective transformations, and thus enable the transformation of clipping halfplanes and halfspaces. Finally the possibility of transforming die rectangular clipping box into the object space is investigated.

Projective and affine symmetries and equivalences of rational curves in arbitrary dimension

Measurability of radiographic images

Jacobi discovered that the motion of a heavy symmetrical top can be decomposed into the motions of two torque-free triaxial tops. In this paper we investigate the connection between the three sets of the dynamical constants in the three top motions. The formulas connecting these constants are found to be projective transformations (fractional linear transformations).

The theory of invariants originally confined itself to forms involving a single set of homogeneous variables; but recent investigations, geometric as well as algebraic, have proved the importance of the study of forms in any number of sets of variables. In passing from the theory of the simple to the theory of the multiple forms, an entirely new feature presents itself: in the latter case the linear transformations which are fundamental in the definition of invariants may be the same for all the variables or they may be distinct, i. e., the sets of variables involved may be cogredient or digredient. Multiple forms thus have two distinct invariant theories, a cogredient and a digredient. The object of this paper is to study the relations between these two theories in the case of forms involving any number of binary variables. Geometrically, such a form may be regarded as establishing a correspondence between the elements of two or more linear manifolds; in the digredient theory the latter are considered as distinct, thus undergoing independent projective transformations, while in the cogredient theory the linear manifolds are considered to be superposed, thus undergoing the same projective transformation. The first part of the paper, ?? 1-5, is devoted to the double forms. The extension of the results is made first, for convenience of presentation, to the triple forms in ? 6, and then to the general case in ? 7. The case of the double binary forms is perhaps the most interesting geometrically. In addition to the general interpretation by means of an algebraic correspondence between two manifolds, such a form may be interpreted as an algebraic curve on a quadric surface, or as a plane algebraic curve from the view point of inversion geometry. In the former of these special interpretations the two binary variables are the (homogeneous) parameters of the two sets of generators on the quadric, while in the latter they are the parameters of the two sets of minimal lines in the plane. These interpretations suggest the

This paper presents a geometric calibration control method based on large-screen interactive projection system. By establishing the mapping relationship between the captured image and the actual projected image captured by the 3D sensor Kinect camera, the checkerboard is selected using the geometric mapping model to realize the geometric calibration. The projective transformation method is utilized to reduce the nonlinear effect of the projector. Then the projective mapping matrix is obtained by the method of linear transformation. The projective transformation relation matrix is used to establish the precise mapping relationship between the projector and the camera. The self-developed large-screen human-computer interaction projection interactive system platform is employed to perform geometric calibration experiments. The experimental results show that the geometric calibration method of the large-screen interactive projection system based on 3D sensor proposed in this paper achieves a good precision positioning and can be widely applied to various human-computer interaction system.Keywords3D sensorHuman-computer interactionProjective transformation methodProjection interactive systemGeometry calibration

In this paper, we present a robust point set registration method based on the cross ratio invariance of 4 collinear points, which is able to deal with point set registration problem under the most general linear transformation, projective transformation. On the basis of all combinations of 4 collinear points extracted by Hough transform, meaningful correspondences are identified by combining the cross ratio invariance of 4 collinear points and Randomized RANSAC. At the end, the underlying projective transformation matrix was estimate in a least square sense. It has been shown in the simulation experiments that the proposed approach remains robust in high level of degradations, including 45% outliers and 40% overlap ratio. Experiments with Oxford corridor sequence and ZuBuD wide baseline image database proved its usefulness in real application.