Showing papers on "Affine transformation published in 1993"

Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition

Abstract: We describe a recursive algorithm to compute representations of functions with respect to nonorthogonal and possibly overcomplete dictionaries of elementary building blocks e.g. affine (wavelet) frames. We propose a modification to the matching pursuit algorithm of Mallat and Zhang (1992) that maintains full backward orthogonality of the residual (error) at every step and thereby leads to improved convergence. We refer to this modified algorithm as orthogonal matching pursuit (OMP). It is shown that all additional computation required for the OMP algorithm may be performed recursively. >

Analysis and synthesis of feedforward neural networks using discrete affine wavelet transformations

Abstract: A representation of a class of feedforward neural networks in terms of discrete affine wavelet transforms is developed. It is shown that by appropriate grouping of terms, feedforward neural networks with sigmoidal activation functions can be viewed as architectures which implement affine wavelet decompositions of mappings. It is shown that the wavelet transform formalism provides a mathematical framework within which it is possible to perform both analysis and synthesis of feedforward networks. For the purpose of analysis, the wavelet formulation characterizes a class of mappings which can be implemented by feedforward networks as well as reveals an exact implementation of a given mapping in this class. Spatio-spectral localization properties of wavelets can be exploited in synthesizing a feedforward network to perform a given approximation task. Two synthesis procedures based on spatio-spectral localization that reduce the training problem to one of convex optimization are outlined. >

3-D motion estimation in model-based facial image coding

Abstract: An approach to estimating the motion of the head and facial expressions in model-based facial image coding is presented. An affine nonrigid motion model is set up. The specific knowledge about facial shape and facial expression is formulated in this model in the form of parameters. A direct method of estimating the two-view motion parameters that is based on the affine method is discussed. Based on the reasonable assumption that the 3-D motion of the face is almost smooth in the time domain, several approaches to predicting the motion of the next frame are proposed. Using a 3-D model, the approach is characterized by a feedback loop connecting computer vision and computer graphics. Embedding the synthesis techniques into the analysis phase greatly improves the performance of motion estimation. Simulations with long image sequences of real-world scenes indicate that the method not only greatly reduces computational complexity but also substantially improves estimation accuracy. >

3D Human interface apparatus using motion recognition based on dynamic image processing

Abstract: A 3D human interface apparatus using a motion recognition based on a dynamic image processing in which the motion of an operator operated object as an imaging target can be recognized accurately and stably. The apparatus includes: an image input unit for entering a plurality of time series images of an object operated by the operator into a motion representing a command; a feature point extraction unit for extracting at least four feature points including at least three reference feature points and one fiducial feature point on the object, from each of the images; a motion recognition unit for recognizing the motion of the object by calculating motion parameters, according to an affine transformation determined from changes of positions of the reference feature points on the images, and a virtual parallax for the fiducial feature point expressing a difference between an actual position change on the images and a virtual position change according to the affine transformation; and a command input unit for inputting the command indicated by the motion of the object recognized by the motion recognition unit.

Affine invariant scale-space

Abstract: A newaffine invariant scale-space for planar curves is presented in this work. The scale-space is obtained from the solution of a novel nonlinear curve evolution equation which admits affine invariant solutions. This flow was proved to be the affine analogue of the well knownEuclidean shortening flow. The evolution also satisfies properties such ascausality, which makes it useful in defining a scale-space. Using an efficient numerical algorithm for curve evolution, this continuous affine flow is implemented, and examples are presented. The affine-invariant progressive smoothing property of the evolution equation is demonstrated as well.

Density of integer points on affine homogeneous varieties

Abstract: (1.2) N(T, V)= {m V(Z): Ilmll T} where we denote by V(A), for any ring A, the set of A-points of V. Hence I1\" is some Euclidean norm on R\". The only general method available for such problems is the Hardy-Littlewood circle method, which however has certain limitations, requiring roughly that the codimension of V in the ambient space A\", as well as the degree of the equations (1.1), be small relative to n. Furthermore, there are restrictions on the size of the singular sets of the related varieties:

Recognizing Planar Objects Using Invariant Image Features

Abstract: Translation, rotation, scale and contrast invariants.- Algebraic and projective invariants.- Invariance to affine transformations.- Invariance to projective transformations.- Recognizing partially occluded objects.- Summary and conclusions.

Isomorphism of two realizations of quantum affine algebra\(U_q (\widehat{\mathfrak{g}\mathfrak{l}{\text{(}}n{\text{)}}})\)

Abstract: We establish an explicit isomorphism between two realizations of the quantum affine algebra $$U_q (\widehat{\mathfrak{g}\mathfrak{l}{\text{(}}n{\text{)}}})$$ given previously by Drinfeld and Reshetikhin-Semenov-Tian-Shansky. Our result can be considered as an affine version of the isomorphism between the Drinfield/Jimbo and the Faddeev-Reshetikhin-Takhtajan constructions of the quantum algebra $$U_q (\mathfrak{g}\mathfrak{l}(n))$$ .

Method and apparatus for encoding pictures including a moving object

Abstract: A method of encoding a sequence of images including a moving object, comprises forming an initial template, extracting a mask outlining the object, dividing the template into a plurality (for example sixteen) sub-templates, searching the next frame to find a match with the template, searching the next frame to find a match with each of the sub-templates, determining the displacements of each of the sub-templates with respect to the template, using the displacements to determine affine transform coefficients and performing an affine transform to produce an updated template and updated mask. Encoding is performed at a higher resolution for portions within the outline than for portions outside the outline.

Affine theorem for two-dimensional Fourier transform

Abstract: The well known shift and similarity theorems for the Fourier transform generalise to two dimensions but new theorems come into existence in two dimensions. Simple theorems for rotation and shear distortion are examples. A theorem is presented which determines what the Fourier transform becomes when the function domain is subjected to an affine co-ordinate transformation. The full theorem contains a variety of simpler theorems as special cases. It may prove useful in its general form in image processing where sequences of affine transformations are applied.

Robust structure from motion using motion parallax

Abstract: An efficient and geometrically intuitive algorithm for reliably interpreting the image velocities of moving objects in 3-D is presented. It is well known that under a weak perspective the image motion of points on a plane can be characterized by an affine transformation. It is shown that the relative image motion of a nearby non-coplanar point and its projection on the plane is equivalent to motion parallax, and because it is independent of view rotations it is a reliable geometric cue to 3-D shape and viewer/object motion. The authors summarize why structure from motion algorithms are often very sensitive to errors in the measured image velocities and then show how to efficiently and reliably extract an incomplete qualitative solution. They also show how to augment this into a complete solution if additional constraints or views are available. A real-time example is presented in which the 3-D visual interpretation of hand gestures or a hand-held object is used as part of a man-machine interface. This is an alternative to the Polhemus coil instrumented Dataglove commonly used in sensing manual gestures. >

Selected Affine Isoperimetric Inequalities

Abstract: Publisher Summary This chapter reviews sharp affine isoperimetric inequality Affine isoperimetric inequalities have occupied a central position in the field of geometric convexity There have been numerous applications of these inequalities to fields, such as ordinary and partial differential equations, functional analysis, the geometry of numbers, discrete geometry and polytopal approximations, stereology and stochastic geometry, and to the field of Minkowskian geometry An attempt has been made to focus on inequalities established in the second half of this century This chapter examines only a few sharp affine isoperimetric inequalities

Characterizations of generalized monotone maps

Abstract: This paper is a sequel to Ref. 1 in which several kinds of generalized monotonicity were introduced for maps. They were related to generalized convexity properties of functions in the case of gradient maps. In the present paper, we derive first-order characterizations of generalized monotone maps based on a geometrical analysis of generalized monotonicity. These conditions are both necessary and sufficient for generalized monotonicity. Specialized results are obtained for the affine case.

Gradient descent method for optimizing various fuzzy rule bases

Abstract: The authors derive the gradient descent optimization equations for Takagi-Sugeno fuzzy rule bases with symmetric and asymmetric triangular membership functions, minimum and multiplication operators, and constant and affine output functions. A new type of affine output Takagi-Sugeno rules called centered Takagi-Sugeno rules is proposed. It makes it possible to avoid a class of local minima. The gradient descent method is systematically tested for the approximation of a one-input, one-output analytical function including a discontinuity and a high curvature point, and for the approximation of a two-input function. >

Quantum affine symmetry in vertex models

Abstract: We study the higher spin analogs of the six-vertex model on the basis of its symmetry under the quantum affine algebra . Using the method developed recently for the XXZ spin chain, we formulate the space of states, transfer matrix, vacuum, creation/ annihilation operators of particles, and local operators, purely in the language of representation theory. We find that, regardless of the level of the representation involved, the particles have spin 1/2, and that the n-particle space has an RSOS type structure rather than a simple tensor product of the one-particle space. This agrees with the picture proposed earlier by Reshetikhin.

The perceptual analysis of structure from motion for rotating objects undergoing affine stretching transformations

Abstract: In two experiments, we evaluated the ability of human observers to make use of second-order temporal relations across three or more views of an apparent motion sequence for the perceptual analysis of three-dimensional form. Ratings of perceived rigidity were obtained in Experiment 1 for objects rotating in depth that were simultaneously subjected to sinusoidal affine stretching transformations along the line of sight or in a direction parallel to the image plane. Such transformations are theoretically interesting because they cannot be detected by analyses that are restricted to first-order temporal relations (i.e., two views), but they can be detected by more conventional analyses of structure from motion in which second-order temporal relations over three or more views are used. The current results show that human observers can perceive stretching transformations of a rotating 3-D object in a direction parallel to the image plane but that they fail to perceive stretching transformations along the line of sight. This result suggests that human observers can make use of some limited second-order temporal information. This finding was confirmed in Experiment 2, in which we investigated the effects of several specific optical consequences of sinusoidal stretching transformations applied in different directions. The results indicate that observers may be sensitive to the sign ofacceleration, but that. they cannot make use of the precise magnitude of second-order relations necessary to recover euclidean metric structure. Human observers have the remarkable ability to perceive an object’s three-dimensional (3-D) form from its projected pattern of motion within a 2-D visual image. This phenomenon, sometimes referred to as the kinetic depth effect, has been widely investigated by perceptual psychologists for over 60 years (Braunstein, 1962; J. J. Gibson & E. J. Gibson, 1957; E. J. Gibson, J. J. Gibson, Smith, & Flock, 1959; Green, 1961; Johansson, 1964; Johansson & Jansson, 1968; Metzger, 1934; Miles, 1931; Wallach & O’Connell, 1953). More recently, this capability has also attracted the attention of researchers in machine vision, who have developed working algorithms for computing an object’s 3-D structure from moving 2-D optical patterns. Most mathematical analyses for computing structure from motion are designed to operate on a small number of identifiable points across a small number of discrete temporal “views.” The goal of these analyses is to discover whether there is a rigid (usually) 3-D structure compatible with the positions of those points over time. Ullman (1979) has shown that one can recover 3-D structure from orthographic projections given the motions of

Affine-invariant contour tracking with automatic control of spatiotemporal scale

Abstract: A framework for visual tracking of contours is presented, based on a synthesis of elastic models, stochastic filtering, and geometric invariance. Flexibly coupled curve templates implement soft prior assumptions about shape. Affine invariance, built into the flexible coupling, ensures that the affine deformations that arise naturally from image projection are favored. The stochastic basis of the framework is shown to result naturally in an automatic mechanism for the control of spatiotemporal scale. >

Projective depth: A geometric invariant for 3D reconstruction from two perspective/orthographic views and for visual recognition

Abstract: The author addresses the problems of reconstructing 3-D space in a projective framework from two views and of artificially generating novel views of the scene from two given views. It is shown that with the correspondences coming from four non-coplanar points in the scene and the corresponding epipoles, it is possible to define and reconstruct a projective invariant, referred to as projective depth, that can be used later to reconstruct the projective or affine structure of the scene or directly to generate novel views of the scene. The derivation has the advantage that the viewing transformation matrix need not be recovered in the course of computations. >

Logo recognition using geometric invariants

Abstract: The problem of logo recognition is of great interest in the document domain, especially for databases, because of its potential for identifying the source of the document and its generality as a recognition problem. By recognizing the logo, one obtains semantic information about the document, which may be useful in deciding whether or not to analyze the textual components. A multi-level stages approach to logo recognition which uses global invariants to prune the database and local affine invariants to obtain a more refined match is presented. An invariant signature which can be used for matching under a variety of transformations is obtained. The authors provide a method of computing Euclidean invariants and show how to extend them to capture similarity, affine, and projective invariants when necessary. They implement feature detection, feature extraction, and local invariant algorithms and successfully demonstrate the approach on a small database. >

Three-dimensional verification of patient placement during radiotherapy using portal images.

Abstract: The use of a single portal image for the three‐dimensional verification of patient placement during radiotherapy has been investigated. In this study, a deviation in the patient positioning is quantified by a three‐dimensional translation and rotation of the patient. The parameter values are obtained by fitting the projections of anatomical match points in the simulator and the portal image, using the three‐dimensional gantry coordinates of these points in the intended treatment setup. Two methods for finding an analytical solution for the fitting problem are presented. One method yields a solution from the affine transformation of the portal image (shift, rotation, magnification, and stretching in a specified direction) that fits the projections of the match points on the simulator image. The second and more accurate method yields a solution that expresses the estimated parameter values and their covariances as functions of image and three‐dimensional gantry coordinates of the selected matchpoints. The robustness and sensitivity of the solution is implicitly given by these expressions. The applications of these methods are illustrated by experiments with a human pelvic bone.

Wavelets and self-affine tilings

Abstract: Given a self-affine periodic tiling ofR n we construct an associatedr-regular multiresolution analysis and wavelet basis with the same lattice of translations and scaling matrix as the tiling.

On the convergence of projection methods: application to the decomposition of affine variational inequalities

Abstract: In this paper, the authors first discuss the global convergence methods for solving non-linear monotone variational inequalities under a co-coercivity assumption. A similar analysis is applied to "assymetric" projection methods, when the mapping is affine and monotone. Under a suitable choice of the "projection" matrix, decomposition can be achieved. It is proved that this scheme achieves a linear convergence rate, thus enhancing results previously obtained by Tseng and Luo and Tseng. (A)

Right coprime factorizations and stabilization for nonlinear systems

Abstract: The problem of constructing right coprime factorizations (which are based on the graph of an input-output map instead of the Bezout identity) of nonlinear input-output maps is considered. The map is assumed to arise from a state variable realization with a fixed initial state. The main result is that the existence of a stabilizing state feedback implies the existence of a right coprime factorization for the map. The technique is illustrated by application to nonlinear systems which are affine in the control and have a controllable linear past and nonlinear systems which are feedback linearizable. A notion of input-output stability that requires a bound on the magnitude of the input signals is introduced. Methods of constructing such bounds are developed. For a locally feedback linearizable system, the problem of input bounds is transferred to the equivalent linear system. This leads to a technique that allows state and input constraints for a feedback linearizable system to be mapped to the equivalent linear system. >