Showing papers on "Affine transformation published in 2003"

The space of human body shapes: reconstruction and parameterization from range scans

Abstract: We develop a novel method for fitting high-resolution template meshes to detailed human body range scans with sparse 3D markers. We formulate an optimization problem in which the degrees of freedom are an affine transformation at each template vertex. The objective function is a weighted combination of three measures: proximity of transformed vertices to the range data, similarity between neighboring transformations, and proximity of sparse markers at corresponding locations on the template and target surface. We solve for the transformations with a non-linear optimizer, run at two resolutions to speed convergence. We demonstrate reconstruction and consistent parameterization of 250 human body models. With this parameterized set, we explore a variety of applications for human body modeling, including: morphing, texture transfer, statistical analysis of shape, model fitting from sparse markers, feature analysis to modify multiple correlated parameters (such as the weight and height of an individual), and transfer of surface detail and animation controls from a template to fitted models.

Affine Processes and Applications in Finance

Abstract: We provide the definition and a complete characterization of regular affine processes. This type of process unifies the concepts of continuousstate branching processes with immigration and Ornstein-Uhlenbeck type processes. We show, and provide foundations for, a wide range of financial applications for regular affine processes.

A DWT-DFT composite watermarking scheme robust to both affine transform and JPEG compression

Abstract: Robustness is a crucially important issue in watermarking. Robustness against geometric distortion and JPEG compression at the same time with blind extraction remains especially challenging. A blind discrete wavelet transform-discrete Fourier transform (DWT-DFT) composite image watermarking algorithm that is robust against both affine transformation and JPEG compression is proposed. The algorithm improves robustness by using a new embedding strategy, watermark structure, 2D interleaving, and synchronization technique. A spread-spectrum-based informative watermark with a training sequence is embedded in the coefficients of the LL subband in the DWT domain while a template is embedded in the middle frequency components in the DFT domain. In watermark extraction, we first detect the template in a possibly corrupted watermarked image to obtain the parameters of an affine transform and convert the image back to its original shape. Then, we perform translation registration using the training sequence embedded in the DWT domain, and, finally, extract the informative watermark. Experimental work demonstrates that the proposed algorithm generates a more robust watermark than other reported watermarking algorithms. Specifically it is robust simultaneously against almost all affine transform related testing functions in StirMark 3.1 and JPEG compression with quality factor as low as 10. While the approach is presented for gray-level images, it can also be applied to color images and video sequences.

Fast anisotropic Gauss filtering

Abstract: We derive the decomposition of the anisotropic Gaussian in a one-dimensional (1-D) Gauss filter in the x-direction followed by a 1-D filter in a nonorthogonal direction /spl phi/. So also the anisotropic Gaussian can be decomposed by dimension. This appears to be extremely efficient from a computing perspective. An implementation scheme for normal convolution and for recursive filtering is proposed. Also directed derivative filters are demonstrated. For the recursive implementation, filtering an 512 /spl times/ 512 image is performed within 40 msec on a current state of the art PC, gaining over 3 times in performance for a typical filter, independent of the standard deviations and orientation of the filter. Accuracy of the filters is still reasonable when compared to truncation error or recursive approximation error. The anisotropic Gaussian filtering method allows fast calculation of edge and ridge maps, with high spatial and angular accuracy. For tracking applications, the normal anisotropic convolution scheme is more advantageous, with applications in the detection of dashed lines in engineering drawings. The recursive implementation is more attractive in feature detection applications, for instance in affine invariant edge and ridge detection in computer vision. The proposed computational filtering method enables the practical applicability of orientation scale-space analysis.

Collision Detection in Interactive 3D Environments

Abstract: 1 Introduction 1.1 Problem Domain 1.2 Historical Background 1.3 Organization 2 Concepts 2.1 Geometry 2.1.1 Notational Conventions 2.1.2 Vector Spaces 2.1.3 Affine Spaces 2.1.4 Euclidean Spaces 2.1.5 Affine Transformations 2.1.6 Three-dimensional Space 2.2 Objects 2.2.1 Polytopes 2.2.2 Polygons 2.2.3 Quadrics 2.2.4 Minkowski Addition 2.2.5 Complex Shapes and Scenes 2.3 Animation 2.4 Time 2.5 Response 2.6 Performance 2.6.1 Frame Coherence 2.6.2 Geometric Coherence 2.6.3 Average Time 2.7 Robustness 2.7.1 Floating-Point Numbers 2.7.2 Stability 2.7.3 Coping with Numerical Problems 3 Basic Primitives 3.1 Spheres 3.1.1 Sphere-Sphere Test 3.1.2 Ray-Sphere Test 3.1.3 Line-Segment-Sphere Test 3.2 Axis-Aligned Boxes 3.2.1 Ray-Box Test 3.2.2 Sphere-Box Test 3.3 Separating Axes 3.3.1 Line-Segment-Box Test 3.3.2 Triangle-Box Test 3.3.3 Box-Box Test 3.4 Polygons 3.4.1 Ray-Triangle Test 3.4.2 Line Segment-Triangle Test 3.4.3 Ray-Polygon Test 3.4.4 Triangle-Triangle Test 3.4.5 Polygon-Polygon Test 3.4.6 Triangle-Sphere Test 3.4.7 Polygon-Volume Tests 4 Convex Objects 4.1 Proximity Queries 4.2 Overview of Algorithms for Polytopes 4.2.1 Finding a Common Point 4.2.2 Finding a Separating Plane 4.2.3 Distance and Penetration Depth Computation 4.3 The Gilbert-Johnson-Keerthi Algorithm 4.3.1 Overview 4.3.2 Convergence and Termination 4.3.3 Johnson's Distance Algorithm 4.3.4 Support Mappings 4.3.5 Implementing the GJK Algorithm 4.3.6 Numerical Aspects of the GJK Algorithm 4.3.7 Testing for Intersections 4.3.8 Penetration Depth 5 Spatial Data Structures 5.1 Nonconvex Polyhedra 5.1.1 Convex Decomposition 5.1.2 Polyhedral Surfaces 5.1.3 Point in Nonconvex Polyhedron 5.2 Space Partitioning 5.2.1 Voxel Grids 5.2.2 Octrees and k-d Trees 5.2.3 Binary Space Partitioning Trees 5.2.4 Discussion 5.3 Model Partitioning 5.3.1 Bounding Volumes 5.3.2 Bounding-Volume Hierarchies 5.3.3 AABB Trees versus OBB Trees 5.3.4 AABB Trees and Deformable Models 5.4 Broad Phase 5.4.1 Sweep and Prune 5.4.2 Implementing the Sweep-and-Prune Algorithm 5.4.3 Ray Casting and AABBs 6 Design of SOLID 6.1 Requirements 6.2 Overview of SOLID 6.3 Design Decisions 6.3.1 Shape Representation 6.3.2 Motion Specification 6.3.3 Response Handling 6.3.4 Algorithms 6.4 Evaluation 6.5 Implementation Notes 6.5.1 Generic Data Types and Algorithms 6.5.2 Fundamental 3D Classes 7 Conclusion 7.1 State of the Art 7.2 Future Work Bibliography Index About the CD-ROM Trademarks

Elastic registration in the presence of intensity variations

Abstract: We have developed a general-purpose registration algorithm for medical images and volumes. This method models the transformation between images as locally affine but globally smooth. The model also explicitly accounts for local and global variations in image intensities. This approach is built upon a differential multiscale framework, allowing us to capture both large- and small-scale transformations. We show that this approach is highly effective across a broad range of synthetic and clinical medical images.

Probabilistic video stabilization using Kalman filtering and mosaicing

Abstract: The removal of unwanted, parasitic vibrations in a video sequence induced by camera motion is an essential part of video acquisition in industrial, military and consumer applications. In this paper, we present a new image processing method to remove such vibrations and reconstruct a video sequence void of sudden camera movements. Our approach to separating unwanted vibrations from intentional camera motion is based on a probabilistic estimation framework. We treat estimated parameters of interframe camera motion as noisy observations of the intentional camera motion parameters. We construct a physics-based state-space model of these interframe motion parameters and use recursive Kalman filtering to perform stabilized camera position estimation. A six-parameter affine model is used to describe the interframe transformation, allowing quite accurate description of typical scene changes due to camera motion. The model parameters are estimated using a p-norm-based multi-resolution approach. This approach is robust to model mismatch and to object motion within the scene (which are treated as outliers). We use mosaicking in order to reconstruct undefined areas that result from motion compensation applied to each video frame. Registration between distant frames is performed efficiently by cascading interframe affine transformation parameters. We compare our method' s performance with that of a commercial product on real-life video sequences, and show a significant improvement in stabilization quality for our method.

Quantum Reduction for Affine Superalgebras

Abstract: We extend the homological method of quantization of generalized Drinfeld--Sokolov reductions to affine superalgebras. This leads, in particular, to a unified representation theory of superconformal algebras.

Maximum Likelihood Estimation of Latent Affine Processes

Abstract: This article develops a direct filtration-based maximum likelihood methodology for estimating the parameters and realizations of latent affine processes. The equivalent of Bayes' rule is derived for recursively updating the joint characteristic function of latent variables and the data conditional upon past data. Likelihood functions can consequently be evaluated directly by Fourier inversion. An application to daily stock returns over 1953-96 reveals substantial divergences from EMM-based estimates: in particular, more substantial and time-varying jump risk.

Algebraic loop groups and moduli spaces of bundles

Abstract: We study algebraic loop groups and affine Grassmannians in positive character- istic. The main results are normality of Schubert-varieties, the construction of line-bundles on the affine Grassmannian, and the proof that they induce line-bundles on the moduli-stack of torsors.

Quantum reduction for affine superalgebras

Abstract: We extend the homological method of quantization of generalized Drinfeld–Sokolov reductions to affine superalgebras. This leads, in particular, to a unified representation theory of superconformal algebras.

3D object modeling and recognition using affine-invariant patches and multi-view spatial constraints

Abstract: This paper presents a representation for three-dimensional objects in terms of affine-invariant image patches and their spatial relationships. Multi-view constraints associated with groups of patches are combined with a normalized representation of their appearance to guide matching and reconstruction, allowing the acquisition of true three-dimensional affine and Euclidean models from multiple images and their recognition in a single photograph taken from an arbitrary viewpoint. The proposed approach does not require a separate segmentation stage and is applicable to cluttered scenes. Preliminary modeling and recognition results are presented.

Novel prospective respiratory motion correction approach for free-breathing coronary MR angiography using a patient-adapted affine motion model.

Abstract: A novel technique is presented which enables the calibration of a 3D affine respiratory motion model to the individual motion pattern of the patient. The concept of multiple navigators and precursory navigators is introduced to address nonlinear properties and hysteresis effects of the model parameters with respect to the conventional diaphragmatic navigator. The optimal combination and weighting of the navigators is determined on the basis of a principal component analysis (PCA). Thus, based on a given navigator measurement the current motion state of the object can be predicted by means of the calibrated motion model. The 3D motion model is applied in high-resolution coronary MR angiography examinations (CMRA) to prospectively correct for respiration-induced motion. The basic feasibility of the proposed calibration procedure was shown in 16 volunteers. Furthermore, the application of the calibrated motion model for CMRA examinations of the right coronary artery (RCA) was tested in 10 volunteers. The superiority of a calibrated 3D translation model over the conventional 1D translation model with a fixed correction factor and the potential of affine prospective motion correction for CMRA are demonstrated.

Computing the uniform component of shape variation.

Abstract: Any change in shape of a configuration of landmark points in two or three dimensions includes a uniform component, a component that is a wholly linear (affine) transformation. The formulas for estimating this component have been standardized for two-dimensional data but not for three-dimensional data. We suggest estimating the component by way of the complementarity between the uniform component and the space of partial warps. The component can be estimated by regression in either one space or the other: regression on the partial warps, followed by their removal, or regression on a basis for the uniform component itself. Either of the new methods can be used for both two- and three-dimensional landmark data and thus generalize Bookstein's (1996, pages 153-168 in Advances in morphometrics [L. F. Marcus et al., eds.], Plenum, New York) linearized Procrustes formula for estimating the uniform component in two dimensions.

Visual identification by signature tracking

Abstract: We propose a new camera-based biometric: visual signature identification. We discuss the importance of the parameterization of the signatures in order to achieve good classification results, independently of variations in the position of the camera with respect to the writing surface. We show that affine arc-length parameterization performs better than conventional time and Euclidean arc-length ones. We find that the system verification performance is better than 4 percent error on skilled forgeries and 1 percent error on random forgeries, and that its recognition performance is better than 1 percent error rate, comparable to the best camera-based biometrics.

A toolbox for cryptanalysis: linear and affine equivalence algorithms

Abstract: This paper presents two algorithms for solving the linear and the affine equivalence problem for arbitrary permutations (S-boxes). For a pair of n × n-bit permutations the complexity of the linear equivalence algorithm (LE) is O(n32n). The affine equivalence algorithm (AE) has complexity O(n322n). The algorithms are efficient and allow to study linear and affine equivalences for bijective S-boxes of all popular sizes (LE is efficient up to n ≤ 32). Using these tools new equivalent representations are found for a variety of ciphers: Rijndael, DES, Camellia, Serpent, Misty, Kasumi, Khazad, etc. The algorithms are furthermore extended for the case of non-bijective n to m-bit S-boxes with a small value of |n - m| and for the case of almost equivalent S-boxes. The algorithms also provide new attacks on a generalized Even-Mansour scheme. Finally, the paper defines a new problem of S-box decomposition in terms of Substitution Permutations Networks (SPN) with layers of smaller S-boxes. Simple information-theoretic bounds are proved for such decompositions.

A Toolbox for Cryptanalysis: Linear and Affine Equivalence Algorithms

Abstract: This paper presents two algorithms for solving the linear and the affine equivalence problem for arbitrary permutations (S-boxes). For a pair of n x n-bit permutations the complexity of the linear equivalence algorithm (LE) is O(n 3 2 n ). The affine equivalence algorithm (AE) has complexity O(n 3 2 2n ). The algorithms are efficient and allow to study linear and affine equivalences for bijective S-boxes of all popular sizes (LE is efficient up to n ≤ 32). Using these tools new equivalent representations are found for a variety of ciphers: Rijndael, DES, Camellia, Serpent, Misty, Kasumi, Khazad, etc. The algorithms are furthermore extended for the case of non-bijective n to m-bit S-boxes with a small value of |n - m| and for the case of almost equivalent S-boxes. The algorithms also provide new attacks on a generalized Even-Mansour scheme. Finally, the paper defines a new problem of S-box decomposition in terms of Substitution Permutations Networks (SPN) with layers of smaller S-boxes. Simple information-theoretic bounds are proved for such decompositions.

Invariant subspaces for LPV systems and their applications

Abstract: The aim of this paper is to extend the notion of invariant subspaces known in the geometric control theory of the linear time invariant systems to the linear parameter-varying (LPV) systems by introducing the concept of parameter-varying invariant subspaces. For LPV systems affine in their parameters, algorithms are given to compute many parameter varying subspaces relevant in the solution of state feedback and observer design problems.

Joint manifold distance: a new approach to appearance based clustering

Abstract: We wish to match sets of images to sets of images where both sets are undergoing various distortions such as viewpoint and lighting changes. To this end we have developed a joint manifold distance (JMD) which measures the distance between two subspaces, where each subspace is invariant to a desired group of transformations, for example affine warping of the image plane. The JMD may be seen as generalizing invariant distance metrics such as tangent distance in two important ways. First, formally representing priors on the image distribution avoids certain difficulties, which in previous work have required ad-hoc correction. The second contribution is the observation that previous distances have been computed using what amounted to "home-grown" nonlinear optimizers, and that more reliable results can be obtained by using generic optimizers which have been developed in the numerical analysis community, and which automatically set the parameters which home-grown methods must set by art. The JMD is used in this work to cluster faces in video. Sets of faces detected in contiguous frames define the subspaces, and distance between the subspaces is computed using JMD. In this way the principal cast of a movie can be 'discovered' as the principal clusters. We demonstrate the method on a feature-length movie.

Multichannel affine and fast affine projection algorithms for active noise control and acoustic equalization systems

Abstract: In the field of adaptive signal processing, it is well known that affine projection algorithms or their low-computational implementations fast affine projection algorithms can produce a good tradeoff between convergence speed and computational complexity. Although these algorithms typically do not provide the same convergence speed as recursive-least-squares algorithms, they can provide a much improved convergence speed compared to stochastic gradient descent algorithms, without the high increase of the computational load or the instability often found in recursive-least-squares algorithms. In this paper, multichannel affine and fast affine projection algorithms are introduced for active noise control or acoustic equalization. Multichannel fast affine projection algorithms have been previously published for acoustic echo cancellation, but the problem of active noise control or acoustic equalization is a very different one, leading to different structures, as explained in the paper. The computational complexity of the new algorithms is evaluated, and it is shown through simulations that not only can the new algorithms provide the expected tradeoff between convergence performance and computational complexity, they can also provide the best convergence performance (even over recursive-least-squares algorithms) when nonideal noisy acoustic plant models are used in the adaptive systems.

Wavelets on Fractals

Abstract: We develop the theory of multiresolutions in the context of Hausdorff measure of fractional dimension between 0 and 1. While our fractal wavelet theory has points of similarity that it shares with the standard case of Lebesgue measure on the line, there are also sharp contrasts. These are stated in our main result, a dichotomy theorem. The first section is the case of the middle-third Cantor set. This is followed by a review of the essentials on Hausdorff measure. The remaining sections of the paper cover multiresolutions in the general context of affine iterated function systems.

System and method for distortion characterization in fingerprint and palm-print image sequences and using this distortion as a behavioral biometrics

Abstract: This invention uses a novel biometrics, called resultant fingerprints and palm-prints, for authentication. The novel biometrics are consecutive traditional print images where the subject physically changes the appearance of the print images by rotating or rotating and translating, or rotating, translating, and shearing the finger or palm. That is, it is a sequence of finger or palm-print images over a short interval of time where the images are modified according to the rotation or a combination of rotation and translation or a combination of rotation, translation, and shear. The rotational and translational and shear components of the motion in the sequence of print images are determined from the image-to-image flow. This flow is either computed from motion-compensation vectors of the sequence compressed in MPEG formats or directly from the uncompressed images. The global image-to-image flow is expressed in terms of an affine transformation, computed from the local flow in blocks around a non-moving central region. The rotational and translational components of this affine transformation are smoothed over a temporal neighborhood resulting in a function of time. This function of time is a behavioral biometrics which can be changed by the user when compromised. Matching of this function for authentication purposes is achieved very much as is done in legacy signature matching authentication systems where two temporal signals are compared.

Quantum group symmetry in sine-Gordon and affine Toda field theories on the half-line

Abstract: We consider the sine-Gordon and affine Toda field theories on the half-line with classically integrable boundary conditions, and show that in the quantum theory a remnant survives of the bulk quantized affine algebra symmetry generated by non-local charges. The paper also develops a general framework for obtaining solutions of the reflection equation by solving an intertwining property for representations of certain coideal subalgebras of Uq(ĝ).

HPAT indexing for fast object/scene recognition based on local appearance

Abstract: The paper describes a fast system for appearance based image recognition. It uses local invariant descriptors and efficient nearest neighbor search. First, local affine invariant regions are found nested at multiscale intensity extremas. These regions are characterized by nine generalized color moment invariants. An efficient novel method called HPAT (hyper-polyhedron with adaptive threshold) is introduced for efficient localization of the nearest neighbor in feature space. The invariants make the method robust against changing illumination and viewpoint. The locality helps to resolve occlusions. The proposed indexing method overcomes the drawbacks of most binary tree-like indexing techniques, namely the high complexity in high dimensional data sets and the boundary problem. The database representation is very compact and the retrieval close to realtime on a standard PC. The performance of the proposed method is demonstrated on a public database containing 1005 images of urban scenes. Experiments with an image database containing objects are also presented.

Pricing Coupon-Bond Options and Swaptions in Affine Term Structure Models

Abstract: This paper provides a numerically accurate and computationally fast approximation to the prices of European options on coupon-bearing instruments that is applicable to the entire family of affine term structure models. Exploiting the typical shapes of the conditional distributions of the risk factors in affine diffusions, we show that one can reliably compute the relevant probabilities needed for pricing options on coupon-bearing instruments by the same Fourier inversion methods used in the pricing of options on zero-coupon bonds. We apply our theoretical results to the pricing of options on coupon bonds and swaptions, and the calculation of "expected exposures" on swap books. As an empirical illustration, we compute the expected exposures implied by several affine term structure models fit to historical swap yields.

Wishart Quadratic Term Structure Models

Abstract: This paper reveals that the class of affine term structure models introduced by Duffie and Kan (1996) is much larger than it has been usually considered in the literature. We study fundamental risk factors, which represent multivariate risk aversion of the consumer or the volatility matrix of the technological activity returns, and argue that they can be defined as symmetric positive matrices. For such matrices we introduce a dynamic affine process called the Wishart autoregressive (WAR) process; this process is used to reveal the associated term structure. In this framework: i) we derive very simple restrictions on the parameters to ensure positive yields at all maturities; ii) we observe that the usual constraint that the volatility matrix of an affine process be diagonal up to a path independent linear invertible transformation can be considerably relaxed. The Wishart Quadratic Term Structure Model is the natural extension of the one-dimensional Cox-Ingersoll-Ross model and of the quadratic models introduced in the literature.

Scale Saliency: a novel approach to salient feature and scale selection

Abstract: This paper presents an overview of the Scale Saliency algorithm introduced in (Kadir and Brady, 2001). Scale Saliency is a novel method for measuring the saliency of image regions and selecting optimal scales for their analysis. The model underlying the algorithm deems image regions salient if they are simultaneously unpredictable in some feature-space and over scale. The algorithm possesses a number of attractive properties: invariance to planar rotation, scaling, intensity shifts and translation; robustness to noise, changes in viewpoint, and intensity scalings. Moreover, the approach offers a more general model of feature saliency compared with conventional ones, such as those based on kernel convolution, for example wavelet analysis, since such techniques define saliency and scale only with respect to a particular set of basis morphologies. Finally, we present a generalised version of the original algorithm which is invariant to affine transformations.