Showing papers on "Affine transformation published in 2002"

An Affine Invariant Interest Point Detector

Abstract: This paper presents a novel approach for detecting affine invariant interest points. Our method can deal with significant affine transformations including large scale changes. Such transformations introduce significant changes in the point location as well as in the scale and the shape of the neighbourhood of an interest point. Our approach allows to solve for these problems simultaneously. It is based on three key ideas : 1) The second moment matrix computed in a point can be used to normalize a region in an affine invariant way (skew and stretch). 2) The scale of the local structure is indicated by local extrema of normalized derivatives over scale. 3) An affine-adapted Harris detector determines the location of interest points. A multi-scale version of this detector is used for initialization. An iterative algorithm then modifies location, scale and neighbourhood of each point and converges to affine invariant points. For matching and recognition, the image is characterized by a set of affine invariant points; the affine transformation associated with each point allows the computation of an affine invariant descriptor which is also invariant to affine illumination changes. A quantitative comparison of our detector with existing ones shows a significant improvement in the presence of large affine deformations. Experimental results for wide baseline matching show an excellent performance in the presence of large perspective transformations including significant scale changes. Results for recognition are very good for a database with more than 5000 images.

Reliable Real-Time Solution of Parametrized Partial Differential Equations: Reduced-Basis Output Bound Methods

Abstract: We present a technique for the rapid and reliable prediction of linear-functional outputs of elliptic (and parabolic) partial differential equations with affine parameter dependence. The essential components are (i) (provably) rapidly convergent global reduced basis approximations, Galerkin projection onto a space W(sub N) spanned by solutions of the governing partial differential equation at N selected points in parameter space; (ii) a posteriori error estimation, relaxations of the error-residual equation that provide inexpensive yet sharp and rigorous bounds for the error in the outputs of interest; and (iii) off-line/on-line computational procedures, methods which decouple the generation and projection stages of the approximation process. The operation count for the on-line stage, in which, given a new parameter value, we calculate the output of interest and associated error bound, depends only on N (typically very small) and the parametric complexity of the problem; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control.

Direct adaptive NN control of a class of nonlinear systems

Abstract: In this paper, direct adaptive neural-network (NN) control is presented for a class of affine nonlinear systems in the strict-feedback form with unknown nonlinearities. By utilizing a special property of the affine term, the developed scheme,avoids the controller singularity problem completely. All the signals in the closed loop are guaranteed to be semiglobally uniformly ultimately bounded and the output of the system is proven to converge to a small neighborhood of the desired trajectory. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. Simulation results are presented to show the effectiveness of the approach.

Systematic errors in digital image correlation due to undermatched subset shape functions

Abstract: Digital image correlation techniques are commonly used to measure specimen displacements by finding correspondences between an image of the specimen in an undeformed or reference configuration and a second image under load. To establish correspondences between the two images, numerical techniques are used to locate an initially square image subset in a reference image within an image taken under load. During this process, shape functions of varying order can be applied to the initially square subset. Zero order shape functions permit the subset to translate rigidly, while first-order shape functions represent an affine transform of the subset that permits a combination of translation, rotation, shear and normal strains. In this article, the systematic errors that arise from the use of undermatched shape function, i.e., shape functions of lower order than the actual displacement field, are analyzed. It is shown that, under certain conditions, the shape functions used can be approximated by a Savitzky-Golay low-pass filter applied to the displacement functions, permitting a convenient error analysis. Furthermore, this analysis is not limited to the displacements, but naturally extends to the higher-order terms included in the shape functions. This permits a direct analysis of the systematic strain errors associated with an undermatched shape function. Detailed numerical studies are presented for the case of a second-order displacement field and first- and second-order shape functions. Finally, the relation of this work to previously published studies is discussed.

Extraction of 2D motion trajectories and its application to hand gesture recognition

Abstract: We present an algorithm for extracting and classifying two-dimensional motion in an image sequence based on motion trajectories. First, a multiscale segmentation is performed to generate homogeneous regions in each frame. Regions between consecutive frames are then matched to obtain two-view correspondences. Affine transformations are computed from each pair of corresponding regions to define pixel matches. Pixels matches over consecutive image pairs are concatenated to obtain pixel-level motion trajectories across the image sequence. Motion patterns are learned from the extracted trajectories using a time-delay neural network. We apply the proposed method to recognize 40 hand gestures of American Sign Language. Experimental results show that motion patterns of hand gestures can be extracted and recognized accurately using motion trajectories.

Sharp Affine LP Sobolev Inequalities

Abstract: A sharp affine Lp Sobolev inequality for functions on Euclidean n-space is established. This new inequality is significantly stronger than (and directly implies) the classical sharp Lp Sobolev inequality of Aubin and Talenti, even though it uses only the vector space structure and standard Lebesgue measure on ℝn. For the new inequality, no inner product, norm, or conformal structure is needed; the inequality is invariant under all affine transformations of ℝn.

On level-zero representation of quantized affine algebras

Abstract: We study the properties of level-zero modules over quantized affine algebras. The proof of the conjecture on the cyclicity of tensor products by T. Akasaka and the author is given. Several properties of modules generated by extremal vectors are proved. The weights of a module generated by an extremal vector are contained in the convex hull of the Weyl group orbit of the extremal weight. The universal extremal weight module with level-zero fundamental weight as an extremal weight is irreducible, and it is isomorphic to the affinization of an irreducible finite-dimensional module.

Observers for Takagi-Sugeno fuzzy systems

Abstract: We focus on the analysis and design of two different sliding mode observers for dynamic Takagi-Sugeno (TS) fuzzy systems. A nonlinear system of this class is composed of multiple affine local linear models that are smoothly interpolated by weighting functions resulting from a fuzzy partitioning of the state space of a given nonlinear system subject to observation. The Takagi-Sugeno fuzzy system is then an accurate approximation of the original nonlinear system. Our approach to the analysis and design of observers for Takagi-Sugeno fuzzy systems is based on extending sliding mode observer schemes to the case of interpolated multiple local affine linear models. Thus, our main contribution is nonlinear observer analysis and design methods that can effectively deal with model/plant mismatches. Furthermore, we consider the difficult case when the weighting functions in the Takagi-Sugeno fuzzy system depend on the estimated state.

Object Recognition using Local Affine Frames on Distinguished Regions

Abstract: A novel approach to appearance based object recognition is introduced. The proposed method, based on matching of local image features, reliably recognises objects under very different viewing conditions. First, distinguished regions of data-dependent shape are robustly detected. On these regions, local affine frames are established using several affine invariant constructions. Direct comparison of photometrically normalised colour intensities in local, geometrically aligned frames results in a matching scheme that is invariant to piecewise-affine image deformations, but still remains very discriminative. The potential of the approach is experimentally verified on COIL-100 and SOIL-47 ‐ publicly available image databases. On SOIL-47, 100% recognition rate is achieved for single training view per object. On COIL-100, 99.9% recognition rate is obtained for 18 training views per object. Robustness to severe occlusions is demonstrated by only a moderate decrease of recognition performance in an experiment where half of each test image is erased.

Mutual information-based rigid and nonrigid registration of ultrasound volumes

Abstract: We investigated the registration of ultrasound volumes based on the mutual information measure, a technique originally applied to multimodality registration of brain images. A prerequisite for successful registration is a smooth, quasi-convex mutual information surface with an unambiguous maximum. We discuss the necessary preprocessing to create such a surface for ultrasound volumes. Abdominal and thoracic organs imaged with ultrasound typically move relative to the exterior of the body and are deformable. Consequently, four specific instances of image registration involving progressively generalized transformations were studied: rigid-body, rigid-body + uniform scaling, rigid-body + nonuniform scaling, and affine. Registration was applied to clinically acquired volumetric images. The accuracy was comparable with the voxel dimension for all transformation modes, although it degraded as the transformation grew more complex. Likewise, the capture range became narrower with the complexity of transformation. As the use of real-time three-dimensional ultrasound becomes more prevalent, the method we present should work well for a variety of applications examining serial anatomic and physiologic changes. Developers of these clinical applications would match the deformation model of their problem to one of the four transformation models presented here.

Averaging and Vibrational Control of Mechanical Systems

Abstract: This paper investigates averaging theory and oscillatory control for a large class of mechanical systems. A link between averaging and controllability theory is presented by relating the key concepts of averaged potential and symmetric product. Both analysis and synthesis results are presented within a coordinate-free framework based on the theory of affine connections. The analysis focuses on characterizing the behavior of mechanical systems forced by high amplitude high frequency inputs. The averaged system is shown to be an affine connection system subject to an appropriate forcing term. If the input codistribution is integrable, the subclass of systems with Hamiltonian equal to "kinetic plus potential energy" is closed under the operation of averaging. This result precisely characterizes when the notion of averaged potential arises and how it is related to the symmetric product of control vector fields. Finally, a notion of vibrational stabilization for mechanical systems is introduced, and sufficient conditions are provided in the form of linear matrix equality and inequality tests.

On Affine Invariant Clustering and Automatic Cast Listing in Movies

Abstract: We develop a distance metric for clustering and classification algorithms which is invariant to affine transformations and includes priors on the transformation parameters. Such clustering requirements are generic to a number of problems in computer vision.We extend existing techniques for affine-invariant clustering, and show that the new distance metric outperforms existing approximations to affine invariant distance computation, particularly under large transformations. In addition, we incorporate prior probabilities on the transformation parameters. This further regularizes the solution, mitigating a rare but serious tendency of the existing solutions to diverge. For the particular special case of corresponding point sets we demonstrate that the affine invariant measure we introduced may be obtained in closed form.As an application of these ideas we demonstrate that the faces of the principal cast of a feature film can be generated automatically using clustering with appropriate invariance. This is a very demanding test as it involves detecting and clustering over tens of thousands of images with the variances including changes in viewpoint, lighting, scale and expression.

Affine Type A Crystal Structure on Tensor Products of Rectangles, Demazure Characters, and Nilpotent Varieties

Abstract: Answering a question of Kuniba, Misra, Okado, Takagi, and Uchiyama, it is shown that certain higher level Demazure characters of affine type A, coincide with the graded characters of coordinate rings of closures of conjugacy classes of nilpotent matrices.

A practical affine equivariant multivariate median

Abstract: SUMMARY A robust affine equivariant estimator of location for multivariate data is proposed which becomes the univariate median for data of dimension one. The estimator is robust in the sense that it has a bounded influence function, a positive breakdown value and has high efficiency compared to the sample mean for heavy-tailed distributions. Perhaps its greatest strength is that, unlike other affine equivariant multivariate medians, it is easily computed for data in any practical dimension.

Estimation of Continuous-Time Processes via the Empirical Characteristic Function

Abstract: This article examines the class of continuous-time stochastic processes commonly known as affine diffusions (AD's) and affine jump diffusions (AJD's). By deriving the joint characteristic function, we are able to examine the statistical properties as well as develop an efficient estimation technique based on empirical characteristic functions (ECF's) and a generalized method of moments (GMM) estimation procedure based on exact moment conditions. We demonstrate that our methods are particularly useful when the diffusions involve latent variables. Our approach is illustrated with a detailed examination of a continuous-time stochastic volatility (SV) model, along with an empirical application using S&P 500 index returns.

Stability analysis and synthesis for an affine fuzzy control system via LMI and ILMI: a continuous case

Abstract: A new stability analysis and controller synthesis methodology for a continuous affine fuzzy system is proposed in this paper. The method suggested is based on the numerical convex optimization techniques. In analysis, the stability condition under which the affine fuzzy system is quadratically stable is derived and is recast in the formulation of linear matrix inequalities (LMIs). The emphasis of this paper, however, is on the synthesis of fuzzy controller based on the derived stability condition. In the synthesis, the stabilizability condition turns out to be in the formulation of bilinear matrix inequalities and is solved numerically in an iterative manner. Fuzzy local controllers also assume the affine form and their bias terms are solved in a numerical manner simultaneously together with the gains. Continuous iterative LMI (ILMI) approach is presented to obtain a feasible solution for the synthesis of the affine fuzzy system.

Multi-Frame Correspondence Estimation Using Subspace Constraints

Abstract: When a rigid scene is imaged by a moving camera, the set of all displacements of all points across multiple frames often resides in a low-dimensional linear subspace. Linear subspace constraints have been used successfully in the past for recovering 3D structure and 3D motion information from multiple frames (e.g., by using the factorization method of Tomasi and Kanade (1992, International Journal of Computer Vision, 9:137–154)). These methods assume that the 2D correspondences have been precomputed. However, correspondence estimation is a fundamental problem in motion analysis. In this paper we show how the multi-frame subspace constraints can be used for constraining the 2D correspondence estimation process itself. We show that the multi-frame subspace constraints are valid not only for affine cameras, but also for a variety of imaging models, scene models, and motion models. The multi-frame subspace constraints are first translated from constraints on correspondences to constraints directly on image measurements (e.g., image brightness quantities). These brightness-based subspace constraints are then used for estimating the correspondences, by requiring that all corresponding points across all video frames reside in the appropriate low-dimensional linear subspace. The multi-frame subspace constraints are geometrically meaningful, and are {not} violated at depth discontinuities, nor when the camera-motion changes abruptly. These constraints can therefore replace {heuristic} constraints commonly used in optical-flow estimation, such as spatial or temporal smoothness.

An ellipsoidal calculus based on propagation and fusion

Abstract: Presents an ellipsoidal calculus based solely on two basic operations: propagation and fusion. Propagation refers to the problem of obtaining an ellipsoid that must satisfy an affine relation with another ellipsoid, and fusion to that of computing the ellipsoid that tightly bounds the intersection of two given ellipsoids. These two operations supersede the Minkowski sum and difference, affine transformation and intersection tight bounding of ellipsoids on which other ellipsoidal calculi are based. Actually, a Minkowski operation can be seen as a fusion followed by a propagation and an affine transformation as a particular case of propagation. Moreover, the presented formulation is numerically stable in the sense that it is immune to degeneracies of the involved ellipsoids and/or affine relations. Examples arising when manipulating uncertain geometric information in the context of the spatial interpretation of line drawings are extensively used as a testbed for the presented calculus.

Hierarchical wavelet networks for facial feature localization

Abstract: We present a technique for facial feature localization using a two-level hierarchical wavelet network. The first level wavelet network is used for face matching, and yields an affine transformation used for a rough approximation of feature locations. Second level wavelet networks for each feature are then used to fine-tune the feature locations. Construction of a training database containing hierarchical wavelet networks of many faces allows features to be detected in most faces. Experiments show that facial feature localization benefits significantly from the hierarchical approach. Results compare favorably with existing techniques for feature localization.

Estimating Affine Multifactor Term Structure Models Using Closed-Form Likelihood Expansions

Abstract: We develop and implement a technique for maximum likelihood estimation in closed-form of multivariate affine yield models of the term structure of interest rates. We derive closed-form approximations to the likelihood functions for all nine of the Dai and Singleton (2000) canonical affine models with one, two, or three underlying factors. Monte Carlo simulations reveal that this technique very accurately approximates true maximum likelihood, which is, in general, infeasible for affine models. We also apply the method to a dataset consisting of synthetic US Treasury strips, and find parameter estimates for nine different affine yield models, each using two different market price of risk specifications. One advantage of maximum likelihood estimation is the ability to compare non-nested models using likelihood ratio tests. We find, using these tests, that the choice of preferred canonical model can depend on the market price of riskspecification. Comparison to other approximation methods, Euler and QML, on both simulated and real data suggest that our approximation technique is much closer to true MLE than alternative methods.

Hybrid system stability and robustness verification using linear matrix inequalities

Abstract: This paper addresses issues concerning exponential stability and robustness of hybrid systems. Stability conditions using Lyapunov techniques are given. The search for the Lyapunov functions is formulated as a linear matrix inequality (LMI) problem for hybrid systems with affine as well as non-linear vector fields. It is shown how the Lyapunov approach most advantageously also can be used to guarantee stability despite the presence of model uncertainties. Several examples are given to illustrate the theory.

t-analogs of q-characters of Kirillov-Reshetikhin modules of quantm affine algebras

Abstract: We prove the Kirillov-Reshetikhin conjecture concerning certain finite dimensional representations of a quantum affine algebra $\Ua$ when $\hat\g$ is an untwisted affine Lie algebra of type $ADE$. We use $t$--analog of $q$--characters introduced by the author in an essential way.

Programmable data encryption engine for advanced encryption standard algorithm

Abstract: A programmable data encryption engine for performing the cipher function of an advanced encryption standard ( AES ) algorithm includes a parallel look-up table system responsive in a first mode to a first data block for implementing an AES selection function and executing the multiplicative inverse in GF -1 ( 2 8 ) and applying an affine over GF( 2 ) transformation to obtain a subbyte transformation and in a second mode to the subbyte transformation to transform the subbyte transformation to obtain a shift row transformation, and a Galois field multiplier for transforming the shift row transformation to obtain a mix column transformation and add a round key resulting in an advanced encryption standard cipher function of the first data block.

Affine transformation resistant watermarking based on image normalization

Abstract: Geometric attacks are among the most challenging problems in present day watermarking. Such attacks are very simple to implement yet they can defeat most of the existing watermarking algorithms without causing serious perceptual image distortion. In this paper we propose a new public watermarking algorithm, which is robust to such attacks. This algorithm uses a normalized with respect to affine transformation representation of the image based on the image moments. Then, a CDMA scheme is used to embed a multi-bit watermark in the discrete cosine transform domain of the normalized image. Numerical experiments are shown where the properties of the proposed algorithm are tested. These numerical experiments show that the proposed algorithm is very robust to wide range of geometric attacks.