Showing papers on "Affine transformation published in 2012"

LDAHash: Improved Matching with Smaller Descriptors

Abstract: SIFT-like local feature descriptors are ubiquitously employed in computer vision applications such as content-based retrieval, video analysis, copy detection, object recognition, photo tourism, and 3D reconstruction. Feature descriptors can be designed to be invariant to certain classes of photometric and geometric transformations, in particular, affine and intensity scale transformations. However, real transformations that an image can undergo can only be approximately modeled in this way, and thus most descriptors are only approximately invariant in practice. Second, descriptors are usually high dimensional (e.g., SIFT is represented as a 128-dimensional vector). In large-scale retrieval and matching problems, this can pose challenges in storing and retrieving descriptor data. We map the descriptor vectors into the Hamming space in which the Hamming metric is used to compare the resulting representations. This way, we reduce the size of the descriptors by representing them as short binary strings and learn descriptor invariance from examples. We show extensive experimental validation, demonstrating the advantage of the proposed approach.

An Evaluation of Popular Copy-Move Forgery Detection Approaches

Abstract: A copy-move forgery is created by copying and pasting content within the same image, and potentially postprocessing it. In recent years, the detection of copy-move forgeries has become one of the most actively researched topics in blind image forensics. A considerable number of different algorithms have been proposed focusing on different types of postprocessed copies. In this paper, we aim to answer which copy-move forgery detection algorithms and processing steps (e.g., matching, filtering, outlier detection, affine transformation estimation) perform best in various postprocessing scenarios. The focus of our analysis is to evaluate the performance of previously proposed feature sets. We achieve this by casting existing algorithms in a common pipeline. In this paper, we examined the 15 most prominent feature sets. We analyzed the detection performance on a per-image basis and on a per-pixel basis. We created a challenging real-world copy-move dataset, and a software framework for systematic image manipulation. Experiments show, that the keypoint-based features Sift and Surf, as well as the block-based DCT, DWT, KPCA, PCA, and Zernike features perform very well. These feature sets exhibit the best robustness against various noise sources and downsampling, while reliably identifying the copied regions.

An Evaluation of Popular Copy-Move Forgery Detection Approaches

Abstract: A copy-move forgery is created by copying and pasting content within the same image, and potentially post-processing it. In recent years, the detection of copy-move forgeries has become one of the most actively researched topics in blind image forensics. A considerable number of different algorithms have been proposed focusing on different types of postprocessed copies. In this paper, we aim to answer which copy-move forgery detection algorithms and processing steps (e.g., matching, filtering, outlier detection, affine transformation estimation) perform best in various postprocessing scenarios. The focus of our analysis is to evaluate the performance of previously proposed feature sets. We achieve this by casting existing algorithms in a common pipeline. In this paper, we examined the 15 most prominent feature sets. We analyzed the detection performance on a per-image basis and on a per-pixel basis. We created a challenging real-world copy-move dataset, and a software framework for systematic image manipulation. Experiments show, that the keypoint-based features SIFT and SURF, as well as the block-based DCT, DWT, KPCA, PCA and Zernike features perform very well. These feature sets exhibit the best robustness against various noise sources and downsampling, while reliably identifying the copied regions.

TILT: Transform Invariant Low-Rank Textures

Abstract: In this paper, we propose a new tool to efficiently extract a class of "low-rank textures" in a 3D scene from user-specified windows in 2D images despite significant corruptions and warping. The low-rank textures capture geometrically meaningful structures in an image, which encompass conventional local features such as edges and corners as well as many kinds of regular, symmetric patterns ubiquitous in urban environments and man-made objects. Our approach to finding these low-rank textures leverages the recent breakthroughs in convex optimization that enable robust recovery of a high-dimensional low-rank matrix despite gross sparse errors. In the case of planar regions with significant affine or projective deformation, our method can accurately recover both the intrinsic low-rank texture and the unknown transformation, and hence both the geometry and appearance of the associated planar region in 3D. Extensive experimental results demonstrate that this new technique works effectively for many regular and near-regular patterns or objects that are approximately low-rank, such as symmetrical patterns, building facades, printed text, and human faces.

Adaptation of context-dependent deep neural networks for automatic speech recognition

Abstract: In this paper, we evaluate the effectiveness of adaptation methods for context-dependent deep-neural-network hidden Markov models (CD-DNN-HMMs) for automatic speech recognition. We investigate the affine transformation and several of its variants for adapting the top hidden layer. We compare the affine transformations against direct adaptation of the softmax layer weights. The feature-space discriminative linear regression (fDLR) method with the affine transformations on the input layer is also evaluated. On a large vocabulary speech recognition task, a stochastic gradient ascent implementation of the fDLR and the top hidden layer adaptation is shown to reduce word error rates (WERs) by 17% and 14%, respectively, compared to the baseline DNN performances. With a batch update implementation, the softmax layer adaptation technique reduces WERs by 10%. We observe that using bias shift performs as well as doing scaling plus bias shift.

Observer-Based Piecewise Affine Output Feedback Controller Synthesis of Continuous-Time T–S Fuzzy Affine Dynamic Systems Using Quantized Measurements

Abstract: This paper is concerned with the problem of robust H∞ output feedback control for a class of continuous-time Takagi-Sugeno (T-S) fuzzy affine dynamic systems using quantized measurements. The objective is to design a suitable observer-based dynamic output feedback controller that guarantees the global stability of the resulting closed-loop fuzzy system with a prescribed H∞ disturbance attenuation level. Based on common/piecewise quadratic Lyapunov functions combined with S-procedure and some matrix inequality convexification techniques, some new results are developed to the controller synthesis for the underlying continuous-time T-S fuzzy affine systems with unmeasurable premise variables. All the solutions to the problem are formulated in the form of linear matrix inequalities (LMIs). Finally, two simulation examples are provided to illustrate the advantages of the proposed approaches.

Online Optimal Control of Affine Nonlinear Discrete-Time Systems With Unknown Internal Dynamics by Using Time-Based Policy Update

Abstract: In this paper, the Hamilton-Jacobi-Bellman equation is solved forward-in-time for the optimal control of a class of general affine nonlinear discrete-time systems without using value and policy iterations. The proposed approach, referred to as adaptive dynamic programming, uses two neural networks (NNs), to solve the infinite horizon optimal regulation control of affine nonlinear discrete-time systems in the presence of unknown internal dynamics and a known control coefficient matrix. One NN approximates the cost function and is referred to as the critic NN, while the second NN generates the control input and is referred to as the action NN. The cost function and policy are updated once at the sampling instant and thus the proposed approach can be referred to as time-based ADP. Novel update laws for tuning the unknown weights of the NNs online are derived. Lyapunov techniques are used to show that all signals are uniformly ultimately bounded and that the approximated control signal approaches the optimal control input with small bounded error over time. In the absence of disturbances, an optimal control is demonstrated. Simulation results are included to show the effectiveness of the approach. The end result is the systematic design of an optimal controller with guaranteed convergence that is suitable for hardware implementation.

Hybrid Linear Modeling via Local Best-Fit Flats

Abstract: We present a simple and fast geometric method for modeling data by a union of affine subspaces. The method begins by forming a collection of local best-fit affine subspaces, i.e., subspaces approximating the data in local neighborhoods. The correct sizes of the local neighborhoods are determined automatically by the Jones' β 2 numbers (we prove under certain geometric conditions that our method finds the optimal local neighborhoods). The collection of subspaces is further processed by a greedy selection procedure or a spectral method to generate the final model. We discuss applications to tracking-based motion segmentation and clustering of faces under different illuminating conditions. We give extensive experimental evidence demonstrating the state of the art accuracy and speed of the suggested algorithms on these problems and also on synthetic hybrid linear data as well as the MNIST handwritten digits data; and we demonstrate how to use our algorithms for fast determination of the number of affine subspaces.

Face Recognition Using Sparse Approximated Nearest Points between Image Sets

Abstract: We propose an efficient and robust solution for image set classification. A joint representation of an image set is proposed which includes the image samples of the set and their affine hull model. The model accounts for unseen appearances in the form of affine combinations of sample images. To calculate the between-set distance, we introduce the Sparse Approximated Nearest Point (SANP). SANPs are the nearest points of two image sets such that each point can be sparsely approximated by the image samples of its respective set. This novel sparse formulation enforces sparsity on the sample coefficients and jointly optimizes the nearest points as well as their sparse approximations. Unlike standard sparse coding, the data to be sparsely approximated are not fixed. A convex formulation is proposed to find the optimal SANPs between two sets and the accelerated proximal gradient method is adapted to efficiently solve this optimization. We also derive the kernel extension of the SANP and propose an algorithm for dynamically tuning the RBF kernel parameter while matching each pair of image sets. Comprehensive experiments on the UCSD/Honda, CMU MoBo, and YouTube Celebrities face datasets show that our method consistently outperforms the state of the art.

On the Power and Limitations of Affine Policies in Two-Stage Adaptive Optimization

Abstract: We consider a two-stage adaptive linear optimization problem under right hand side uncertainty with a min–max objective and give a sharp characterization of the power and limitations of affine policies (where the second stage solution is an affine function of the right hand side uncertainty). In particular, we show that the worst-case cost of an optimal affine policy can be $${\Omega(m^{1/2-\delta})}$$ times the worst-case cost of an optimal fully-adaptable solution for any δ > 0, where m is the number of linear constraints. We also show that the worst-case cost of the best affine policy is $${O(\sqrt m)}$$ times the optimal cost when the first-stage constraint matrix has non-negative coefficients. Moreover, if there are only k ≤ m uncertain parameters, we generalize the performance bound for affine policies to $${O(\sqrt k)}$$ , which is particularly useful if only a few parameters are uncertain. We also provide an $${O(\sqrt k)}$$ -approximation algorithm for the general case without any restriction on the constraint matrix but the solution is not an affine function of the uncertain parameters. We also give a tight characterization of the conditions under which an affine policy is optimal for the above model. In particular, we show that if the uncertainty set, $${{\mathcal U} \subseteq {\mathbb R}^m_+}$$ is a simplex, then an affine policy is optimal. However, an affine policy is suboptimal even if $${{\mathcal U}}$$ is a convex combination of only (m + 3) extreme points (only two more extreme points than a simplex) and the worst-case cost of an optimal affine policy can be a factor (2 − δ) worse than the worst-case cost of an optimal fully-adaptable solution for any δ > 0.

Relative entropy of cone measures and Lp centroid bodies

Abstract: Let K be a convex body in R n . We introduce a new affine invariant, which we call ΩK ,t hat can be found in three different ways: (a) as a limit of normalized Lp-affine surface areas; (b) as the relative entropy of the cone measure of K and the cone measure of K ◦ ; (c) as the limit of the volume difference of K and Lp-centroid bodies. We investigate properties of ΩK and of related new invariant quantities. In particular, we show new affine isoperimetric inequalities and we show an ‘information inequality’ for convex bodies.

Identification and Estimation of Gaussian Affine Term Structure Models

Abstract: This paper develops new results for identification and estimation of Gaussian affine term structure models. We establish that three popular canonical representations are unidentified, and demonstrate how unidentified regions can complicate numerical optimization. A separate contribution of the paper is the proposal of minimum-chi-square estimation as an alternative to MLE. We show that, although it is asymptotically equivalent to MLE, it can be much easier to compute. In some cases, MCSE allows researchers to recognize with certainty whether a given estimate represents a global maximum of the likelihood function and makes feasible the computation of small-sample standard errors.

An asymmetric affine Pólya–Szegö principle

Abstract: An affine rearrangement inequality is established which strengthens and implies the recently obtained affine Polya–Szego symmetrization principle for functions on \({\mathbb R^n}\) . Several applications of this new inequality are derived. In particular, a sharp affine logarithmic Sobolev inequality is established which is stronger than its classical Euclidean counterpart.

A road to classification in high dimensional space: the regularized optimal affine discriminant

Abstract: For high-dimensional classification, it is well known that naively performing the Fisher discriminant rule leads to poor results due to diverging spectra and noise accumulation. Therefore, researchers proposed independence rules to circumvent the diverging spectra, and sparse independence rules to mitigate the issue of noise accumulation. However, in biological applications, there are often a group of correlated genes responsible for clinical outcomes, and the use of the covariance information can significantly reduce misclassification rates. In theory the extent of such error rate reductions is unveiled by comparing the misclassification rates of the Fisher discriminant rule and the independence rule. To materialize the gain based on finite samples, a Regularized Optimal Affine Discriminant (ROAD) is proposed. ROAD selects an increasing number of features as the regularization relaxes. Further benefits can be achieved when a screening method is employed to narrow the feature pool before hitting the ROAD. An efficient Constrained Coordinate Descent algorithm (CCD) is also developed to solve the associated optimization problems. Sampling properties of oracle type are established. Simulation studies and real data analysis support our theoretical results and demonstrate the advantages of the new classification procedure under a variety of correlation structures. A delicate result on continuous piecewise linear solution path for the ROAD optimization problem at the population level justifies the linear interpolation of the CCD algorithm.

Non-affine deformations in polymer hydrogels

Abstract: Most theories of soft matter elasticity assume that the local strain in a sample after deformation is identical everywhere and equal to the macroscopic strain, or equivalently that the deformation is affine. We discuss the elasticity of hydrogels of crosslinked polymers with special attention to affine and non-affine theories of elasticity. Experimental procedures to measure non-affine deformations are also described. Entropic theories, which account for gel elasticity based on stretching out individual polymer chains, predict affine deformations. In contrast, simulations of network deformation that result in bending of the stiff constituent filaments generally predict non-affine behavior. Results from experiments show significant non-affine deformation in hydrogels even when they are formed by flexible polymers for which bending would appear to be negligible compared to stretching. However, this finding is not necessarily an experimental proof of the non-affine model for elasticity. We emphasize the insights gained from experiments using confocal rheoscope and show that, in addition to filament bending, sample micro-inhomogeneity can be a significant alternative source of non-affine deformation.

Dynamical systems : differential equations, maps, and chaotic behaviour

Abstract: Part 1 Introduction: preliminary ideas autonomous equations autonomous systems in the plane construction of phase portraits in the plane flows and evolution. Part 2 Linear systems: linear changes of variable similarity types for 2x2 real matrices phase portraits for canonical systems in the plane classification of simple linear phase portraits in the plane the evolution operator affine systems linear systems of dimension greater than two. Part 3 Non-linear systems in the plane: local and global behaviour linearization at a fixed point the linearization theorem non-simple fixed points stability of fixed points ordinary points and global behaviour first integrals limit points and limit cycles Poincare-Bendixson theory. Part 4 Flows on non-planar phase spaces: fixed points closed orbits attracting sets and attractors further integrals. Part 5 Applications I - planar phase spaces: linear models affine models non-linear models relaxation oscillations piecewise modelling. Part 6 Applications II - non-planar phase spaces, families of systems and bifurcations: the Zeeman models of heart beat and nerve impulse a model of animal conflict families of differential equations and bifurcations a mathematical model of tumor growth some bifurcations in families of one-dimensional maps some bifurcations in families of two-dimensional maps area-preserving maps, homoclinic tangles and strange attractors symbolic dynamics new directions.

A Simple and Robust Feature Point Matching Algorithm Based on Restricted Spatial Order Constraints for Aerial Image Registration

Abstract: Accurate point matching is a critical and challenging process in feature-based image registration. In this paper, a simple and robust feature point matching algorithm, called Restricted Spatial Order Constraints (RSOC), is proposed to remove outliers for registering aerial images with monotonous backgrounds, similar patterns, low overlapping areas, and large affine transformation. In RSOC, both local structure and global information are considered. Based on adjacent spatial order, an affine invariant descriptor is defined, and point matching is formulated as an optimization problem. A graph matching method is used to solve it and yields two matched graphs with a minimum global transformation error. In order to eliminate dubious matches, a filtering strategy is designed. The strategy integrates two-way spatial order constraints and two decision criteria restrictions, i.e., the stability and accuracy of transformation error. Twenty-nine pairs of optical and Synthetic Aperture Radar (SAR) aerial images are utilized to evaluate the performance. Compared with RANdom SAmple Consensus (RANSAC), Graph Transformation Matching (GTM), and Spatial Order Constraints (SOC), RSOC obtained the highest precision and stability.

A deterministic algorithm for robust location and scatter

Abstract: Most algorithms for highly robust estimators of multivariate location and scatter start by drawing a large number of random subsets. For instance, the FASTMCD algorithm of Rousseeuw and Van Driessen starts in this way, and then takes so-called concentration steps to obtain a more accurate approximation to the MCD. The FASTMCD algorithm is affine equivariant but not permutation invariant. In this article, we present a deterministic algorithm, denoted as DetMCD, which does not use random subsets and is even faster. It computes a small number of deterministic initial estimators, followed by concentration steps. DetMCD is permutation invariant and very close to affine equivariant. We compare it to FASTMCD and to the OGK estimator of Maronna and Zamar. We also illustrate it on real and simulated datasets, with applications involving principal component analysis, classification, and time series analysis. Supplemental material (Matlab code of the DetMCD algorithm and the datasets) is available online.

A Sparsification Approach to Set Membership Identification of Switched Affine Systems

Abstract: This paper addresses the problem of robust identification of a class of discrete-time affine hybrid systems, switched affine models, in a set membership framework. Given a finite collection of noisy input/output data and some minimal a priori information about the set of admissible plants, the objective is to identify a suitable set of affine models along with a switching sequence that can explain the available experimental information, while minimizing either the number of switches or subsystems. For the case where it is desired to minimize the number of switches, the key idea of the paper is to reduce this problem to a sparsification form, where the goal is to maximize sparsity of a suitably constructed vector sequence. Our main result shows that in the case of l∞ bounded noise, this sparsification problem can be exactly solved via convex optimization. In the general case where the noise is only known to belong to a convex set N, the problem is generically NP-hard. However, as we show in the paper, efficient convex relaxations can be obtained by exploiting recent results on sparse signal recovery. Similarly, we present both a sparsification formulation and a convex relaxation for the (known to be NP hard) case where it is desired to minimize the number of subsystems. These results are illustrated using two non-trivial problems arising in computer vision applications: video-shot and dynamic texture segmentation.

Optimal control for discrete-time affine non-linear systems using general value iteration

Abstract: In this study, the authors propose a novel adaptive dynamic programming scheme based on general value iteration (VI) to obtain near optimal control for discrete-time affine non-linear systems with continuous state and control spaces. First, the selection of initial value function is different from the traditional VI, and a new method is introduced to demonstrate the convergence property and convergence speed of value function. Then, the control law obtained at each iteration can stabilise the system under some conditions. At last, an error-bound-based condition is derived considering the approximation errors of neural networks, and then the error between the optimal and approximated value functions can also be estimated. To facilitate the implementation of the iterative scheme, three neural networks with Levenberg-Marquardt training algorithm are used to approximate the unknown system, the value function and the control law. Two simulation examples are presented to demonstrate the effectiveness of the proposed scheme.

Integral closure of ideals

Abstract: The Qth-power algorithm for computing structured global presentations of integral closures of affine domains over finite fields is modified to compute structured presentations of integral closures of ideals in affine domains over finite fields relative to a local monomial ordering. A non-homogeneous version of the standard (homogeneous) Rees algebra is introduced as well.

Polynomial processes and their applications to mathematical Finance

Abstract: We introduce a class of Markov processes, called m-polynomial, for which the calculation of (mixed) moments up to order m only requires the computation of matrix exponentials. This class contains affine processes, processes with quadratic diffusion coefficients, as well as Levy-driven SDEs with affine vector fields. Thus, many popular models such as exponential Levy models or affine models are covered by this setting. The applications range from statistical GMM estimation procedures to new techniques for option pricing and hedging. For instance, the efficient and easy computation of moments can be used for variance reduction techniques in Monte Carlo methods.

Nonparametric Inference on Manifolds: With Applications to Shape Spaces

Abstract: This book introduces in a systematic manner a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes. The theory has important and varied applications in medical diagnostics, image analysis, and machine vision. An early chapter of examples establishes the effectiveness of the new methods and demonstrates how they outperform their parametric counterparts. Inference is developed for both intrinsic and extrinsic Frchet means of probability distributions on manifolds, then applied to shape spaces defined as orbits of landmarks under a Lie group of transformations - in particular, similarity, reflection similarity, affine and projective transformations. In addition, nonparametric Bayesian theory is adapted and extended to manifolds for the purposes of density estimation, regression and classification. Ideal for statisticians who analyze manifold data and wish to develop their own methodology, this book is also of interest to probabilists, mathematicians, computer scientists and morphometricians with mathematical training.

Fuzzy approximation-based indirect adaptive controller for multi-input multi-output non-affine systems with unknown control direction

Abstract: A fuzzy approximation-based indirect adaptive control is investigated for a class of unknown non-affine non-linear systems with unknown control direction. An equivalent model in affine-like form is first derived for the original non-affine system by using a Taylor series expansion. Next, a fuzzy indirect adaptive control is designed based on this affine-like equivalent model. In this control scheme, the adaptive fuzzy systems are used to appropriately approximate the equivalent affine model’s unknown non-linearities, whereas the Nussbaum gain function is used to deal with the unknown control directions (being closely related to the sign of control gain matrix). A decomposition property of the control gain matrix is fully exploited in the controller design and the stability analysis. It is proven that, under some appropriate assumptions, the proposed control scheme can achieve that all the signals in the closed-loop control system are bounded and the tracking errors converge to a small neighbourhood around zero. Effectiveness of the developed scheme is illustrated by two simulation examples.

The classical origin of quantum affine algebra in squashed sigma models

Abstract: We consider a quantum affine algebra realized in two-dimensional non-linear sigma models with target space three-dimensional squashed sphere. Its affine generators are explicitly constructed and the Poisson brackets are computed. The defining relations of quantum affine algebra in the sense of the Drinfeld first realization are satisfied at classical level. The relation to the Drinfeld second realization is also discussed including higher conserved charges. Finally we comment on a semiclassical limit of quantum affine algebra at quantum level.