Showing papers on "Affine transformation published in 2013"

Rotation, Scaling and Deformation Invariant Scattering for Texture Discrimination

Abstract: An affine invariant representation is constructed with a cascade of invariants, which preserves information for classification. A joint translation and rotation invariant representation of image patches is calculated with a scattering transform. It is implemented with a deep convolution network, which computes successive wavelet transforms and modulus non-linearities. Invariants to scaling, shearing and small deformations are calculated with linear operators in the scattering domain. State-of-the-art classification results are obtained over texture databases with uncontrolled viewing conditions.

Static-Output-Feedback ${\mathscr H}_{\bm \infty }$ Control of Continuous-Time T - S Fuzzy Affine Systems Via Piecewise Lyapunov Functions

Abstract: This paper investigates the problem of robust H∞ output feedback control for a class of continuous-time Takagi-Sugeno (T-S) fuzzy affine dynamic systems with parametric uncertainties and input constraints. The objective is to design a suitable constrained piecewise affine static output feedback controller, guaranteeing the asymptotic stability of the resulting closed-loop fuzzy control system with a prescribed H∞ disturbance attenuation level. Based on a smooth piecewise quadratic Lyapunov function combined with S-procedure and some matrix inequality convexification techniques, some new results are developed for static output feedback controller synthesis of the underlying continuous-time T-S fuzzy affine systems. It is shown that the controller gains can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, three examples are provided to illustrate the effectiveness of the proposed methods.

A Comparative Study of SIFT and its Variants

Abstract: SIFT is an image local feature description algorithm based on scale-space. Due to its strong matching ability, SIFT has many applications in different fields, such as image retrieval, image stitching, and machine vision. After SIFT was proposed, researchers have never stopped tuning it. The improved algorithms that have drawn a lot of attention are PCA-SIFT, GSIFT, CSIFT, SURF and ASIFT. In this paper, we first systematically analyze SIFT and its variants. Then, we evaluate their performance in different situations: scale change, rotation change, blur change, illumination change, and affine change. The experimental results show that each has its own advantages. SIFT and CSIFT perform the best under scale and rotation change. CSIFT improves SIFT under blur change and affine change, but not illumination change. GSIFT performs the best under blur change and illumination change. ASIFT performs the best under affine change. PCA-SIFT is always the second in different situations. SURF performs the worst in different situations, but runs the fastest.

FasT-Match: Fast Affine Template Matching

Abstract: Fast-Match is a fast algorithm for approximate template matching under 2D affine transformations that minimizes the Sum-of-Absolute-Differences (SAD) error measure. There is a huge number of transformations to consider but we prove that they can be sampled using a density that depends on the smoothness of the image. For each potential transformation, we approximate the SAD error using a sub linear algorithm that randomly examines only a small number of pixels. We further accelerate the algorithm using a branch-and-bound scheme. As images are known to be piecewise smooth, the result is a practical affine template matching algorithm with approximation guarantees, that takes a few seconds to run on a standard machine. We perform several experiments on three different datasets, and report very good results. To the best of our knowledge, this is the first template matching algorithm which is guaranteed to handle arbitrary 2D affine transformations.

Policy-Based Reserves for Power Systems

Abstract: This paper introduces the concept of affine reserve policies for accommodating large, fluctuating renewable in feeds in power systems. The approach uses robust optimization with recourse to determine operating rules for power system entities such as generators and storage units. These rules, or policies, establish several hours in advance how these entities are to respond to errors in the prediction of loads and renewable infeeds once their values are discovered. Affine policies consist of a nominal power schedule plus a series of planned linear modifications that depend on the prediction errors that will become known at future times. We describe how to choose optimal affine policies that respect the power network constraints, namely matching supply and demand, respecting transmission line ratings, and the local operating limits of power system entities, for all realizations of the prediction errors. Crucially, these policies are time-coupled, exploiting the spatial and temporal correlation of these prediction errors. Affine policies are compared with existing reserve operation under standard modeling assumptions, and operating cost reductions are reported for a multi-day benchmark study featuring a poorly-predicted wind infeed. Efficient prices for such “policy-based reserves” are derived, and we propose new reserve products that could be traded on electricity markets.

Nonsynchronized Robust Filtering Design for Continuous-Time T–S Fuzzy Affine Dynamic Systems Based on Piecewise Lyapunov Functions

Abstract: This paper investigates the problem of robust H∞ state estimation for a class of continuous-time nonlinear systems via Takagi-Sugeno (T-S) fuzzy affine dynamic models. Attention is focused on the analysis and design of an admissible full-order filter such that the resulting filtering error system is asymptotically stable with a guaranteed H∞ disturbance attenuation level. It is assumed that the plant premise variables, which are often the state variables or their functions, are not measurable so that the filter implementation with state-space partition may not be synchronous with the state trajectories of the plant. Based on piecewise quadratic Lyapunov functions combined with S-procedure and some matrix inequality linearization techniques, some new results are presented for the filtering design of the underlying continuous-time T-S fuzzy affine systems. Illustrative examples are given to validate the effectiveness and application of the proposed design approaches.

Transition between Phantom and Affine Network Model Observed in Polymer Gels with Controlled Network Structure

Abstract: The elastic moduli of elastomeric materials are predicted by the affine or phantom or junction affine network models. Although these models are often used, we do not know the requirement conditions for each model or even the validity of each model. The validation of these models is difficult because of the network heterogeneity. In this study, we tried to evaluate these models using Tetra-PEG gel, which has extremely homogeneous network structure. We performed the stretching and tearing tests, and for the first time, observed the transition between the phantom and affine network models around the overlapping concentration of prepolymers.

Robust Sampled – Data Control of Switched Affine Systems

Abstract: This technical note considers the stabilization problem for switched affine systems with a sampled-data switching law. The switching law is assumed to be a function of the system state at sampling instants and the sampling interval may be subject to variations or uncertainty. We provide a robust switching law design that takes into account the sampled-data implementation and uncertainties. The problem is addressed from the continuous-time point of view. The method is illustrated by numerical examples.

Complete characterization of the macroscopic deformations of periodic unimode metamaterials of rigid bars and pivots

Abstract: A complete characterization is given of the possible macroscopic deformations of periodic non-linear affine unimode metamaterials constructed from rigid bars and pivots. The materials are affine in the sense that their macroscopic deformations can only be affine deformations: on a local level the deformation may vary from cell to cell. Unimode means that macroscopically the material can only deform along a one dimensional trajectory in the six dimensional space of invariants describing the deformation (excluding translations and rotations). We show by explicit construction that any continuous trajectory is realizable to an arbitrarily high degree of approximation provided at all points along the trajectory the geometry does not collapse to a lower dimensional one. In particular, we present two and three dimensional dilational materials having an arbitrarily large flexibility window. These are perfect auxetic materials for which a dilation is the only easy mode of deformation. They are free to dilate to arbitrarily large strain with zero bulk modulus.

Fast polygon-based method for calculating computer-generated holograms in three-dimensional display

Abstract: In the holographic three-dimensional (3D) display, the numerical synthesis of the computer-generated holograms needs tremendous calculation. To solve the problem, a fast polygon-based method based on two-dimensional Fourier analysis of 3D affine transformation is proposed. From one primitive polygon, the proposed method calculates the diffracted optical field of each arbitrary polygon in the 3D model, where the pseudo-inverse matrix, the interpolation, and the compensation of the power spectral density are employed. The proposed method could save the computation time in the hologram synthesis since it does not need the fast Fourier transform for each polygonal surface and the additional diffusion computation. The numerical simulation and the optical experimental results are presented to demonstrate the effectiveness of the method. The results reveal the proposed method could reconstruct the 3D scene with the solid effect and without the depth limitation. The factors that influence the image quality are discussed, and the thresholds are proposed to ensure the reconstruction quality.

On Sound Compilation of Reals

Abstract: Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued implementation and specification language that explicitly includes different types of uncertainties. We then present a compilation algorithm that generates a conventional implementation that is guaranteed to meet the desired precision with respect to real numbers. Our verification step generates verification conditions that treat different uncertainties in a unified way and encode reasoning about floating-point roundoff errors into reasoning about real numbers. Such verification conditions can be used as a standardized format for verifying the precision and the correctness of numerical programs. Due to their often non-linear nature, precise reasoning about such verification conditions remains difficult. We show that current state-of-the art SMT solvers do not scale well to solving such verification conditions. We propose a new procedure that combines exact SMT solving over reals with approximate and sound affine and interval arithmetic. We show that this approach overcomes scalability limitations of SMT solvers while providing improved precision over affine and interval arithmetic. Using our initial implementation we show the usefullness and effectiveness of our approach on several examples, including those containing non-linear computation.

Myocardial Motion Estimation From Medical Images Using the Monogenic Signal

Abstract: We present a method for the analysis of heart motion from medical images. The algorithm exploits monogenic signal theory, recently introduced as an N-dimensional generalization of the analytic signal. The displacement is computed locally by assuming the conservation of the monogenic phase over time. A local affine displacement model is considered to account for typical heart motions as contraction/expansion and shear. A coarse-to-fine B-spline scheme allows a robust and effective computation of the model's parameters, and a pyramidal refinement scheme helps to handle large motions. Robustness against noise is increased by replacing the standard point-wise computation of the monogenic orientation with a robust least-squares orientation estimate. Given its general formulation, the algorithm is well suited for images from different modalities, in particular for those cases where time variant changes of local intensity invalidate the standard brightness constancy assumption. This paper evaluates the method's feasibility on two emblematic cases: cardiac tagged magnetic resonance and cardiac ultrasound. In order to quantify the performance of the proposed method, we made use of realistic synthetic sequences from both modalities for which the benchmark motion is known. A comparison is presented with state-of-the-art methods for cardiac motion analysis. On the data considered, these conventional approaches are outperformed by the proposed algorithm. A recent global optical-flow estimation algorithm based on the monogenic curvature tensor is also considered in the comparison. With respect to the latter, the proposed framework provides, along with higher accuracy, superior robustness to noise and a considerably shorter computation time.

Control-Point Representation and Differential Coding Affine-Motion Compensation

Abstract: The affine-motion model is able to capture rotation, zooming, and the deformation of moving objects, thereby providing a better motion-compensated prediction. However, it is not widely used due to difficulty in both estimation and efficient coding of its motion parameters. To alleviate this problem, a new control-point representation that favors differential coding is proposed for efficient compression of affine parameters. By exploiting the spatial correlation between adjacent coding blocks, motion vectors at control points can be predicted and thus efficiently coded, leading to overall improved performance. To evaluate the proposed method, four new affine prediction modes are designed and embedded into the high-efficiency video coding test model HM1.0. The encoder adaptively chooses whether to use the new affine mode in an operational rate-distortion optimization. Bitrate savings up to 33.82% in low-delay and 23.90% in random-access test conditions are obtained for low-complexity encoder settings. For high-efficiency settings, bitrate savings up to 14.26% and 4.89% for these two modes are observed.

Affine Characterizations of Minimal and Mode-Dependent Dwell-Times for Uncertain Linear Switched Systems

Abstract: An alternative approach for minimum and mode-dependent dwell-time characterization for switched systems is derived. While minimum-dwell time results require the subsystems to be asymptotically stable, mode-dependent dwell-time results can consider unstable subsystems and dwell-times within a, possibly unbounded, range of values. The proposed approach is related to Lyapunov looped-functionals, a new type of functionals leading to stability conditions affine in the system matrices, unlike standard results for minimum dwell-time. These conditions are expressed as infinite-dimensional LMIs which can be solved using recent polynomial optimization techniques such as sum-of-squares. The specific structure of the conditions is finally utilized in order to derive dwell-time stability results for uncertain switched systems. Several examples illustrate the efficiency of the approach.

Supermodularity and Affine Policies in Dynamic Robust Optimization

Abstract: This paper considers a particular class of dynamic robust optimization problems, where a large number of decisions must be made in the first stage, which consequently fix the constraints and cost structure underlying a one-dimensional, linear dynamical system. We seek to bridge two classical paradigms for solving such problems, namely, (1) dynamic programming (DP), and (2) policies parameterized in model uncertainties (also known as decision rules), obtained by solving tractable convex optimization problems. We show that if the uncertainty sets are integer sublattices of the unit hypercube, the DP value functions are convex and supermodular in the uncertain parameters, and a certain technical condition is satisfied, then decision rules that are affine in the uncertain parameters are optimal. We also derive conditions under which such rules can be obtained by optimizing simple (i.e., linear) objective functions over the uncertainty sets. Our results suggest new modeling paradigms for dynamic robust optimiz...

Locally Affine Sparse-to-Dense Matching for Motion and Occlusion Estimation

Abstract: Estimating a dense correspondence field between successive video frames, under large displacement, is important in many visual learning and recognition tasks. We propose a novel sparse-to-dense matching method for motion field estimation and occlusion detection. As an alternative to the current coarse-to-fine approaches from the optical flow literature, we start from the higher level of sparse matching with rich appearance and geometric constraints collected over extended neighborhoods, using an occlusion aware, locally affine model. Then, we move towards the simpler, but denser classic flow field model, with an interpolation procedure that offers a natural transition between the sparse and the dense correspondence fields. We experimentally demonstrate that our appearance features and our complex geometric constraints permit the correct motion estimation even in difficult cases of large displacements and significant appearance changes. We also propose a novel classification method for occlusion detection that works in conjunction with the sparse-to-dense matching model. We validate our approach on the newly released Sintel dataset and obtain state-of-the-art results.

Optimal sampling-based planning for linear-quadratic kinodynamic systems

Abstract: We propose a new method for applying RRT* to kinodynamic motion planning problems by using finite-horizon linear quadratic regulation (LQR) to measure cost and to extend the tree. First, we introduce the method in the context of arbitrary affine dynamical systems with quadratic costs. For these systems, the algorithm is shown to converge to optimal solutions almost surely. Second, we extend the algorithm to non-linear systems with non-quadratic costs, and demonstrate its performance experimentally.

Weighted averages on surfaces

Abstract: We consider the problem of generalizing affine combinations in Euclidean spaces to triangle meshes: computing weighted averages of points on surfaces. We address both the forward problem, namely computing an average of given anchor points on the mesh with given weights, and the inverse problem, which is computing the weights given anchor points and a target point. Solving the forward problem on a mesh enables applications such as splines on surfaces, Laplacian smoothing and remeshing. Combining the forward and inverse problems allows us to define a correspondence mapping between two different meshes based on provided corresponding point pairs, enabling texture transfer, compatible remeshing, morphing and more. Our algorithm solves a single instance of a forward or an inverse problem in a few microseconds. We demonstrate that anchor points in the above applications can be added/removed and moved around on the meshes at interactive framerates, giving the user an immediate result as feedback.

Stable and convergent iterative feedback tuning of fuzzy controllers for discrete-time SISO systems

Abstract: This paper proposes new stability analysis and convergence results applied to the Iterative Feedback Tuning (IFT) of a class of Takagi-Sugeno-Kang proportional-integral-fuzzy controllers (PI-FCs). The stability analysis is based on a convenient original formulation of Lyapunov's direct method for discrete-time systems dedicated to discrete-time input affine Single Input-Single Output (SISO) systems. An IFT algorithm which sets the step size to guarantee the convergence is suggested. An inequality-type convergence condition is derived from Popov's hyperstability theory considering the parameter update law as a nonlinear dynamical feedback system in the parameter space and iteration domain. The IFT-based design of a low-cost PI-FC is applied to a case study which deals with the angular position control of a direct current servo system laboratory equipment viewed as a particular case of input affine SISO system. A comparison of the performance of the IFT-based tuned PI-FC and the performance of the PI-FC tuned by an evolutionary-based optimization algorithm shows the performance improvement and advantages of our IFT approach to fuzzy control. Real-time experimental results are included.

An affine index polynomial invariant of virtual knots

Abstract: This paper describes a polynomial invariant of virtual knots that is defined in terms of an integer labeling of the virtual knot diagram. This labeling is seen to derive from an essentially unique structure of affine flat biquandle for flat virtual diagrams. The invariant is discussed in detail with many examples, including its relation to previous invariants of this type and we show how to construct Vassiliev invariants from the same data.

Continuous-Discrete Observer for State Affine Systems With Sampled and Delayed Measurements

Abstract: The observation of a class of multi-input multi-output (MIMO) state affine systems with both sampled and delayed output measurements is addressed. These two constraints disturb simultaneously the convergence of the observer. Assuming some persistent excitation conditions to hold, and by using Lyapunov tools adapted to impulsive systems, two classes of global exponential observers are proposed. Some explicit relations between maximum allowable delay and maximum allowable sampling period are given. An extension to some classes of nonlinear systems is also given.

Affine recourse for the robust network design problem: Between static and dynamic routing

Abstract: Affinely Adjustable Robust Counterparts provide tractable alternatives to (two-stage) robust programs with arbitrary recourse. Following Ouorou and Vial, we apply them to robust network design with polyhedral demand uncertainty, introducing the notion of affine routing. We compare the new affine routing scheme to the well-studied static and dynamic routing schemes for robust network design. It is shown that affine routing can be seen as a generalization of the widely used static routing while still being tractable and providing cheaper solutions. We investigate properties of the demand polytope under which affine routings reduce to static routings and also develop conditions on the uncertainty set leading to dynamic routings being affine. We show however that affine routings suffer from the drawback that (even totally) dominated demand vectors are not necessarily supported by affine solutions. Uncertainty sets have to be designed accordingly. Finally, we present computational results on networks from SNDlib. We conclude that for these instances the optimal solutions based on affine routings tend to be as cheap as optimal network designs for dynamic routings. In this respect the affine routing principle can be used to approximate the cost for two-stage solutions with free recourse which are hard to compute

The maximum likelihood degree of a very affine variety

Abstract: We show that the maximum likelihood degree of a smooth very affine variety is equal to the signed topological Euler characteristic. This generalizes Orlik and Terao’s solution to Varchenko’s conjecture on complements of hyperplane arrangements to smooth very affine varieties. For very affine varieties satisfying a genericity condition at infinity, the result is further strengthened to relate the variety of critical points to the Chern–Schwartz–MacPherson class. The strengthened version recovers the geometric deletion–restriction formula of Denham et al. for arrangement complements, and generalizes Kouchnirenko’s theorem on the Newton polytope for nondegenerate hypersurfaces.

Asymmetric Correlation: A Noise Robust Similarity Measure for Template Matching

Abstract: We present an efficient and noise robust template matching method based on asymmetric correlation (ASC). The ASC similarity function is invariant to affine illumination changes and robust to extreme noise. It correlates the given non-normalized template with a normalized version of each image window in the frequency domain. We show that this asymmetric normalization is more robust to noise than other cross correlation variants, such as the correlation coefficient. Direct computation of ASC is very slow, as a DFT needs to be calculated for each image window independently. To make the template matching efficient, we develop a much faster algorithm, which carries out a prediction step in linear time and then computes DFTs for only a few promising candidate windows. We extend the proposed template matching scheme to deal with partial occlusion and spatially varying light change. Experimental results demonstrate the robustness of the proposed ASC similarity measure compared to state-of-the-art template matching methods.