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This paper attempts to differentiate between two models of visual space. One model suggests that visual space is a simple affine transformation of physical space. The other proposes that it is a transformation of physical space via the laws of perspective. The present paper reports two experiments in which participants are asked to judge the size of the interior angles of squares at five different distances from the participant. The perspective-based model predicts that the angles within each square on the side nearest to the participant should seem smaller than those on the far side. The simple affine model under our conditions predicts that the perceived size of the angles of each square should remain 90°. Results of both experiments were most consistent with the perspective-based model. The angles of each square on the near side were estimated to be significantly smaller than the angles on the far side for all five squares in both experiments. In addition, the sum of the estimated size of the four angles of each square declined with increasing distance from the participant to the square and was less than 360° for all but the nearest square.

Interest points (corners and blobs) play an important role in computer vision tasks such as image matching, image retrieval, and 3D reconstruction. Existing deep learning based interest point detection methods mainly focus on the interest point detection with high repeatability under image affine transformations while neglecting the importance of the characteristics of interest points. This will affect the detection and localization accuracy of interest points. In this paper, we design an effective corner feature representations network based on the characteristics of corners. The designed network has the ability to effectively learn corner feature information from images. A novel loss function is proposed to minimize the localization error between the corner positions of the original image block and the transformed image blocks. Furthermore, a novel corner detection architecture is proposed. The criteria on detection accuracy, localization accuracy, average repeatability, region repeatability, and image matching score are used to evaluate the proposed method against fourteen state-of-the-art methods. The experimental results show that the proposed performs significantly better than the state-of-the-arts. • The existing machine learning-based interest point detection methods are reviewed. • A novel network is designed to extract multi-scale corner feature. • A new multi-scale corner detection mechanism with a novel loss function is proposed. • The designed architecture has considered how to detect corners more accurately. [ABSTRACT FROM AUTHOR]

• DSS uses a temporal displacement rate, D, to scale time-dependent bubble dynamics. • D consists of the sum of dimensionless groups that govern the bubble dynamics. • Inertial controlled bubble growth occurs when D = 0. • Thermally controlled bubble growth occurs when D = 1. • Distortion analyses shows that modified Mikic model and Hooper data compare well. Dynamical System Scaling (DSS) provides a useful method for analyzing, categorizing and scaling time-dependent processes. A key feature of DSS is the temporal displacement rate, D , which relates the natural process time to the reference clock time. Because of its property of being invariant under a two-parameter affine transformation, it provides an underlying basis for process scaling. Application of DSS to bubble dynamics serves to elucidate the physical significance of the temporal displacement rate and its role in scaling a variety of bubble dynamics processes. In particular, prior studies in bubble dynamics did not recognize the role that bubble interfacial acceleration has on scaling. It is a central feature in the definition of the temporal displacement rate. This paper shows that the temporal displacement rate consists of the sum of the internal dimensionless groups that govern the bubble dynamics. Preserving the temporal displacement rate and boundary conditions for a prototype and a scaled model results in similitude of the time-dependent normalized bubble size, growth rates and interfacial accelerations for different fluid conditions. For vapor bubble growth in a superheated liquid, it is shown that inertial controlled bubble growth occurs when D = 0 and thermally controlled bubble growth occurs when D = 1. [ABSTRACT FROM AUTHOR]

This article focuses on the distributed event-triggered affine formation control problem for multiple underactuated marine surface vehicles (UMSVs) considering affine transformation and communication energy consumption under a directed interaction topology. Firstly, the affine transformation mechanism is adopted to improve the flexibility and maneuverability of the formation. The proposed technique allows a rich collection of collective motions such as translation, rotation, scaling, and the combination of these transformations. Then, unlike the event-triggered control of a single marine vehicle, this paper considers reducing communication frequency between vehicles. Thus, an event-triggered mechanism is proposed, which can save computation resources compared with traditional ones while excluding the Zeno behavior. Subsequently, it is proved that all signals in the closed-loop system are ultimately uniformly bounded (UUB), meanwhile, all tracking errors converge to a small compact set under the proposed control strategy. Finally, numerical simulations illustrate the effectiveness of the proposed formation controller. • A distributed event-triggered affine formation control algorithm is developed to solve the trajectory tracking problem for UMSVs formation. • A novel affine transformation mechanism is devised to enables UMSVs to move as a group in formation translation, shearing, rotation and scaling maneuvers. • An event-triggered scheme is designed to update the measurement signal so as to save the communication resource. [ABSTRACT FROM AUTHOR]

The paper is devoted to searching algorithms which will allow to generate images of attractors of generalized iterated function systems (GIFS in short), which are certain generalization of classical iterated function systems, defined by Mihail and Miculescu in 2008, and then intensively investigated in the last years (the idea is that instead of selfmaps of a metric space X, we consider mappings form the Cartesian product X×...× X to X). Two presented algorithms are counterparts of classical deterministic algorithm and so-called chaos game. The third and fourth one is fitted to special kind of GIFSs - to affine GIFS, which are, in turn, also investigated. [ABSTRACT FROM AUTHOR]

A generalized polygon is an ordered set of vertices. This notion generalizes the concept of the boundary of a polygonal shape because self-intersections are allowed. In this paper we study the problem of matching generalized polygons under affine transformations. Our approach is based on invariants. Firstly we associate an ordered set of complex numbers with each polygon and construct a collection of complex scalar functions on the space of plane polygons. These invariant functions are defined as quotients of the so-called Fourier descriptors, also known as discrete Fourier transforms. Each one of these functions is invariant under similarity transformations; that is, the function associates the same complex number to similar polygons. Moreover, if two polygons are affine related (one of them is the image of the other under an affine transformation), the pseudo-hyperbolic distance between their associated values is a constant that depends only on the affine transformation involved, but independent of the polygons. More formally, given a collection { Z 1 , Z 2 , … , Z m } of n -sided polygons in the plane and a query polygon W , we give algorithms to find all Z ℓ such that f ( Z ℓ ) = W + Δ W , where f is an unknown affine transformation and Δ W = ( Δ w 1 , … , Δ w n ) with | Δ w k | ≤ ρ , where ρ is certain tolerance. [ABSTRACT FROM AUTHOR]

In this paper, we solve the rigidity problem on geodesic maps in the hyperbolic space. The main result is that a geodesic-to-geodesic injection in hyperbolic space Dn is an isometry or a composition of an isometry and an affine transformation under the Klein model if and only if it is non-degenerate. We first solve the rigidity problems on Euclidean space and the n-sphere and show that a line-to-line injection in Euclidean space ℝn is an affine transformation if and only if it is non-degenerate and that a circle-to-circle injection on the n-sphere ℝn is a Möbius transformation if and only if it is non-degenerate. More general results for hyperplane-to-hyperplane maps are obtained. The key method is to establish a new version of the celebrated Pappas' Theorem. [ABSTRACT FROM AUTHOR]

A local rigidity theorem was proved by Selberg and Weil for Riemannian symmetric spaces and generalized by Kobayashi for a non-Riemannian homogeneous space , determining explicitly which homogeneous spaces allow nontrivial continuous deformations of co-compact discontinuous groups. When is assumed to be exponential solvable and is a maximal subgroup, an analog of such a theorem states that the local rigidity holds if and only if is isomorphic to the group Aff() of affine transformations of the real line (cf. [L. Abdelmoula, A. Baklouti and I. Kédim, The Selberg-Weil-Kobayashi rigidity theorem for exponential Lie groups, Int. Math. Res. Not. 17 (2012) 4062-4084.]). The present paper deals with the more general context, when is a connected solvable Lie group and a maximal nonnormal subgroup of . We prove that any discontinuous group for a homogeneous space is abelian and at most of rank 2. Then we discuss an analog of the Selberg-Weil-Kobayashi local rigidity theorem in this solvable setting. In contrast to the semi-simple setting, the -action on is not always effective, and thus the space of group theoretic deformations (formal deformations) could be larger than geometric deformation spaces. We determine and also its quotient modulo uneffective parts when the rank . Unlike the context of exponential solvable case, we prove the existence of formal colored discontinuous groups. That is, the parameter space admits a mixture of locally rigid and formally nonrigid deformations. [ABSTRACT FROM AUTHOR]

Multi-atlas segmentation has become a frequently used tool for medical image segmentation due to its outstanding performance. A computational bottleneck is that all atlas images need to be registered to a new target image. In this paper, we propose an intermediate representation of the whole atlas set – an überatlas – that can be used to speed up the registration process. The representation consists of feature points that are similar and detected consistently throughout the atlas set. A novel feature-based registration method is presented which uses the überatlas to simultaneously and robustly find correspondences and affine transformations to all atlas images. The method is evaluated on 20 CT images of the heart and 30 MR images of the brain with corresponding ground truth. Our approach succeeds in producing better and more robust segmentation results compared to three baseline methods, two intensity-based and one feature-based, and significantly reduces the running times. [ABSTRACT FROM AUTHOR]

The error-in-variable (EIV) model takes the error of all variables into account and has been widely applied to many practical problems arising in environmental study, geology, geographic information science (GIS), and geodesy. Coordinate transformations are among the most frequently encountered problems in spatial data processing, and the EIV model can be built based on two sets of coordinates. In some applications, physical parameters-such as the shift, rotation angle, and scale factor-have constraints. Current implementations of the constrained EIV (CEIV) model do not consider physical constraints explicitly. The purpose of this paper is to convert physical constraints into mathematical forms and to use constrained total least squares (CTLS) to solve the CEIV problem of two-dimensional (2D) affine transformation. The effectiveness of this method is illustrated through a numerical example. [ABSTRACT FROM AUTHOR]

The study of stability problems of functional equations was motivated by a question of S. M. Ulam asked in 1940. The first result giving answer to this question is due to D.H. Hyers. Subsequently, his result was extended and generalized in several ways. In this paper we prove some hyperstability results for the equation g(ax + by) + g(cx + dy) = Ag(x) + Bg(y) on restricted domain. Namely, we show, under some weak natural assumptions, functions satisfying the above equation approximately (in some sense) must be actually solutions to it. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the Orlicz geominimal surface area and give an integral representation by the Orlicz- Petty body. The notion of Orlicz mixed geominimal surface area will be introduced as an extension of the Orlicz geominimal surface area. Furthermore, some related inequalities are established, including Alexandrov-Fenchel type inequality, analogous cyclic inequality, Blaschke-Santaló type inequality, and affine isoperimetric inequality. [ABSTRACT FROM AUTHOR]

The goal of this paper is to clarify when a stochastic partial differential equation with an affine realization admits affine state processes. This includes a characterization of the set of initial points of the realization. Several examples, as the HJMM equation from mathematical finance, illustrate our results. [ABSTRACT FROM AUTHOR]

This paper deals essentially with affine or projective transformations of Lie groups endowed with a flat left invariant affine or projective structure. These groups are called flat affine or flat projective Lie groups. We give necessary and sufficient conditions for the existence of flat left invariant projective structures on Lie groups. We also determine Lie groups admitting flat bi-invariant affine or projective structures. These groups could play an essential role in the study of homogeneous spaces M = G / H having a flat affine or flat projective structures invariant under the natural action of G on M . A. Medina asked several years ago if the group of affine transformations of a flat affine Lie group is a flat projective Lie group. In this work we provide a partial positive answer to this question. [ABSTRACT FROM AUTHOR]

In this paper, we obtain upper bounds of the class dimension of flat association schemes in affine and affine-symplectic spaces and construct resolving sets for these schemes. [ABSTRACT FROM AUTHOR]

This paper presents an alternative form of the Heston model that preserves an essential advantage of the Heston model, its analytic tractability, by imposing the necessary and sufficient conditions for the existence of a solution in affine form, while it is in a different form so that it offers certain advantages in parameter determination. To demonstrate this, we conducted some empirical studies, exploring if this new form does have certain advantages over the original version under certain market conditions. [ABSTRACT FROM AUTHOR]

In this paper, an improved sparse-aware affine projection (AP) algorithm for sparse system identification is proposed and investigated. The proposed sparse AP algorithm is realized by integrating a non-uniform norm constraint into the cost function of the conventional AP algorithm, which can provide a zero attracting on the filter coefficients according to the value of each filter coefficient. Low complexity is obtained by using a linear function instead of the reweighting term in the modified AP algorithm to further improve the performance of the proposed sparse AP algorithm. The simulation results demonstrate that the proposed sparse AP algorithm outperforms the conventional AP and previously reported sparse-aware AP algorithms in terms of both convergence speed and steady-state error when the system is sparse. [ABSTRACT FROM AUTHOR]

For piecewise-smooth maps, new dynamics can be created by varying parameters such that a fixed point collides with a surface on which the map is nonsmooth. If the map is continuous and has bounded derivatives near but not on the surface, this is referred to as a border-collision bifurcation. Dynamics near border-collision bifurcations are well approximated by piecewise-linear continuous maps. A lack of differentiability allows for substantial complexity and a wide variety of invariant sets can be created in border-collision bifurcations, such as invariant circles and chaotic sets, and several attractors may be created simultaneously. Yet many calculations that would be intractable for smooth nonlinear maps can be performed exactly for piecewise-linear maps and in recent years several new results have been obtained for border-collision bifurcations. This article reviews bordercollision bifurcations with a general emphasis on results that apply to maps of any number of dimensions. The paper covers applications, the border-collision normal form, basic properties and dynamics such as fixed points, periodic solutions and mode-locking regions, and more complex phenomena such as multistability, multidimensional attractors, attractors at infinity, homoclinic bifurcations, and unfoldings of codimension-two scenarios. [ABSTRACT FROM AUTHOR]

For piecewise-smooth maps, new dynamics can be created by varying parameters such that a fixed point collides with a surface on which the map is nonsmooth. If the map is continuous and has bounded derivatives near but not on the surface, this is referred to as a border-collision bifurcation. Dynamics near border-collision bifurcations are well approximated by piecewise-linear continuous maps. A lack of differentiability allows for substantial complexity and a wide variety of invariant sets can be created in border-collision bifurcations, such as invariant circles and chaotic sets, and several attractors may be created simultaneously. Yet many calculations that would be intractable for smooth nonlinear maps can be performed exactly for piecewise-linear maps and in recent years several new results have been obtained for border-collision bifurcations. This article reviews bordercollision bifurcations with a general emphasis on results that apply to maps of any number of dimensions. The paper covers applications, the border-collision normal form, basic properties and dynamics such as fixed points, periodic solutions and mode-locking regions, and more complex phenomena such as multistability, multidimensional attractors, attractors at infinity, homoclinic bifurcations, and unfoldings of codimension-two scenarios. [ABSTRACT FROM AUTHOR]

The mosaicking of Unmanned Aerial Vehicle (UAV) imagery usually requires information from additional sensors, such as Global Position System (GPS) and Inertial Measurement Unit (IMU), to facilitate direct orientation, or 3D reconstruction approaches (e.g., structure-from-motion) to recover the camera poses. In this paper, we propose a novel mosaicking method for UAV imagery in which neither direct nor indirect orientation procedures are required. Inspired by the embedded deformation model, a widely used non-rigid mesh deformation model, we present a novel objective function for image mosaicking. Firstly, we construct a feature correspondence energy term that minimizes the sum of the squared distances between matched feature pairs to align the images geometrically. Secondly, we model a regularization term that constrains the image transformation parameters directly by keeping all transformations as rigid as possible to avoid global distortion in the final mosaic. Experimental results presented herein demonstrate that the accuracy of our method is twice as high as an existing (purely image-based) approach, with the associated benefits of significantly faster processing times and improved robustness with respect to reference image selection. [ABSTRACT FROM AUTHOR]

In order to reduce the steady-state misalignment of real-coefficient proportionate affine projection sign algorithm (RP-APSA) for sparse impulse responses, a memory RP-APSA is proposed in this paper by exploiting the historical values of proportionate factors, called MP-APSA. Further, to improve the robustness of MP-APSA and the recently proposed memory-improved RP-APSA (MIP-APSA) for impulse responses with mutative sparseness, two sparseness-controlled algorithms (SC-MP-APSA and SC-MIP-APSA) are developed by estimating the sparseness of the impulse response at each iteration. Simulation results in the context of acoustic echo cancellation show that the proposed algorithms retain good robustness against impulsive interferences. More importantly, the proposed sparseness-controlled algorithms can not only obtain low steady-state misalignment in both the sparse and dispersive situations, but also adapt to the variations in the sparseness of the impulse response. [ABSTRACT FROM AUTHOR]

When X = Xn is a blowup of P2 at n points x1, . . . , xn with n≤ 9, there is a canonical (affine) Lie algebra bundle ε0En over it, where E9 is the affine E8. In this paper, we will give a detail study of the relationship between the geometry of Xn and the deformability of ε0En. [ABSTRACT FROM AUTHOR]

Research in skeleton-based human action recognition has generated great interest from the computer vision community, owing to the feasibility and popularity of skeleton data. Some broadly used 2D pose estimation methods, which can be used to generate high-quality skeletons in real time using only low-power equipment, improve 2D skeleton-based action recognition. However, view variations in action representations influence their performance. In this paper, a view agnostic network for 2D skeleton-based action recognition, which narrows the representation differences in view variations by applying an adaptive frame-level skeleton deformation before feature extraction, is proposed. Specifically, the deformation is realized by a body-level affine transformation and a joint-level offset compensation, which aims to approximatively determine a new observation viewpoint for better intragroup consistency in a learning-based data-driven manner. Meanwhile, an adaptive spatial–temporal graph convolutional LSTM (ASTGCN-LSTM), which can model the co-occurrence relationship in the spatial–temporal domain for skeleton sequences more effectively, is introduced. Experiments are conducted on Kinetics-Skeleton and NTU120 RGB+D action recognition datasets, which are used to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Bone age is an important index in the measurement of the biological maturity in children. Although many machine learning methods have been developed to classify bone radiographs, a number of limitations like the need for large datasets still exists. In this paper, we propose an efficient method based on convolutional neural networks to automatically predict bone age given radiographs. The proposed approach considers the differences between male and female skeletal development in order to classify the sex from radiographs, in conjunction with the use of a bone age assessment (BAA) network to significantly improve the prediction performance of bone age. The dataset used is from the 2017 Pediatric Bone Age Challenge, which contains 12,611 left-hand radiographs. Pre-processing of the radiographs is first performed, followed by detection of key-points of the hand for the application of affine transformation to register the hand pose. Transfer learning is then applied to the sex determination and BAA models with the pre-trained weights on ImageNet, to leverage on the generic features from millions of real-world images. Three BAA models were trained on three separated portions of the dataset, and utilized with the sex information to obtain the bone age. Results indicate that the method outperforms existing BAA methods as the mean absolute error (MAE) obtained was 5.31 months (0.44 years) while an accuracy of 94.7% was achieved for the sex determination. When sex labels were provided for the testing radiographs, the MAE of our method was further reduced to 4.68 months (0.39 years). The advantage of our method is that it eliminates the need for hand crafting features and utilizes sex as an important information in the prediction of bone age. • An efficient method for prediction of bone age and sex from left-hand radiographs. • Pre-processing can significantly improve the performance of bone age assessment. • Very good performance in sex determination from left-hand radiographs. • Sex information and sex-based models should be incorporated in bone age assessment. [ABSTRACT FROM AUTHOR]

The use of geographic data from early maps is a common approach to understanding urban geography as well as to study the evolution of cities over time. The specific goal of this paper is to provide a means for the integration of the first 1:500 urban map of the city of València (Spain) on a tile-based geospatial system. We developed a workflow consisting of three stages: the digitization of the original 421 map sheets, the transformation to the European Terrestrial Reference System of 1989 (ETRS89), and the conversion to a tile-based file format, where the second stage is clearly the most mathematically involved. The second stage actually consists of two steps, one transformation from the pixel reference system to the 1929 local reference system followed by a second transformation from the 1929 local to the ETRS89 system. The last stage comprises a map reprojection to adapt to tile-based geospatial standards. The paper describes a pilot study of one map sheet and results showed that the affine and bilinear transformations performed well in both transformations with average residuals under 6 and 3 cm respectively. The online viewer developed in this study shows that the derived tile-based map conforms to common standards and lines up well with other raster and vector datasets. [ABSTRACT FROM AUTHOR]

Let E be a two-dimensional real normed space. In this paper we show that if the unit circle of E does not contain any line segment such that the distance between its endpoints is greater than 1, then every transformation ϕ : E → E which preserves the unit distance is automatically an affine isometry. In particular, this condition is satisfied when the norm is strictly convex. [ABSTRACT FROM AUTHOR]

In the paper we consider the problem of computation of characters of relatively integrable irreducible highest weight modules L over finite-dimensional basic Lie superalgebras and over affine Lie superalgebras $${\mathfrak{g}}$$ . The problem consists of two parts. First, it is the reduction of the problem to the $${\overline{\mathfrak{g}}}$$ -module F( L), where $${\overline{\mathfrak{g}}}$$ is the associated to L integral Lie superalgebra and F( L) is an integrable irreducible highest weight $${\overline{\mathfrak{g}}}$$ -module. Second, it is the computation of characters of integrable highest weight modules. There is a general conjecture concerning the first part, which we check in many cases. As for the second part, we prove in many cases the KW-character formula, provided that the KW-condition holds, including almost all finite-dimensional $${\mathfrak{g}}$$ -modules when $${\mathfrak{g}}$$ is basic, and all maximally atypical non-critical integrable $${\mathfrak{g}}$$ -modules when $${\mathfrak{g}}$$ is affine with non-zero dual Coxeter number. [ABSTRACT FROM AUTHOR]

Aerial surveillance system provides a large amount of data compared with traditional surveillance system. But, it usually suffers from undesired motion of cameras, which presents new challenges. These challenges must be overcome before such video can be widely used. In this paper, we present a novel video stabilization and moving object detection system based on camera motion estimation. We use local feature extraction and matching to estimate global motion and we demonstrate that Scale Invariant Feature Transform (SIFT) keypoints are suitable for the stabilization task. After estimating the global camera motion parameters using affine transformation, we detect moving object by Kalman filtering. For motion smoothing, we use a median filter to retain the desired motion. Finally, motion compensation is carried out to obtain a stabilized video sequence. A number of aerial video examples demonstrate the effectiveness of our proposed system. We use the software Virtual Dub with the Deshaker-Plugin for test purposes. For objective evaluation, we use Interframe Transformation Fidelity for video stabilization tasks and Detection Ratio for moving object detection task. [ABSTRACT FROM AUTHOR]

This paper proposes a Kalman filter formulation for parameter estimation of doubly stochastic Poisson processes (DSPP) with stochastic affine intensities. To achieve this aim, an analytical expression for the probability distribution functions of the corresponding DSPP for any intensity from the class of affine diffusions is obtained. More detailed results are provided for one- and two-factor Feller and Ornstein-Uhlenbeck diffusions. A Monte Carlo study indicates that the proposed method is a reliable procedure for moderate sample sizes. An empirical analysis of one- and two-factor Feller and Ornstein-Uhlenbeck models is carried out using high frequency transaction data. [ABSTRACT FROM AUTHOR]

The main contribution of this paper is to propose a convex formulation of sufficient conditions for both stability analysis and synthesis of stabilizing controllers for stochastic piecewise affine (PWA) systems with multiplicative noise. One of the main difficulties in PWA systems is the fact that the affine terms in the dynamics make it extremely difficult to formulate the synthesis problem as a convex optimization or even convex feasibility program. The presence of multiplicative noise modeled as a Wiener process adds an additional level of difficulty to the analysis and synthesis procedures. Sufficient conditions for stability of stochastic PWA slab systems in the mean square sense are developed first using a stochastic globally quadratic Lyapunov function. Second, PWA state feedback controllers are designed such that the closed-loop system is stochastically exponentially mean square stable. The conditions for both stability and stabilization are formulated as LMIs, which can then be solved efficiently using currently available software packages. A numerical example shows the effectiveness of the approach. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

For contactless palm vein images, particularly substantial changes in hand positioning between one image and the next, it is difficult to achieve a satisfactory recognition performance with geometry- or statistics-based methods due to issues such as non-uniform illumination and affine transformation. Therefore, with a multi-sampling and feature-level fusion strategy, a novel palm vein recognition method based on local invariant features is presented for addressing the aforementioned issues. As most of the contactless palm vein images are unclear and have low contrast, if a SIFT algorithm is directly adopted for feature extraction on the center region of a palm vein image, it will be difficult to obtain sufficient features for effective recognition. Therefore, in this paper, we first propose to take the entire palm as a Region of Interest (ROI) and perform new hierarchical enhancement on the ROI to ensure that additional features will be obtained from the subsequent feature extraction. Then, we take full advantage of the multiple samples collected in the registration stage to generate the registered template using feature-level fusion. Finally, bidirectional matching is proposed for mismatch removal. The experiments on the CASIA Palm vein Image Database and our palm vein database collected under the posture changes show that the proposed method was superior in terms of recognition performance, especially for palm vein image recognition under remarkable posture changes. In particular, the values of Equal Error Rate (EER) on the aforementioned two databases were 0.16% and 0.73%, respectively. [ABSTRACT FROM AUTHOR]

This paper presents a new algorithm for image co-registration using dominant corners located on the image's edges under the assumption that the deformation between the successive images is modeled by an affine transformation. This assumption is guaranteed when the time interval between acquired images is small like in a video sequence. Therefore, it is mainly dedicated for motion analysis. The method detects first straight edges of an object contour then classifies their intersection points as contour's corners characterized by their angles and adjacent segments lengths. The suppressor starts then to eliminate iteratively the weak corners until reaching a set of dominant ones called "Dominant Corners". These dominant corners are shown to be very repeatable under affinity transformation. A Primitive is constructed by four consecutive dominant corners located on the same contour. The invariant measure that characterizes each primitive is the ratio of areas of two triangles constructed by two triplets selected from these four corners and the corners directions difference. The primitives are formed in the two studied images from an image sequence. All primitives are used to vote for the best affine model that relates the two images. The method used in primitive construction will lead to an important enhancement over existing methods in the voting process in time and accuracy. This method is tested on real images and good results are reported. [ABSTRACT FROM AUTHOR]

A generalized model of the dynamics (GMD) of DC-DC power electronic converters (PECs) is discussed in this paper. It is a geometrical piecewise-affine continuous-time model. The general idea of the GMD is to determine the local dynamic behavior of trajectories on the faces of the PEC commutation structure, which is a geometrical model of its commutation. This allows us to establish the direction of PEC dynamics on these faces. It can be either 'entering' into specific regions in state space or 'exiting' from them. Therefore, the local PEC dynamics can be treated as logical (two-state). In practice, the GMD can be used for the analysis of PEC practical stability, which is a completely different concept from the concept of PEC stability in the classical Lyapunov sense. An outline of the design-oriented approach to PEC practical stability analysis, which is based on the GMD, has also been presented. As illustrative examples, the GMD of a boost converter under peak current-mode control and its application are presented. These examples show that the Lyapunov stability of a given PEC does not imply its practical stability, and that the results of PEC Lyapunov stability analysis and practical stability analysis are complementary to each other. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

As a novel type of light-weight and reticulated structures, tensegrities have found many technologically important applications. In this paper, a facile method is developed to construct a class of large-scale tensegrities consisting of bar-bar connection using prismatic elementary cells. We tune the orientation of the structural axis of each cell by the affine transformation technique. Then, the cells can be assembled easily in any directions required by the structural design. The method proposed here allows us to construct various types of large-scale tensegrity structures satisfying the demands of sizes and topology. A number of representative examples are provided, including straight and curved beams, plates, shells, and three-dimensional large-scale tensegrities. [ABSTRACT FROM AUTHOR]

The covariance descriptor has received an increasing amount of interest in visual tracking. However, the conventional covariance tracking algorithms fail to estimate both the scale and orientation of an object. In this paper, we present a kernel-based region covariance descriptor to address this issue. An affine kernel function is incorporated to the covariance matrix to effectively control the correlations among extracted features inside the object region. Under the Log-Euclidean Riemannian metric, we construct a region similarity measure function that describes the relationship between the candidate and a given appearance template. The tracking task is then implemented by minimizing the similarity measure, in which the gradient descent method is utilized to iteratively optimize affine transformation parameters. In addition, the template is dynamically updated by computing the geometric mean of covariance matrices in Riemannian manifold for adapting to the appearance changes of the object over time. Experimental results compared with several relevant tracking methods demonstrate the good performance of the proposed algorithm under challenging conditions. [ABSTRACT FROM AUTHOR]

The image registration problem involves determining a geometric transformation to properly align images of interest. This paper proposes a transformation approach called Continuous Piecewise Affine Transformation (CPAT) to model the geometric distortion in images. The associated design methodology for the 2D registration problem is also discussed. Registration on CPAT has two advantages: (1) The optimal transformation has a closed form analytical solution; and (2) the transformation is invertible and transitive. Because of these advantages, CPAT could be used for real-time registration and progressive registration, where the registration speed and transitivity property are important for the successful completion of the tasks. The results of experiments demonstrate the efficacy of CPAT in resolving the image registration problem. [ABSTRACT FROM AUTHOR]

Feature matching is an important problem and has extensive uses in computer vision. However, existing feature matching methods support either a specific or a small set of transformation models. In this paper, we propose a unified feature matchingframework which supports a large family of transformation models. We call the family of transformation models the affine-functionfamily, in which all transformations can be expressed by affine functions with convex constraints. In this framework, the goal is to recover transformation parameters for every feature point in a template point set to calculate their optimal matching positions in an input image. Given pairwise feature dissimilarity values between all points in the template set and the input image, we create a convexdissimilarity function for each template point. Composition of such convex functions with any transformation model in the affine-function family is shown to have an equivalent convex optimization form that can be optimized efficiently. Four example transformation models in the affine-function family are introduced to show the flexibility of our proposed framework. Our framework achieves 0.0 percent matching errors for both CMU House and Hotel sequences following the experimental setup in [6]. [ABSTRACT FROM AUTHOR]

SUMMARY An encryption scheme is a tuple of algorithms used to ensure secrecy while exchanging messages over a public channel. Spatial encryption is a generalized extension of id-based encryption with the ability of partial order role delegation. In this paper, we propose an efficient spatial encryption with vector privacy preservation, which is derived from the technique of static assumption from dual system encryption in composite order groups. The proposed scheme achieves the cryptosystem properties of message confidentiality, recipient anonymity, adaptively full security, and short constant ciphertext. Provable security in our setting consists of three steps: the first one is giving a rigorous definition of security, the second one is giving the construction of a scheme, and the last one is giving a rigorous mathematical proof showing that the scheme satisfies the security definition given in the first stage. Compared with related schemes, our proposed scheme has a comparable advantage in security while it holds an approximate computing efficiency and communicating payload such as public parameters, private keys, and ciphertexts. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Let K denote a field and let V denote a vector space over K with finite positive dimension. By a tridiagonal pair , we mean an ordered pair A , A ⁎ of K -linear transformations from V to V that satisfy the following conditions: (i) each of A , A ⁎ is diagonalizable; (ii) there exists an ordering { V i } i = 0 d of the eigenspaces of A such that A ⁎ V i ⊆ V i − 1 + V i + V i + 1 ( 0 ≤ i ≤ d ), where V − 1 = 0 , V d + 1 = 0 ; (iii) there exists an ordering { V i ⁎ } i = 0 δ of the eigenspaces of A ⁎ such that A V i ⁎ ⊆ V i − 1 ⁎ + V i ⁎ + V i + 1 ⁎ ( 0 ≤ i ≤ δ ), where V − 1 ⁎ = 0 , V δ + 1 ⁎ = 0 ; (iv) there is no subspace W of V such that A W ⊆ W , A ⁎ W ⊆ W , W ≠ 0 , W ≠ V . It is known that η A + μ I , η ⁎ A ⁎ + μ ⁎ I is also a tridiagonal pair on V , where η , μ , η ⁎ , μ ⁎ are scalars in K with η , η ⁎ nonzero. In this paper we give the necessary and sufficient conditions for these tridiagonal pairs to be isomorphic to A , A ⁎ or A ⁎ , A . We do this under a mild assumption, called the sharp condition. [ABSTRACT FROM AUTHOR]

An affine arithmetic (AA) method is proposed in this paper to solve the optimal power flow (OPF) problem with uncertain generation sources. In the AA-based OPF problem, all the state and control variables are treated in affine form, comprising a center value and the corresponding noise magnitudes, to represent forecast, model error, and other sources of uncertainty without the need to assume a probability density function (pdf). The proposed AA-based OPF problem is used to determine the operating margins of the thermal generators in systems with uncertain wind and solar generation dispatch. The AA-based approach is benchmarked against Monte Carlo simulation (MCS) intervals in order to determine its effectiveness. The proposed technique is tested and demonstrated on the IEEE 30-bus system and also a real 1211-bus European system. [ABSTRACT FROM AUTHOR]

Most of the existing handcrafted and learning-based local descriptors are still at best approximately invariant to affine image transformations, often disregarding deformable surfaces. In this paper, we take one step further by proposing a new approach to compute descriptors from RGB-D images (where RGB refers to the pixel color brightness and D stands for depth information) that are invariant to isometric non-rigid deformations, as well as to scale changes and rotation. Our proposed description strategies are grounded on the key idea of learning feature representations on undistorted local image patches using surface geodesics. We design two complementary local descriptors strategies to compute geodesic-aware features efficiently: one efficient binary descriptor based on handcrafted binary tests (named GeoBit), and one learning-based descriptor (GeoPatch) with convolutional neural networks (CNNs) to compute features. In different experiments using real and publicly available RGB-D data benchmarks, they consistently outperforms state-of-the-art handcrafted and learning-based image and RGB-D descriptors in matching scores, as well as in object retrieval and non-rigid surface tracking experiments, with comparable processing times. We also provide to the community a new dataset with accurate matching annotations of RGB-D images of different objects (shirts, cloths, paintings, bags), subjected to strong non-rigid deformations, for evaluation benchmark of deformable surface correspondence algorithms. • An efficient geodesic patch sampling scheme is proposed. • Development of a learned descriptor that is invariant to non-rigid deformations. • We provide to the community a new RGB-D benchmark with ground-truth correspondences. • An in-depth analysis that shows the benefit of using our local descriptors. [ABSTRACT FROM AUTHOR]

This paper presents a generalization of chaotic systems using two-dimensional affine transformations with six introduced parameters to achieve scaling, reflection, rotation, translation and/or shearing. Hence, the location of the strange attractor in space can be controlled without changing its chaotic dynamics. In addition, the embedded parameters enhance the randomness and sensitivity of the system and control its response. This approach overpasses performing the transformations as post-processing stages by applying them on the resulting time series. Trajectory control through dynamic parameters is demonstrated. Simulation results validate the proposed analysis for both the simplest and Lorenz chaotic systems. An image encryption scheme is implemented using transformed Lorenz system resulting in a more secure encryption scheme in comparison to Lorenz and other recent related works. The scheme exhibits good performance when assessed using the PRNG properties, encrypted image histogram and its uniformity through chi square test, pixel correlation, Mean Squared Error (MSE), entropy, Peak Signal-to-Noise Ratio (PSNR), the National Institute of Standards & Technology (NIST) test, key space, key sensitivity, resistance to differential, ciphertext-only, known plaintext, and chosen plaintext attacks, robustness against noise and computation time.

Fast and accurate motion estimation takes an important place in many fields of computer vision and image processing. Using Radon transform to compute projections of the images along specified directions is an effective way to show the relationship between the 2D image object and its projections and estimate motions between the images. All existing projection-based motion estimation methods without the use of iteration have a severe defect that only five of the six affine parameters can be estimated. There are some other methods that can estimate the six parameters, but most of them are usually based on a certain iterative framework, which is computationally intensive and sensitively dependent on the initial values. In this paper, a novel method based on Radon transform is proposed to estimate all the six affine parameters directly. The relationship in the projection domain between a pair of images connected by an affine motion is studied and a linear model is established, by which all the six affine parameters can be directively found. The employment of a hierarchical framework can produce more accurate results. The experimental results reveal that the proposed method has a much better performance than the state-of-the-art methods in this field. [ABSTRACT FROM AUTHOR]

The objective of the present paper is the study of affine transformations of the plane, which provide self-affine curves as attractors. The properties of these curves depend decisively of the coefficients of the system of affnities involved. The corresponding functions are continuous on a compact interval. If the scale factors are properly chosen one can define Schauder bases ofC[a,b] composed by affine fractal functions close to polygonals. They can be chosen bounded. The basis constants and the biorthogonal sequence of coefficient functionals are studied. [ABSTRACT FROM AUTHOR]

The study of denominator identities for Lie superalgebras was recently developed by M. Gorelik, V. G. Kac, P. Moseneder Frajria, I. Musson, P. Papi, M. Wakimoto, D. Zagier, and the author. In this paper, we generalize these identities to the twisted affine case, completing the result for all affine Lie superalgebras. [ABSTRACT FROM AUTHOR]

In copy-move forgery, the copied region may be rotated and/or scaled to fit the scene better. Most of the existing methods fail when the region is subject to affine transforms. This paper presents a method for detecting this kind of image tampering based on circular pattern matching. The image is first filtered and divided into circular blocks. A rotation and scaling invariant feature is then extracted from each block using Polar Harmonic Transform (PHT). The feature vectors are then lexicographically sorted, and the forged regions are detected by finding the similar block pairs after proper post-processing. Experimental results demonstrate the efficiency of the method. [ABSTRACT FROM AUTHOR]