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In this study, we have managed to model the energy surface of the aminophenol derivative azomethine molecule mathematically depending on two torsion angles SC1(C9C10C12N14) and SC2(C2C1C6C11). For this purpose, firstly, discrete data obtained from Density Functional Theory calculations have been converted into continuous data with the help of the Fuzzy Inference System. Thus, it is possible to calculate energy values for untested data, which are very costly in terms of time to obtain with other methods/experiments. Then, the continuous and non-smooth surface obtained from the fuzzy inference system and representing the energy values of the molecule has been transformed into a differentiable surface with the help of Bezier surfaces. Thus, an objective function has been obtained in which global optimization methods based on the derivative (or gradient) operator could be used. [ABSTRACT FROM AUTHOR]

Standard interpolatory subdivision schemes and their underlying interpolating refinable functions are of interest in CAGD, numerical PDEs, and approximation theory. Generalizing these notions, we introduce and study n s -step interpolatory M -subdivision schemes and their interpolating M -refinable functions with n s ∈ N ∪ { ∞ } and a dilation factor M ∈ N \ { 1 } . We completely characterize C m -convergence and smoothness of n s -step interpolatory subdivision schemes and their interpolating M -refinable functions in terms of their masks. Inspired by n s -step interpolatory stationary subdivision schemes, we further introduce the notion of r-mask quasi-stationary subdivision schemes, and then we characterize their C m -convergence and smoothness properties using only their masks. Moreover, combining n s -step interpolatory subdivision schemes with r-mask quasi-stationary subdivision schemes, we can obtain r n s -step interpolatory subdivision schemes. Examples and construction procedures of convergent n s -step interpolatory M -subdivision schemes are provided to illustrate our results with dilation factors M = 2 , 3 , 4 . In addition, for the dyadic dilation M = 2 and r = 2 , 3 , using r masks with only two-ring stencils, we provide examples of C r -convergent r-step interpolatory r-mask quasi-stationary dyadic subdivision schemes. [ABSTRACT FROM AUTHOR]

Composition detection and semantic line detection are important research topics in computer vision and play an important auxiliary role in the analysis of image esthetics. However, at present, few researchers have considered the internal relationship between these two related tasks for comprehensive research. In order to solve this problem, we propose a synchronous detection network of composition class and semantic lines based on cross-attention, which can realize the mutual supervision and guidance between composition class detection and semantic line detection, to improve the accuracy of each other’s detection. First, the pre-trained composition detection model and the pre-trained semantic line detection model as two teacher models to provide data labels of composition and semantic line information for the student model. Then, we train a student model with the help of the teacher model. The student model adopts the multi-task learning architecture by combining soft and hard parameter sharing, as we propose. At the same time, we develop a cross-attention module to ensure that both tasks get the help and supervision they need from each other. Experimental results show that our method can draw semantic lines while detecting composition classes, which increases the interpretability of composition class detection. Our composition detection accuracy reaches 92.57%, and for benchmark semantic lines, the accuracy of our AUC_A metric can reach 92.00%. [ABSTRACT FROM AUTHOR]

This article is devoted to introducing new spline quasi-interpolants for the sharp approximation of data in one and several dimensions. The new construction aims to obtain accurate approximations close to singularities of the function from which the data are obtained. The technique relies in an accurate knowledge of the position of the singularity, which can be known or approximated, and that allows for the obtention of accurate approximations of the jumps of the function and its derivatives at this point. With this information, it is possible to compute correction terms for the B-spline bases of the spline that are affected by the presence of singularities. The result is a piecewise smooth reconstruction with full accuracy (meaning by full accuracy, the accuracy of the spline at smooth zones). The numerical experiments presented support the theoretical results obtained. [ABSTRACT FROM AUTHOR]

Linear approximation methods suffer from Gibbs oscillations when approximating functions with jumps. Essentially non oscillatory subcell-resolution (ENO-SR) is a local technique avoiding oscillations and with a full order of accuracy, but a loss of regularity of the approximant appears. The goal of this paper is to introduce a new approach having both properties of full accuracy and regularity. In order to obtain it, we propose a three-stage algorithm: first, the data is smoothed by subtracting an appropriate non-smooth data sequence; then a chosen high order linear approximation operator is applied to the smoothed data and finally, an approximation with the proper jump or corner (jump in the first order derivative) discontinuity structure is reinstated by correcting the smooth approximation with the non-smooth element used in the first stage. This new procedure can be applied as subdivision scheme to design curves and surfaces both in point-value and in cell-average contexts. Using the proposed algorithm, we are able to construct approximations with high precision, with high piecewise regularity, and without smearing nor oscillations in the presence of discontinuities. These are desired properties in real applications as computer aided design or car design, among others. [ABSTRACT FROM AUTHOR]

Hermite interpolation is classically used to reconstruct smooth data when the function and its first order derivatives are available at certain nodes. If first order derivatives are not available, it is easy to set a system of equations imposing some regularity conditions at the data nodes in order to obtain them. This process leads to the construction of a Hermite spline. The problem of the described Hermite splines is that the accuracy is lost if the data contains singularities. The consequence is the appearance of oscillations, if there is a jump discontinuity in the function, that globally affects the accuracy of the spline, or the smearing of singularities, if the discontinuities are in the derivatives of the function. This paper is devoted to the construction and analysis of a new technique that allows for the computation of accurate first order derivatives of a function close to singularities using a Hermite spline. The idea is to correct the system of equations of the spline in order to attain the desired accuracy even close to the singularities. Once we have computed the first order derivatives with enough accuracy, a correction term is added to the Hermite spline in the intervals that contain a singularity. The aim is to reconstruct piecewise smooth functions with O (h 4) accuracy even close to the singularities. The process of adaption will require some knowledge about the position of the singularity and the jumps of the function and some of its derivatives at the singularity. The whole process can be used as a post-processing, where a correction term is added to the classical cubic Hermite spline. Proofs for the accuracy and regularity of the corrected spline and its derivatives are given. We also analyse the mechanism that eliminates the Gibbs phenomenon close to jump discontinuities in the function. The numerical experiments presented confirm the theoretical results obtained. [ABSTRACT FROM AUTHOR]

In this paper, a new Hermite interpolatory subdivision scheme for curve interpolation is introduced. The scheme is constructed from the Rational [3/2] Bernstein Bezier polynomial. We call it the [3/2]-scheme. The limit function of the [3/2]-scheme interpolates both the function values and their derivatives. The proposed scheme has three shape parameters w 0 , w 1 and w 2 . It is shown that if w 1 = w 0 + w 2 2 , then the [3/2]-scheme reproduces linear polynomial and is C 1 provided w 0 and w 2 lie in a region of convergence. The scheme also satisfies the shape preserving properties, i.e., monotonicity and convexity. We also compare the [3/2]-scheme with other existing schemes like the [2/2]-scheme and the Merrien scheme introduced recently. An error analysis shows that the [3/2]-scheme is better than the [2/2]-scheme and the Merrien scheme. Further, it is observed that in case w 0 = w 1 = w 2 , the [3/2]-scheme reduces to the Merrien scheme. [ABSTRACT FROM AUTHOR]

Digitized handwritten documents have been used for various purposes, including age detection, a crucial area of research in fields like forensic investigation and medical diagnosis. Automated age recognition is deemed to be a difficult task, due to the great degree of similarity and overlap across people's handwriting. Consequently, the efficiency of the classification system is determined by extracting pertinent features from handwritten documents. This research proposes a set of age-related features suggested by a graphologist to classify handwritten documents into two age groups: youth adult and mature adult. The extracted features are: slant irregularity (SI), pen pressure irregularity (PPI), text lines irregularity (TLI) and the percentage of black and white pixels (PWB). Support Vector Machines (SVM) and Neural Network (NN) classifiers have been used to train, validate and test the proposed approach using two different datasets: the FSHS and the Khatt datasets. When applied to the FSHS dtaset using SVM and NN approaches, the proposed method resulted in a classification accuracy of 71% and 63.5%, respectively. Meanwhile, when applied to the Khatt dataset, our method outperformed state-of-the-art methods with a classification accuracy of 65.2% and 67% utilising SVM and NN classifiers, respectively. These are the best rates available right now in this field. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of constructing C 2 cubic spline functions on a given arbitrary triangulation T . To this end, we endow every triangle of T with a Wang–Shi macro-structure. The C 2 cubic space on such a refined triangulation has a stable dimension and optimal approximation power. Moreover, any spline function in this space can be locally built on each of the macro-triangles independently via Hermite interpolation. We provide a simplex spline basis for the space of C 2 cubics defined on a single macro-triangle which behaves like a Bernstein/B-spline basis over the triangle. The basis functions inherit recurrence relations and differentiation formulas from the simplex spline construction, they form a nonnegative partition of unity, they admit simple conditions for C 2 joins across the edges of neighboring triangles, and they enjoy a Marsden-like identity. Also, there is a single control net to facilitate control and early visualization of a spline function over the macro-triangle. Thanks to these properties, the complex geometry of the Wang–Shi macro-structure is transparent to the user. Stable global bases for the full space of C 2 cubics on the Wang–Shi refined triangulation T are deduced from the local simplex spline basis by extending the concept of minimal determining sets. [ABSTRACT FROM AUTHOR]

This paper deals with the construction of the Algebraic Trigonometric Pythagorean Hodograph (ATPH) cubic-like Hermite interpolant. A characterization of solutions according to the tangents at both ends and a global free shape parameter α is performed. Since this degree of freedom can be used for adjustments, we study how the curve evolves with respect to α. Several examples illustrating the construction process and a simple fitting method to determine the unique ATPH curve passing through a given point are proposed. [ABSTRACT FROM AUTHOR]

The intersection of surfaces is a fundamental process in computational geometry and computer-aided design applications to build and interrogate complex shapes in the computer. This paper presents a novel and simple dual quaternion-based osculating circle DQOC algorithm to find the intersection curve of two regular surfaces based on the osculating circle concept and dual quaternions. Additionally, we expressed the natural equations of the intersection curve. We have also demonstrated the superiority of our method through numerical examples.

Facial expression generation has always been an intriguing task for scientists and researchers all over the globe. In this context, we present our novel approach for generating videos of the six basic facial expressions. Starting from a single neutral facial image and a label indicating the desired facial expression, we aim to synthesize a video of the given identity performing the specified facial expression. Our approach, referred to as FEV-GAN (Facial Expression Video GAN), is based on Spatio-temporal Convolutional GANs, that are known to model both content and motion in the same network. Previous methods based on such a network have shown a good ability to generate coherent videos with smooth temporal evolution. However, they still suffer from low image quality and low identity preservation capability. In this work, we address this problem by using a generator composed of two image encoders. The first one is pre-trained for facial identity feature extraction and the second for spatial feature extraction. We have qualitatively and quantitatively evaluated our model on two international facial expression benchmark databases: MUG and Oulu-CASIA NIR&VIS. The experimental results analysis demonstrates the effectiveness of our approach in generating videos of the six basic facial expressions while preserving the input identity. The analysis also proves that the use of both identity and spatial features enhances the decoder ability to better preserve the identity and generate high-quality videos. The code and the pre-trained model will soon be made publicly available.

In this work, we construct a class of Hermite-type interpolation basis functions based on the sixth-order ordinary differential equation S (6) (t) - τ 4 S (2) (t) = 0 . Using them, we propose a kind of C 2 tension interpolation splines with a local tension parameter τ i . For C 2 interpolation, the given interpolant has O (h 2) convergence. Some applications of the C 2 tension interpolation splines on the construction of interest rate term structure in Chinese financial market are given. Moreover, a kind of generalized non-uniform B-splines of the space spanned by span 1 , t , ... , t n - 4 , sin (τ t) , cos (τ t) , sinh (τ t) , cosh (τ t) is constructed. [ABSTRACT FROM AUTHOR]

The algebraic characterization of dual univariate interpolating subdivision schemes is investigated. Specifically, we provide a constructive approach for finding dual univariate interpolating subdivision schemes based on the solutions of certain associated polynomial equations. The proposed approach also makes it possible to identify conditions for the existence of the sought schemes. [ABSTRACT FROM AUTHOR]

• New model for scene text VQA that jointly reasons about textual and visual modalities. • Attending on multi-modal features is better than attending separately to each modality. • Grid features from an object detection backbone proves to work well in this task. • The proposed model is up to 5 times faster than current state of the art models. • Combined with a standard VQA model reaches state of the art on mixed datasets. This paper presents a new model for the task of scene text visual question answering. In this task questions about a given image can only be answered by reading and understanding scene text. Current state of the art models for this task make use of a dual attention mechanism in which one attention module attends to visual features while the other attends to textual features. A possible issue with this is that it makes difficult for the model to reason jointly about both modalities. To fix this problem we propose a new model that is based on an single attention mechanism that attends to multi-modal features conditioned to the question. The output weights of this attention module over a grid of multi-modal spatial features are interpreted as the probability that a certain spatial location of the image contains the answer text to the given question. Our experiments demonstrate competitive performance in two standard datasets with a model that is × 5 faster than previous methods at inference time. Furthermore, we also provide a novel analysis of the ST-VQA dataset based on a human performance study. Supplementary material, code, and data is made available through this link. [ABSTRACT FROM AUTHOR]

In this paper, we concern with the data interpolation by using extended cubic uniform B-splines with shape parameters. Two iterative formats, namely the progressive iterative approximation (PIA) and the weighted progressive iterative approximation (WPIA), are proposed to interpolate given data points. We study the optimal shape parameter and the optimal weight for the proposed methods by solving the eigenvalues of the collocation matrix. The optimal shape parameter can make the iterative methods not only have the fastest convergence speed but also have smallest initial interpolation error. Numerical experiments are given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

• A mental stress state diagnostic for timely intervention from clinicians. • Deep neural network with hierarchical learning capabilities using IoT based biomarkers. • Learns using both wrist-based and chest-based sensor bio-signal features. • Model-level fusion of high-level representations for stress state classification. Affective state recognition at an early stage can help in mood stabilization, stress and depression management for mental well-being. Pro-active and remote mental healthcare warrants the use of various biomarkers to detect the affective mental state of the individual by evaluating the daily activities. With the easy accessibility of IoT-based sensors for healthcare, observable and quantifiable characteristics of our body, physiological changes in the body can be measured and tracked using various wearable devices. This work puts forward a model for mental stress state detection using sensor-based bio-signals. A multi-level deep neural network with hierarchical learning capabilities of convolution neural network is proposed. Multivariate time-series data consisting of both wrist-based and chest-based sensor bio-signals is trained using a hierarchy of networks to generate high-level features for each bio-signal feature. A model-level fusion strategy is proposed to combine the high-level features into one unified representation and classify the stress states into three categories as baseline, stress and amusement. The model is evaluated on the WESAD benchmark dataset for mental health and compares favourably to state-of-the-art approaches giving a superlative performance accuracy of 87.7%. [ABSTRACT FROM AUTHOR]

We offer the algorithm for choosing tension parameters of the generalized splines for convexity preserving interpolation. The resulting spline minimally differs from the classical cubic spline and coincides with it if sufficient convexity conditions are satisfied for the last one. We consider specific algorithms for different generalized cubic splines such as rational, exponential, variable power, hyperbolic splines, and splines with additional knots. [ABSTRACT FROM AUTHOR]

This document summarises the current theoretical and experimental status of the di-Higgs boson production searches, and of the direct and indirect constraints on the Higgs boson self-coupling, with the wish to serve as a useful guide for the next years. The document discusses the theoretical status, including state-of-the-art predictions for di-Higgs cross sections, developments on the effective field theory approach, and studies on specific new physics scenarios that can show up in the di-Higgs final state. The status of di-Higgs searches and the direct and indirect constraints on the Higgs self-coupling at the LHC are presented, with an overview of the relevant experimental techniques, and covering all the variety of relevant signatures. Finally, the capabilities of future colliders in determining the Higgs self-coupling are addressed, comparing the projected precision that can be obtained in such facilities. The work has started as the proceedings of the Di-Higgs workshop at Colliders, held at Fermilab from the 4th to the 9th of September 2018, but it went beyond the topics discussed at that workshop and included further developments. FERMILAB-CONF-19-468-E-T, LHCHXSWG-2019-005

In 2012 the ATLAS and CMS collaborations discovered at the LHC the Higgs boson decaying to vector bosons. This discovery has provided a strong indication that the mechanism of Electroweak Symmetry Breaking (EWSB) is similar to the one predicted by Brout-Englert-Higgs (BEH) nearly 50 years before. Since then, one of the priorities of the LHC program, as well as of the majority of the future collider proposals, is to measure directly the parameters of the EWSB potential. The goal is to identify if it has indeed the straightforward quartic shape predicted by BEH or it is more complex, as the result of an unexplored physics nature. The answer to this major scientific question will have a considerable impact on our understanding of vacuum properties and the history of the universe through the EWSB during the Big Bang. The only direct way to probe these couplings is through the measure of the production of multiple Higgs bosons, two being the simplest case. In this paper, we present a comprehensive review of the current searches and the state of the art insights on the topic. In particular, we explain why this ambitious project is even more challenging than the discovery of the Higgs boson itself. Finally, we sketch the plans of the HEP community for how to access the parameters of the BEH mechanism. This review is adapted to a curious reader familiar with particle physics in general or a scientist who wants to have a landscape overview of the topic.

Imaging methods based on the absorption or scattering of atmospheric muons, collectively named under the neologism “muography”, exploit the abundant natural flux of muons produced from cosmic-ray interactions in the atmosphere. Recent years have seen a steep rise in the development of muography methods in a variety of innovative multidisciplinary approaches to study the interior of natural or human-made structures, establishing synergies between usually disconnected academic disciplines such as particle physics, geology, and archaeology. Muography also bears promise of immediate societal impact through geotechnical investigations, nuclear waste surveys, homeland security, and natural hazard monitoring. Our aim is to provide an introduction to this vibrant research area, starting from the physical principles at the basis of the methods and describing the main detector technologies and imaging tools, including their combination with conventional techniques from other disciplines, where appropriate. Then, we discuss critically some outstanding issues that affect a broad variety of applications, and the current state of the art in addressing them. Finally, we review several recent developments in the application of muography methods to specific use cases, without any pretence of exhaustiveness.

Demonstration of the light radiation pressure on a microscopic level by A. Ashkin led to the invention of optical tweezers (OT). Applied in the studies of living systems, OT have become a preferable instrument for the noninvasive study of microobjects, allowing manipulation and measurement of the mechanical properties of molecules, organelles, and cells. In the present paper, we overview OT applications in hemorheological research, placing emphasis on red blood cells but also discussing OT applications for the investigation of the biomechanics of leukocytes and platelets. Blood properties have always served as a primary parameter in medical diagnostics due to the interconnection with the physiological state of an organism. Despite blood testing being a well-established procedure of conventional medicine, there are still many complex processes that must be unraveled to improve our understanding and contribute to future medicine. OT are advancing single-cell research, promising new insights into individual cell characteristics compared to the traditional approaches. We review the fundamental and practical findings revealed in blood research through the optical manipulation, stretching, guiding, immobilization, and inter-/intracellular force measurements of single blood cells.

The complexity of collider data analyses has dramatically increased from early colliders to the CERN LHC. Reconstruction of the collision products in the particle detectors has reached a point that requires dedicated publications documenting the techniques, and periodic retuning of the algorithms themselves. Analysis methods evolved to account for the increased complexity of the combination of particles required in each collision event (final states) and for the need of squeezing every last bit of sensitivity from the data; physicists often seek to fully reconstruct the final state, a process that is mostly relatively easy at lepton colliders but sometimes exceedingly difficult at hadron colliders to the point of requiring sometimes using advanced statistical techniques such as machine learning. The need for keeping the publications documenting results to a reasonable size implies a greater level of compression or even omission of information with respect to publications from twenty years ago. The need for compression should however not prevent sharing a reasonable amount of information that is essential to understanding a given analysis. Infrastructures like Rivet or HepData have been developed to host additional material, but physicists in the experimental Collaborations often still send an insufficient amount of material to these databases. In this manuscript I advocate for an increase in the information shared by the Collaborations, and try to define a minimum standard for acceptable level of information when reporting the results of statistical procedures in High Energy Physics publications.

This article deals with univariate binary approximating subdivision schemes and their generalization to non-tensor product bivariate subdivision schemes. The two algorithms are presented with one tension and two integer parameters which generate families of univariate and bivariate schemes. The tension parameter controls the shape of the limit curve and surface while integer parameters identify the members of the family. It is demonstrated that the proposed schemes preserve monotonicity of initial data. Moreover, continuity, polynomial reproduction and generation of the schemes are also discussed. Comparison with existing schemes is also given.

• Enhance face verification performance for demographics effected by decision bias. • Operates on comparison score-level to enable using existing face recognition models. • Based on the notation of individual fairness to treat similar face groups similarly. • Effectiveness proved on three databases and two face embeddings. • Unsupervised enhancement of the overall and intra-class recognition performance. Current face recognition systems achieve high progress on several benchmark tests. Despite this progress, recent works showed that these systems are strongly biased against demographic sub-groups. Consequently, an easily integrable solution is needed to reduce the discriminatory effect of these biased systems. Previous work mainly focused on learning less biased face representations, which comes at the cost of a strongly degraded overall recognition performance. In this work, we propose a novel unsupervised fair score normalization approach that is specifically designed to reduce the effect of bias in face recognition and subsequently lead to a significant overall performance boost. Our hypothesis is built on the notation of individual fairness by designing a normalization approach that leads to treating "similar" individuals "similarly". Experiments were conducted on three publicly available datasets captured under controlled and in-the-wild circumstances. Results demonstrate that our solution reduces demographic biases, e.g. by up to 82.7% in the case when gender is considered. Moreover, it mitigates the bias more consistently than existing works. In contrast to previous works, our fair normalization approach enhances the overall performance by up to 53.2% at false match rate of 10 − 3 and up to 82.9% at a false match rate of 10 − 5. Additionally, it is easily integrable into existing recognition systems and not limited to face biometrics. [ABSTRACT FROM AUTHOR]

In this paper, the properties of a new family of nonlinear dyadic subdivision schemes are presented and studied depending on the conditions imposed to the mean used to rewrite the linear scheme upon which the new scheme is based. The convergence, stability, and order of approximation of the schemes of the family are analyzed in general. Also, the elimination of the Gibbs oscillations close to discontinuities is proved in particular cases. It is proved that these schemes converge towards limit functions that are Hölder continuous with exponent larger than 1. The results are illustrated with several examples. [ABSTRACT FROM AUTHOR]

In this paper, we propose a variational method in order to solve Bratu's problem for two dimensions in an adequate space of biquadratic spline functions. The solution is obtained by resolving a sequence of boundary value problems. We study some characterizations of the functions of such sequence and we express them as some linear combination of biquadratic spline bases functions. We finish by showing some numerical and graphical examples in order to prove the validity and the effectiveness of our method. [ABSTRACT FROM AUTHOR]

In this work, we use a kind of C 1 rational interpolation splines in one and two dimensions to generate curves and surfaces with region control. Simple data-dependent sufficient constraints are derived on the local control parameters to generate C 1 interpolation curves lying strictly between two given piecewise linear curves and C 1 interpolation surfaces lying strictly between two given piecewise bi-cubic blending linear interpolation surfaces. [ABSTRACT FROM AUTHOR]

We present an approximation problem of surfaces of a generalized offset surface with offset variable distances and directions. Such approximating surface fits some given data points and minimizes a Sobolev's semi-norm of order 3. The study of the new results, from a mathematical point of view, carefully establishing the proof of the convergence between the generalized offset surface and its approximating spline in an adequate parametric bicubic spline space. Moreover, the approximating spline function is computed and an estimation of the relative error is introduced. Finally, some numerical and graphic examples are shown in order to prove the useful and the effectiveness of our method. [ABSTRACT FROM AUTHOR]

• We propose a module to predict boundary shapes and boxes with a new masking scheme. • We comprehensively investigate proposed frameworks with various masking methods. • The proposed modularizable component can easily be applied to existing models. • BshapeNet + improves accuracy notably compared to the baselines, Faster and Mask RCNN. • We achieved highly competitive results with SOTA detection and segmentation models. We propose a modularizable component that can predict the boundary shapes and boxes of an image, along with a new masking scheme for improving object detection and instance segmentation. Specifically, we introduce two types of novel masks: a bounding box (bbox) mask and a bounding shape (bshape) mask. For each of these types, we consider two variants—the "Thick" model and the "Scored" model—both of which have the same morphology but differ in ways that make their boundaries thicker. To evaluate our masks, we design extended frameworks by adding a bshape mask (or a bbox mask) branch to a Faster R-CNN, and call this BshapeNet (or BboxNet). Furthermore, we propose BshapeNet+, a network that combines a bshape mask branch with a Mask R-CNN. Among our various models, BshapeNet+ demonstrates the best performance in both tasks. In addition, BshapeNet+ markedly outperforms the baseline models on MS COCO and Cityscapes and achieves highly competitive results with state-of-the-art models. In particular, the experimental results show that our branch works well on small objects and is easily applicable to various models, such as PANet as well as Faster R-CNN and Mask R-CNN. [ABSTRACT FROM AUTHOR]

In this paper, we study how to construct a planar cubic G1 Hermite interpolation curve with minimal length and curvature variation energy. This problem is solved by a bi-objective optimization model. We prove that there is a unique solution to this problem and give the expression of the solution. Some numerical examples show that the proposed method makes the curvature variation energy of the curve as small as possible when the length of the curve as short as possible. [ABSTRACT FROM AUTHOR]

This paper introduces the software TiGL: TiGL is an open source geometry modeler that is used in the conceptual and preliminary aircraft and helicopter design phase. It creates full three-dimensional models of aircraft from their parametric CPACS description. Due to its parametric nature, it is typically used for aircraft design analysis and optimization. First, we present the use-case and architecture of TiGL. Then, we discuss its geometry module, which is used to generate the B-spline based surfaces of the aircraft. The backbone of TiGL is its surface generator for curve network interpolation, based on Gordon surfaces. One major part of this paper explains the mathematical foundation of Gordon surfaces on B-splines and how we achieve the required curve network compatibility. Finally, TiGL's aircraft component module is introduced, which is used to create the external and internal parts of aircraft, such as wings, flaps, fuselages, engines or structural elements. [ABSTRACT FROM AUTHOR]

This paper studies well-definedness and convergence of subdivision schemes which operate on Riemannian manifolds with nonpositive sectional curvature. These schemes are constructed from linear ones by replacing affine averages by the Riemannian centre of mass. In contrast to previous work, we consider schemes without any sign restriction on the mask, and our results apply to all input data. We also analyse the Hölder continuity of the resulting limit curves. Our main result states that if the norm of the derived scheme (resp. iterated derived scheme) is smaller than the corresponding dilation factor then the adapted scheme converges. In this way, we establish that convergence of a linear subdivision scheme is almost equivalent to convergence of its nonlinear manifold counterpart. [ABSTRACT FROM AUTHOR]

Interpolatory splines are usually useful to reconstruct data that present certain regularity. This paper is devoted to the construction and analysis of a new technique that allows to improve the accuracy of splines near corner singularities in the point values and jump discontinuities in the cell averages. The detection of discontinuities is easily done through the processing of the right hand side of the system of equations of the spline, that contains divided differences. The process of adaption will require some knowledge about the position of the discontinuity and the values of the function and its derivatives at the discontinuity. Using Harten's multiresolution we can adapt splines to the presence of corner singularities and jump discontinuities. Thanks to the adaption, the smearing of corner singularities does not appear in the reconstruction obtained in the point values and Gibbs phenomenon and diffusion of jump discontinuities is also eliminated. These numerical effects are a consequence of assuming that the data used in the reconstruction comes from the discretization of a continuous function with certain regularity and this might not be true. [ABSTRACT FROM AUTHOR]

We introduce a new class of Pythagorean-Hodograph (PH) space curves - called Algebraic-Trigonometric Pythagorean-Hodograph (ATPH) space curves - that are defined over a six-dimensional space mixing algebraic and trigonometric polynomials. After providing a general definition for this new class of curves, their quaternion representation is introduced and the fundamental properties are discussed. Then, as previously done with their quintic polynomial counterpart, a constructive approach to solve the first-order Hermite interpolation problem in ℝ3 is provided. Comparisons with the polynomial case are illustrated to point out the greater flexibility of ATPH curves with respect to polynomial PH curves. [ABSTRACT FROM AUTHOR]

Highlights • We propose trainable feature extractors for representation of skeleton poses. • We employ the proposed feature extractor for classification of human actions. • We designed an human action classification method based on string kernel. • We carried out experiments on the MHAD, MSRDA and MIVIA-S action datasets. • We publicly released the MIVIA-S dataset for research purpose. Abstract Automatic interpretation of human actions gained strong interest among researchers in patter recognition and computer vision because of its wide range of applications, such as in social and home robotics, elderly people health care, surveillance, among others. In this paper, we propose a method for recognition of human actions by analysis of skeleton poses. The method that we propose is based on novel trainable feature extractors, which can learn the representation of prototype skeleton examples and can be employed to recognize skeleton poses of interest. We combine the proposed feature extractors with an approach for classification of pose sequences based on string kernels. We carried out experiments on three benchmark data sets (MIVIA-S, MSRSDA and MHAD) and the results that we achieved are comparable or higher than the ones obtained by other existing methods. A further important contribution of this work is the MIVIA-S dataset, that we collected and made publicly available. [ABSTRACT FROM AUTHOR]

We consider the problem of reconstructing 3D objects via meshfree interpolation methods. In this framework, we usually deal with large data sets and thus develop an efficient local scheme via the well-known partition of unity method. The main contribution in this paper consists in constructing the local interpolants for the implicit interpolation by means of rational radial basis functions. Numerical experiments, devoted to test the accuracy of the scheme, confirm that the proposed method is particularly performing when 3D objects, or more in general implicit functions defined by scattered points, need to be approximated. [ABSTRACT FROM AUTHOR]

Multi-output least-squares support vector regression machines (MLS-SVR) is proposed by Xu et al. [29] to handle multi-output regression problems. However, the prohibitive cost of model selection severely hinders MLS-SVR’s application. In this paper, an efficient gradient-based model selection algorithm for MLS-SVR is proposed. Firstly, a new training algorithm for MLS-SVR is developed, which allows one to obtain the solution vector for each output independently by dealing with matrices of much lower order. Based on the new training algorithm, a new leave-one-out error estimate is derived through virtual leave-one-out cross-validation. The model selection criterion is based on the new leave-one-out error estimate and its derivatives with respect to the hyper-parameters are also derived analytically. Both the model selection criterion and its partial derivatives can be obtained straightway once a training process ended. Finally, the hyper-parameters corresponding to the lowest model selection criterion is obtained through gradient decent method. The effectiveness and generalization performance of the proposed algorithm are validated through experiments on several multi-output datasets. Experiment results show that the proposed algorithm can save computational time dramatically without losing accuracy. [ABSTRACT FROM AUTHOR]

We propose a novel single face image super-resolution method, which is named Face Conditional Generative Adversarial Network (FCGAN), based on boundary equilibrium generative adversarial networks. Without taking any prior facial information, our approach combines the pixel-wise L 1 loss and GAN loss to optimize our super-resolution model and to generate a high-quality face image from a low-resolution one robustly (with upscaling factor 4 × ). Additionally, Compared with existing peer researches, both training and testing phases of FCGAN are end-to-end pipeline without pre/post-processing. To enhance the convergence speed and strengthen feature propagation, the Generator and Discriminator networks are designed with a skip-connection architecture, and both using an auto-encoder structure. Quantitative experiments demonstrate that our model achieves competitive performance compared with the state-of-the-art models based on both visual quality and quantitative criterions. We believe this high-quality face image generated method can impact many applications in face identification and intelligent monitor. [ABSTRACT FROM AUTHOR]

Recently convolutional neural networks (CNN) have demonstrated remarkable performance in various classification problems. In this paper, we also introduce CNN into in-air handwritten Chinese character recognition (IAHCCR) and propose new directional feature maps, named bend directional feature maps. Then we integrate the combination of various types of directional feature maps with the CNN and obtain better recognition performance compared with other methods reported for IAHCCR. For further improving recognition rate, we propose a new data augmentation method dedicated to in-air handwritten Chinese characters. The proposed data augmentation method combines global transformation with local distortion and effectively enlarges the training dataset. Experimental results demonstrate that our proposed methods can greatly improve the recognition rate for IAHCCR. [ABSTRACT FROM AUTHOR]

Decision Trees and Random Forests are among the most popular methods for classification tasks. Two key issues faced by these methods are: how to select the best attribute to associate with a node and how to split the samples given the selected attribute. This paper addresses an important challenge that arises when nominal attributes with a large number of values are present: the computational time required to compute splits of good quality. We present a framework to generate computationally efficient splitting criteria that handle, with theoretical approximation guarantee, multi-valued nominal attributes for classification tasks with a large number of classes. Experiments with a number of datasets suggest that a method derived from our framework is competitive in terms of accuracy and speed with the Twoing criterion, one of few criteria available that is able to handle, with optimality guarantee, nominal attributes with a large number of distinct values. However, this method has the advantage of also efficiently handling datasets with a large number of classes. These experiments also give evidence of the potential of aggregating attributes to improve the classification power of decision trees. [ABSTRACT FROM AUTHOR]