Invariant Description Research Articles

On a generalisation of Krein's example

We generalise a classical example given by Krein in 1953. We compute the difference of the resolvents and the difference of the spectral projections explicitly. We further give a full description of the unitary invariants, i.e., of the spectrum and the multiplicity. Moreover, we observe a link between the difference of the spectral projections and Hankel operators.

Extended Riemannian Geometry I: Local Double Field Theory

We present an extended version of Riemannian geometry suitable for the description of current formulations of double field theory (DFT). This framework is based on graded manifolds and it yields extended notions of symmetries, dynamical data and constraints. In special cases, we recover general relativity with and without 1-, 2- and 3-form gauge potentials as well as DFT. We believe that our extended Riemannian geometry helps to clarify the role of various constructions in DFT. For example, it leads to a covariant form of the strong section condition. Furthermore, it should provide a useful step towards global and coordinate invariant descriptions of T- and U-duality invariant field theories.

A Gauge Invariant Description for the General Conic Constrained Particle from the FJBW Iteration Algorithm

We consider a second-degree algebraic curve describing a general conic constraint imposed on the motion of a massive spinless particle. The problem is trivial at classical level but becomes involved and interesting concerning its quantum counterpart with subtleties in its symplectic structure and symmetries. We start with a second-class version of the general conic constrained particle, which encompasses previous versions of circular and elliptical paths discussed in the literature. By applying the symplectic FJBW iteration program, we proceed on to show how a gauge invariant version for the model can be achieved from the originally second-class system. We pursue the complete constraint analysis in phase space and perform the Faddeev-Jackiw symplectic quantization following the Barcelos-Wotzasek iteration program to unravel the essential aspects of the constraint structure. While in the standard Dirac-Bergmann approach there are four second-class constraints, in the FJBW they reduce to two. By using the symplectic potential obtained in the last step of the FJBW iteration process, we construct a gauge invariant model exhibiting explicitly its BRST symmetry. We obtain the quantum BRST charge and write the Green functions generator for the gauge invariant version. Our results reproduce and neatly generalize the known BRST symmetry of the rigid rotor, clearly showing that this last one constitutes a particular case of a broader class of theories.

Improved image retrieval and classification with combined invariant features and color descriptor

As the quantity of digital images grows in many applications in our daily life, users experience an increased difficulty in finding relevant images within their image collections and common image repositories. This paper proposes a novel image search scheme that extracts the features of an image using a combined invariant features and color description to retrieve specific images using query-by-example. The proposed method can be executed in real-time on an iPhone, and can be easily used to identify a natural color image with its invariant visual features. The proposed scheme is evaluated by assessing the performance of a simulation in terms of the average precision and F-score in image databases that are commonly used for image retrieval. The experimental results reveal that the proposed algorithm offers a significant improvement of more than 7.35 and 18.09% in retrieval effectiveness when compared to open source OpenSURF and MPEG-7 color and texture descriptor, respectively. The main contribution of this paper is that the proposed approach achieves a high accuracy and stability by using a combination of the improved SURF and color descriptor when searching for a natural image.

Weak Galilean invariance as a selection principle for coarse-grained diffusive models

How does the mathematical description of a system change in different reference frames? Galilei first addressed this fundamental question by formulating the famous principle of Galilean invariance. It prescribes that the equations of motion of closed systems remain the same in different inertial frames related by Galilean transformations, thus imposing strong constraints on the dynamical rules. However, real world systems are often described by coarse-grained models integrating complex internal and external interactions indistinguishably as friction and stochastic forces. Since Galilean invariance is then violated, there is seemingly no alternative principle to assess a priori the physical consistency of a given stochastic model in different inertial frames. Here, starting from the Kac-Zwanzig Hamiltonian model generating Brownian motion, we show how Galilean invariance is broken during the coarse-graining procedure when deriving stochastic equations. Our analysis leads to a set of rules characterizing systems in different inertial frames that have to be satisfied by general stochastic models, which we call "weak Galilean invariance." Several well-known stochastic processes are invariant in these terms, except the continuous-time random walk for which we derive the correct invariant description. Our results are particularly relevant for the modeling of biological systems, as they provide a theoretical principle to select physically consistent stochastic models before a validation against experimental data.

Mesh motion scale invariant feature and collaborative learning for visual recognition

Visual recognition has been gradually played important roles in many fields. An effective feature descriptor, with higher discrimination and higher descriptiveness for the different visual recognition tasks, is a challenging issue. In this paper, we propose a novel feature, called mesh motion scale invariant feature description, to facilitate the different visual task description and balance discrimination and efficiency. Then, a hierarchical collaborative feature learning model for multi-visual tasks in complex scenes is presented for obtaining the recognition results. Four large databases, FRGC, CASIA, BU-3DFE and 3D Online Action, are introduced to the performance comparison and the experimental results show a better performance for face recognition, expression recognition and activity recognition based on our proposed method.

Infinite (continuous) spin fields in the frame-like formalism

In this paper we elaborate on the gauge invariant frame-like Lagrangian description for the wide class of the so-called infinite (or continuous) spin representations of Poincaré group. We use our previous results on the gauge invariant formalism for the massive mixed symmetry fields corresponding to the Young tableau with two rows Y(k,l) (Y(k+1/2,l+1/2) for the fermionic case). We have shown that the corresponding infinite spin solutions can be constructed as a limit where k goes to infinity, while l remain to be fixed and label different representations. Moreover, our gauge invariant formalism provides a natural generalization to (Anti) de Sitter spaces as well. As in the completely symmetric case considered earlier by Metsaev we have found that there are no unitary solutions in de Sitter space, while there exists a rather wide spectrum of Anti de Sitter ones. In this, the question what representations of the Anti de Sitter group such solutions correspond to remains to be open.

Robust local feature descriptor for multisource remote sensing image registration

Distinctive and robust local feature description is crucial for remote sensing application, such as image matching and image retrieval. A descriptor for multisource remote sensing image matching that is robust to significant geometric and illumination differences is presented. In the proposed method, a traditional scale-invariant feature transform algorithm is applied for local feature extraction and a feature descriptor, named robust center-symmetric local-ternary-pattern (CSLTP) based self-similarity descriptor, is constructed for each extracted feature point. The main idea of the proposed descriptor is a rotation invariance description strategy on local correlation surface. Unlike common distribution-based descriptors or geometric-based spatial pooling descriptors, the proposed descriptor uses rotation invariance statistically strategic for CSLTP description on a correlation surface, which is inherently rotation invariant and robust to complex intensity differences. Then, a bilateral matching strategy followed by a reliable outlier removal procedure in the geometric transformation model is implemented for feature matching and mismatch elimination. The proposed method is successfully applied for matching various multisource satellite images and the results demonstrate its robustness and discriminability compared to common local feature descriptors.

Description of images using a configuration equivalence relation

An approach to constructing a description of data and images based on the search for an optimal configuration (permutation) of their components (pixels, regions, feature vectors, etc.) is proposed. The quality criterion of the configuration, which may be selected in accordance with the application, determines the concept of optimal configuration. With specific configurations, the whole set of analyzed data / images is broken down into equivalent subclasses characterized by identical descriptors. Issues of invariant description, robustness of the proposed presentation, and the relationship of the proposed approach with the existing ones (Local Binary Patterns (LBP) and image representation by sign data) are considered. By way of illustration, an applied problem is solved using the proposed approach.

Robust video copy detection based on ring decomposition based binarized statistical image features and invariant color descriptor (RBSIF-ICD)

Content based video copy detection (CBVCD) is considered as an active research field due to the requirement of copyright protection, business intelligence, video retrieval, etc. In this paper, we propose a CBVCD scheme using Ring decomposition based Binarized Statistical Image Features (RBSIF) and Invariant Color Descriptor (ICD), namely RBSIF-ICD. This hybrid descriptor is based on the combination of texture features extracted using RBSIF and a color characteristics derived using ICD. Firstly, a pre-processing is applied on each video sequence to remove borders. Secondly, the RBSIF descriptor is applied to each video frame to obtain the texture features. Then, ICD is applied to the video frames to construct an invariant color description which is very robust to geometrical attacks. Finally, RBSIF and ICD are fused to develop the RBSIF-ICD that will be very robust against several attacks such as rotation, flipping, strong compression, ... etc. For the evaluation purpose, the TRECVID 2009 database is used to test the robustness of the proposed system. Experiments reveal that the proposed RBSIF-ICD system outperforms the state-of-the-art algorithms under all the attacks and manipulations considered in this framework.

New approaches to integrable hierarchies of topological type

This survey is devoted to a large class of systems of partial differential equations which on the one hand appear in classical problems of mathematical physics and on the other hand provide an efficient tool for the description of enumerative invariants in algebraic geometry. Particular attention is paid to new approaches to these systems, in particular, to the approach proposed in a recent paper of the author. Bibliography: 57 titles.

Semi-direct products of Lie algebras and covariants

Let Q be a connected algebraic group with Lie algebra q. Symmetric invariants of q, i.e., the Q-invariants in the symmetric algebra S(q) of q, is a first approximation to the understanding of the coadjoint action (Q:q⁎) and coadjoint Q-orbits. In this article, we study a class of non-reductive Lie algebras, where the description of the symmetric invariants is possible and the coadjoint representation has a number of nice invariant-theoretic properties. If G is a semisimple group with Lie algebra g and V is G-module, then we define q to be the semi-direct product of g and V. Then we are interested in the case, where the generic isotropy group for the G-action on V is reductive and commutative. It turns out that in this case symmetric invariants of q can be constructed via certain G-equivariant maps from g to V (“covariants”).

Fivebranes and 3-manifold homology

Motivated by physical constructions of homological knot invariants, we study their analogs for closed 3-manifolds. We show that fivebrane compactifications provide a universal description of various old and new homological invariants of 3-manifolds. In terms of 3d/3d correspondence, such invariants are given by the Q-cohomology of the Hilbert space of partially topologically twisted 3d mathcal{N}=2 theory T[M3] on a Riemann surface with defects. We demonstrate this by concrete and explicit calculations in the case of monopole/Heegaard Floer homology and a 3-manifold analog of Khovanov-Rozansky link homology. The latter gives a categorification of Chern-Simons partition function. Some of the new key elements include the explicit form of the S-transform and a novel connection between categorification and a previously mysterious role of Eichler integrals in Chern-Simons theory.

Affine Invariant Description and Large-Margin Dimensionality Reduction for Target Detection in Optical Remote Sensing Images

A novel target detection method based on affine invariant interest point detection, feature encoding, and large-margin dimensionality reduction (LDR) is proposed for optical remote sensing images. First, four types of interest point detectors are introduced, and their performance in extracting low-level affine invariant descriptors using affine shape estimation is compared. Such a description can deal with significant affine transformations, including viewpoints. Second, feature encoding, which extends bag-of-words (BOW) by encoding high-order statistics, is selected to generate mid-level representation. Finally, LDR based on the large-margin constraint and stochastic subgradient is introduced to make the high-dimensional mid-level representation applicable for target detection. The experiments on aircraft and vehicle detections illustrate the effectiveness of the affine invariant description and LDR (compared with principal component analysis) in improving the detection performance. The experiments also demonstrate the effectiveness of the proposed method compared with popular approaches including Gabor, HOG, LBP, BOW, and R-CNN.

Local Intensity Ordering based Binary Patterns for Image Region Description

Local image region description is a fundamental task for image feature matching in the field of Computer Vision. A good image region descriptor should have the ability to discriminate image features even though the images differ due to photometric variations and geometric transformations. Over these years, many local region descriptors have been proposed to tackle the aforementioned challenges. Achieving rotation invariance in keypoint description is considered one of the main challenges in local region description and matching. Previous approaches proposed to tackle rotation variations depend on unreliable dominant orientation estimation. In this paper, two novel local image region descriptors called Local Intensity Order-based Center Symmetric Local Binary Patterns (LIOCSLBP) and Local Intensity Order-based Orthogonally Combined Local Binary Patterns (LIOOCLBP) are proposed to build rotation invariant local region descriptions. The rotation invariance characteristic of the proposed binary pattern-based local region description is achieved by applying a simple and efficient mechanism called Local Intensity Ordering (LIO). The proposed descriptors use double interest regions for each interest point to improve feature discrimination. In order to further improve the feature discrimination ability RGBLIOCSLBP, RGBLIOOCLBP, HSVLIOCSLBP and HSVLIOOCLBP are also proposed exploiting RGB and HSV color models. Extensive experiments are conducted to evaluate the performance of the proposed descriptors on standard benchmark datasets for image matching, object recognition and scene recognition against the state-of-the-art descriptors. The experimental results show that the proposed descriptors are highly competitive to several state-of-the-art local region descriptors where the proposed descriptors outperformed the comparative approaches in many cases.

Beyond E11

We study the non-linear realisation of E11 originally proposed by West with particular emphasis on the issue of linearised gauge invariance. Our analysis shows even at low levels that the conjectured equations can only be invariant under local gauge transformations if a certain section condition that has appeared in a different context in the E11 literature is satisfied. This section condition also generalises the one known from exceptional field theory. Even with the section condition, the E11 duality equation for gravity is known to miss the trace component of the spin connection. We propose an extended scheme based on an infinite-dimensional Lie superalgebra, called the tensor hierarchy algebra, that incorporates the section condition and resolves the above issue. The tensor hierarchy algebra defines a generalised differential complex, which provides a systematic description of gauge invariance and Bianchi identities. It furthermore provides an E11 representation for the field strengths, for which we define a twisted first order self-duality equation underlying the dynamics.

On the Microscopic Structure of {varvec{pi }}NN, {varvec{pi }}N{varvec{Delta }} and {varvec{{pi }Delta Delta }} Vertices

We use a hybrid constituent-quark model for the microscopic description of pi N N, pi N Delta and pi Delta Delta vertices. In this model quarks are confined by an instantaneous potential and are allowed to emit and absorb a pion, which is also treated as dynamical degree of freedom. The point form of relativistic quantum mechanics is employed to achieve a relativistically invariant description of this system. Starting with an SU(6) spin-flavor symmetric wave function for N_0 and Delta _0, i.e. the eigenstates of the pure confinement problem, we calculate the strength of the pi N_0 N_0, pi N_0 Delta _0 and pi Delta _0 Delta _0 couplings and the corresponding vertex form factors. Interestingly the ratios of the resulting couplings resemble strongly those needed in purely hadronic coupled-channel models, but deviate significantly from the ratios following from SU(6) spin-flavor symmetry in the non-relativistic constituent-quark model.

New Methods of Three-Dimensional Images Recognition Based on Stochastic Geometry and Functional Analysis

A new approach to 3D objects recognition based on modern methods of stochastic geometry and functional analysis is proposed in the paper. A detailed mathematical description of the method developed on the approach is also presented. The 3D trace transform allows creating an invariant description of spatial objects, which better resist distortion and coordinate noise than the one, obtained as a result of the object normalization procedure, does. The ability to control properties of developed features increases intellectual capacities of the 3D trace transform significantly, which can be mentioned as its undeniable advantage. The justification of the proposed theory and mathematical model is a variety of worked out theoretical examples of hypertriplet features that have particular described properties. The paper considers in detail scan techniques of the hypertrace transform and its mathematical model as well as approaches to developing and distinguishing informative features.

Hamiltonian positivity of massive spin-2 particles via a rank-2 tensor

There are three families of Lagrangians describing massive spin-2 particles via a general (nonsymmetric) rank-2 tensor. Each of those families depends on an arbitrary real parameter, one of them includes the paradigmatic Fierz–Pauli theory whose Hamiltonian positivity is known and reviewed here. Here we apply the plain Dirac–Bergmann procedure in the two remaining families. We identify all Hamiltonian constraints and prove both positivity of the reduced Hamiltonian and correct counting of degrees of freedom. The positivity of each spin mode contribution is demonstrated by using spin projection operators. The massless cases are also examined. In particular, we prove positivity of the reduced Hamiltonian and correct counting of degrees of freedom of a Weyl invariant description of massless spin-2 particles.

High-speed visual target tracking with mixed rotation invariant description and skipping searching

This paper proposes a novel high-speed visual target tracking system based on mixed rotation invariant description (MRID) and skipping searching method. MRID is a novel rotation invariant description of texture and edge information by annular histograms and dominant direction. It overcomes rotation variant and large computation issues in conventional LBP-HOG feature description. The skipping searching method used in tracking can remarkably decrease the computation time by avoiding repeated searching operations. The proposed tracking system contains an image sensor, a hierarchical vision processor and an actuator with 2 dimensions of freedom (DOF). The vision processor integrates processors with pixel- and row-level parallelism to speed up the tracking algorithm. Experiment results show that the proposed system can achieve over 1000-fps processing speed of the tracking algorithm under 750 × 480 resolution image.