Structural Tensor

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Bogusław Cyganek - One of the best experts on this subject based on the ideXlab platform.

  • Real-Time Image Content Assessment for Underwater Robot Manoeuvring Based on Structural Tensor Analysis
    Proceedings of the 10th International Conference on Computer Recognition Systems CORES 2017, 2018
    Co-Authors: Jakub Nawała, Bogusław Cyganek
    Abstract:

    The paper presents an efficient method for real-time image analysis for manoeuvring of the underwater robot. Image analysis is done after computing the Structural Tensor components which unveil rich texture and texture-less areas. To allow a power efficient underwater operation in real-time the method is implemented on the Jetson TK1 self-standing graphics card using the CUDA compute architecture. The laboratory experimental results show that the system is capable of processing about 40 Full HD images per second while allowing orientation toward texture specific regions for obstacle avoidance.

  • CORES - Real-Time Image Content Assessment for Underwater Robot Manoeuvring Based on Structural Tensor Analysis
    Advances in Intelligent Systems and Computing, 2017
    Co-Authors: Jakub Nawała, Bogusław Cyganek
    Abstract:

    The paper presents an efficient method for real-time image analysis for manoeuvring of the underwater robot. Image analysis is done after computing the Structural Tensor components which unveil rich texture and texture-less areas. To allow a power efficient underwater operation in real-time the method is implemented on the Jetson TK1 self-standing graphics card using the CUDA compute architecture. The laboratory experimental results show that the system is capable of processing about 40 Full HD images per second while allowing orientation toward texture specific regions for obstacle avoidance.

  • A learning-based colour image segmentation with extended and compact Structural Tensor feature representation
    Pattern Analysis and Applications, 2017
    Co-Authors: Konrad Jackowski, Bogusław Cyganek
    Abstract:

    In this paper a novel Tensor-Based Image Segmentation Algorithm (TBISA) is presented, which is dedicated for segmentation of colour images. A purpose of TBISA is to distinguish specific objects based on their characteristics, i.e. shape, colour, texture, or a mixture of these features. All of those information are available in colour channel data. Nonetheless, performing image analysis on the pixel level using RGB values, does not allow to access information on texture which is hidden in relation between neighbouring pixels. Therefore, to take full advantage of all available information, we propose to incorporate the Structural Tensors as a feature extraction method. It forms enriched feature set which, apart from colour and intensity, conveys also information of texture. This set is next processed by different classification algorithms for image segmentation. Quality of TBISA is evaluated in a series of experiments carried on benchmark images. Obtained results prove that the proposed method allows accurate and fast image segmentation.

  • HAIS - Ensemble of HOSVD Generated Tensor Subspace Classifiers with Optimal Tensor Flattening Directions
    Lecture Notes in Computer Science, 2016
    Co-Authors: Bogusław Cyganek, Michał Woźniak, Dariusz Jankowski
    Abstract:

    The paper presents a modified method of building ensembles of Tensor classifiers for direct multidimensional pattern recognition in Tensor subspaces. The novelty of the proposed solution is a method of lowering Tensor subspace dimensions by rotation of the training pattern to their optimal directions. These are obtained computing and analyzing phase histograms of the Structural Tensor computed from the training images. The proposed improvement allows for a significant increase of the classification accuracy which favorably compares to the best methods cited in literature.

  • Hybrid ensemble of classifiers for logo and trademark symbols recognition
    Soft Computing, 2015
    Co-Authors: Bogusław Cyganek
    Abstract:

    The paper presents a hybrid ensemble of diverse classifiers for logo and trademark symbols recognition. The proposed ensemble is composed of four types of different member classifiers. The first one compares color distribution of the logo patterns and is responsible for sifting out images of different color distribution. The second of the classifiers is based on the Structural Tensor recognition of local phase histograms. A proposed modification in this module consists of Tensor computation in the space of the morphological scale-space. Thanks to this, more discriminative histograms describing global shapes are obtained. Next in the chain, is a novel member classifier that joins the Hausdorff distance with the correspondence measure of the log-polar patches computed around the corner points. This sparse classifier allows reliable comparison of even highly deformed patterns. The last member classifier relies on the statistical affine moment invariants which describe global shapes. However, a real advantage is obtained by joining the aforementioned base classifiers into a hybrid ensemble of classifiers, as proposed in this paper. Thanks to this a more accurate response and generalizing properties are obtained at reasonable computational requirements. Experimental results show good recognition accuracy even for the highly deformed logo patterns, as well as fair generalization properties which support human search and logo assessment tasks.

Michael S Sacks - One of the best experts on this subject based on the ideXlab platform.

  • isogeometric finite element based simulation of the aortic heart valve integration of neural network Structural material model and Structural Tensor fiber architecture representations
    International Journal for Numerical Methods in Biomedical Engineering, 2021
    Co-Authors: Wenbo Zhang, Giovanni Rossini, David Kamensky, Tan Buithanh, Michael S Sacks
    Abstract:

    The functional complexity of native and replacement aortic heart valves are well known, incorporating such physical phenomenons as time-varying non-linear anisotropic soft tissue mechanical behavior, geometric non-linearity, complex multi-surface time varying contact, and fluid-structure interactions to name a few. It is thus clear that computational simulations are critical in understanding AV function and for the rational basis for design of their replacements. However, such approaches continued to be limited by ad-hoc approaches for incorporating tissue fibrous structure, high-fidelity material models, and valve geometry. To this end, we developed an integrated tri-leaflet valve pipeline built upon an isogeometric analysis (IGA) framework. A high-order Structural Tensor (HOST) based method was developed for efficient storage and mapping the two-dimensional fiber Structural data onto the valvular 3D geometry. We then developed a neural network (NN) material model that learned the responses of a detailed mesoStructural model for exogenously cross-linked planar soft tissues. The NN material model not only reproduced the full anisotropic mechanical responses but also demonstrated a considerable efficiency improvement, as it was trained over a range of realizable fibrous structures. Results of parametric simulations were then performed, as well as population based bicuspid aortic heart valve fiber structure, that demonstrated the efficiency and robustness of the present approach. In summary, the present approach that integrates HOST and NN material model provides an efficient computational analysis framework with increased physical and functional realism for the simulation of native and replacement tri-leaflet heart valves. This article is protected by copyright. All rights reserved.

  • Isogeometric finite element‐based simulation of the aortic heart valve: Integration of neural network Structural material model and Structural Tensor fiber architecture representations
    International journal for numerical methods in biomedical engineering, 2021
    Co-Authors: Wenbo Zhang, Giovanni Rossini, David Kamensky, Tan Bui-thanh, Michael S Sacks
    Abstract:

    The functional complexity of native and replacement aortic heart valves are well known, incorporating such physical phenomenons as time-varying non-linear anisotropic soft tissue mechanical behavior, geometric non-linearity, complex multi-surface time varying contact, and fluid-structure interactions to name a few. It is thus clear that computational simulations are critical in understanding AV function and for the rational basis for design of their replacements. However, such approaches continued to be limited by ad-hoc approaches for incorporating tissue fibrous structure, high-fidelity material models, and valve geometry. To this end, we developed an integrated tri-leaflet valve pipeline built upon an isogeometric analysis (IGA) framework. A high-order Structural Tensor (HOST) based method was developed for efficient storage and mapping the two-dimensional fiber Structural data onto the valvular 3D geometry. We then developed a neural network (NN) material model that learned the responses of a detailed mesoStructural model for exogenously cross-linked planar soft tissues. The NN material model not only reproduced the full anisotropic mechanical responses but also demonstrated a considerable efficiency improvement, as it was trained over a range of realizable fibrous structures. Results of parametric simulations were then performed, as well as population based bicuspid aortic heart valve fiber structure, that demonstrated the efficiency and robustness of the present approach. In summary, the present approach that integrates HOST and NN material model provides an efficient computational analysis framework with increased physical and functional realism for the simulation of native and replacement tri-leaflet heart valves. This article is protected by copyright. All rights reserved.

Michał Woźniak - One of the best experts on this subject based on the ideXlab platform.

  • HAIS - Ensemble of HOSVD Generated Tensor Subspace Classifiers with Optimal Tensor Flattening Directions
    Lecture Notes in Computer Science, 2016
    Co-Authors: Bogusław Cyganek, Michał Woźniak, Dariusz Jankowski
    Abstract:

    The paper presents a modified method of building ensembles of Tensor classifiers for direct multidimensional pattern recognition in Tensor subspaces. The novelty of the proposed solution is a method of lowering Tensor subspace dimensions by rotation of the training pattern to their optimal directions. These are obtained computing and analyzing phase histograms of the Structural Tensor computed from the training images. The proposed improvement allows for a significant increase of the classification accuracy which favorably compares to the best methods cited in literature.

  • An Improved Vehicle Logo Recognition Using a Classifier Ensemble Based on Pattern Tensor Representation and Decomposition
    New Generation Computing, 2015
    Co-Authors: Bogusław Cyganek, Michał Woźniak
    Abstract:

    The paper presents a vehicle logo recognition system based on novel combination of Tensor based feature extraction and ensemble of Tensor subspace classifiers. Each originally two-dimensional vehicle logotype is transformed to a three-dimensional feature Tensor applying the extended Structural Tensor method. All such exemplary logo-Tensors which correspond to a single class are stacked to form a 4D logo-class-Tensor. Decomposing each 4D logo-class-Tensor into the orthogonal Tensor subspace allows classification of unknown logotypes. The proposed system allows reliable vehicle logo recognition in real conditions as shown by experiments.

  • ACIIDS (2) - Vehicle Logo Recognition with an Ensemble of Classifiers
    Intelligent Information and Database Systems, 2014
    Co-Authors: Bogusław Cyganek, Michał Woźniak
    Abstract:

    The paper presents a system for vehicle logo recognition from real digital images. The process starts with license plates localization, followed by vehicle logo detection. For this purpose the Structural Tensor is employed which allows fast and reliable detections even in low quality images. Detected logo areas are classified to the car brands with help of the classifier operating in the multi-dimensional Tensor spaces. These are obtained after the Higher-Order Singular Value Decomposition of the prototype logo Tensors. The proposed method shows high accuracy and fast operation, as verified by the experiments.

  • ICCCI (1) - Pixel-Based object detection and tracking with ensemble of support vector machines and extended Structural Tensor
    Computational Collective Intelligence. Technologies and Applications, 2012
    Co-Authors: Bogusław Cyganek, Michał Woźniak
    Abstract:

    In this paper we propose a system for visual object detection and tracking based on the extended Structural Tensor and the ensemble of one-class support vector machines. First, the input color image is transformed with the anisotropic process into the extended Structural Tensor. Then the Tensor space is clustered into the number of partitions which are used to train a corresponding number of one-class support vector machines composing an ensemble of classifiers. In run-time the ensemble classifies the input video stream into an object and background. Thanks to high discriminative properties of the extended Structural Tensor and to the diversity of the ensemble of classifiers the method shows very good properties which were shown by experiments on real video sequences.

Virginia Vassilevska Williams - One of the best experts on this subject based on the ideXlab platform.

  • Limits on All Known (and Some Unknown) Approaches to Matrix Multiplication
    arXiv: Computational Complexity, 2018
    Co-Authors: Josh Alman, Virginia Vassilevska Williams
    Abstract:

    We study the known techniques for designing Matrix Multiplication algorithms. The two main approaches are the Laser method of Strassen, and the Group theoretic approach of Cohn and Umans. We define a generalization based on zeroing outs which subsumes these two approaches, which we call the Solar method, and an even more general method based on monomial degenerations, which we call the Galactic method. We then design a suite of techniques for proving lower bounds on the value of $\omega$, the exponent of matrix multiplication, which can be achieved by algorithms using many Tensors $T$ and the Galactic method. Some of our techniques exploit `local' properties of $T$, like finding a sub-Tensor of $T$ which is so `weak' that $T$ itself couldn't be used to achieve a good bound on $\omega$, while others exploit `global' properties, like $T$ being a monomial degeneration of the Structural Tensor of a group algebra. Our main result is that there is a universal constant $\ell>2$ such that a large class of Tensors generalizing the Coppersmith-Winograd Tensor $CW_q$ cannot be used within the Galactic method to show a bound on $\omega$ better than $\ell$, for any $q$. We give evidence that previous lower-bounding techniques were not strong enough to show this. We also prove a number of complementary results along the way, including that for any group $G$, the Structural Tensor of $\mathbb{C}[G]$ can be used to recover the best bound on $\omega$ which the Coppersmith-Winograd approach gets using $CW_{|G|-2}$ as long as the asymptotic rank of the Structural Tensor is not too large.

  • FOCS - Limits on All Known (and Some Unknown) Approaches to Matrix Multiplication
    2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS), 2018
    Co-Authors: Josh Alman, Virginia Vassilevska Williams
    Abstract:

    We study the known techniques for designing Matrix Multiplication algorithms. The two main approaches are the Laser method of Strassen, and the Group theoretic approach of Cohn and Umans. We define a generalization based on zeroing outs which subsumes these two approaches, which we call the Solar method, and an even more general method based on monomial degenerations, which we call the Galactic method. We then design a suite of techniques for proving lower bounds on the value of omega, the exponent of matrix multiplication, which can be achieved by algorithms using many Tensors T and the Galactic method. Some of our techniques exploit 'local' properties of T, like finding a sub-Tensor of T which is so 'weak' that T itself couldn't be used to achieve a good bound on omega, while others exploit 'global' properties, like T being a monomial degeneration of the Structural Tensor of a group algebra. Our main result is that there is a universal constant l>2 such that a large class of Tensors generalizing the Coppersmith-Winograd Tensor CW_q cannot be used within the Galactic method to show a bound on omega better than ell, for any q. We give evidence that previous lower-bounding techniques were not strong enough to show this. We also prove a number of complementary results along the way, including that for any group G, the Structural Tensor of C[G] can be used to recover the best bound on omega which the Coppersmith-Winograd approach gets using CW_|G|-2 as long as the asymptotic rank of the Structural Tensor is not too large.

  • further limitations of the known approaches for matrix multiplication
    Conference on Innovations in Theoretical Computer Science, 2018
    Co-Authors: Josh Alman, Virginia Vassilevska Williams
    Abstract:

    We consider the techniques behind the current best algorithms for matrix multiplication. Our results are threefold. (1) We provide a unifying framework, showing that all known matrix multiplication running times since 1986 can be achieved from a single very natural Tensor - the Structural Tensor T_q of addition modulo an integer q. (2) We show that if one applies a generalization of the known techniques (arbitrary zeroing out of Tensor powers to obtain independent matrix products in order to use the asymptotic sum inequality of Schonhage) to an arbitrary monomial degeneration of T_q, then there is an explicit lower bound, depending on q, on the bound on the matrix multiplication exponent omega that one can achieve. We also show upper bounds on the value alpha that one can achieve, where alpha is such that n * n^alpha * n matrix multiplication can be computed in n^{2+o(1)} time. (3) We show that our lower bound on omega approaches 2 as q goes to infinity. This suggests a promising approach to improving the bound on omega: for variable q, find a monomial degeneration of T_q which, using the known techniques, produces an upper bound on omega as a function of q. Then, take q to infinity. It is not ruled out, and hence possible, that one can obtain omega=2 in this way.

  • further limitations of the known approaches for matrix multiplication
    arXiv: Computational Complexity, 2017
    Co-Authors: Josh Alman, Virginia Vassilevska Williams
    Abstract:

    We consider the techniques behind the current best algorithms for matrix multiplication. Our results are threefold. (1) We provide a unifying framework, showing that all known matrix multiplication running times since 1986 can be achieved from a single very natural Tensor - the Structural Tensor $T_q$ of addition modulo an integer $q$. (2) We show that if one applies a generalization of the known techniques (arbitrary zeroing out of Tensor powers to obtain independent matrix products in order to use the asymptotic sum inequality of Sch\"{o}nhage) to an arbitrary monomial degeneration of $T_q$, then there is an explicit lower bound, depending on $q$, on the bound on the matrix multiplication exponent $\omega$ that one can achieve. We also show upper bounds on the value $\alpha$ that one can achieve, where $\alpha$ is such that $n\times n^\alpha \times n$ matrix multiplication can be computed in $n^{2+o(1)}$ time. (3) We show that our lower bound on $\omega$ approaches $2$ as $q$ goes to infinity. This suggests a promising approach to improving the bound on $\omega$: for variable $q$, find a monomial degeneration of $T_q$ which, using the known techniques, produces an upper bound on $\omega$ as a function of $q$. Then, take $q$ to infinity. It is not ruled out, and hence possible, that one can obtain $\omega=2$ in this way.

Wenbo Zhang - One of the best experts on this subject based on the ideXlab platform.

  • isogeometric finite element based simulation of the aortic heart valve integration of neural network Structural material model and Structural Tensor fiber architecture representations
    International Journal for Numerical Methods in Biomedical Engineering, 2021
    Co-Authors: Wenbo Zhang, Giovanni Rossini, David Kamensky, Tan Buithanh, Michael S Sacks
    Abstract:

    The functional complexity of native and replacement aortic heart valves are well known, incorporating such physical phenomenons as time-varying non-linear anisotropic soft tissue mechanical behavior, geometric non-linearity, complex multi-surface time varying contact, and fluid-structure interactions to name a few. It is thus clear that computational simulations are critical in understanding AV function and for the rational basis for design of their replacements. However, such approaches continued to be limited by ad-hoc approaches for incorporating tissue fibrous structure, high-fidelity material models, and valve geometry. To this end, we developed an integrated tri-leaflet valve pipeline built upon an isogeometric analysis (IGA) framework. A high-order Structural Tensor (HOST) based method was developed for efficient storage and mapping the two-dimensional fiber Structural data onto the valvular 3D geometry. We then developed a neural network (NN) material model that learned the responses of a detailed mesoStructural model for exogenously cross-linked planar soft tissues. The NN material model not only reproduced the full anisotropic mechanical responses but also demonstrated a considerable efficiency improvement, as it was trained over a range of realizable fibrous structures. Results of parametric simulations were then performed, as well as population based bicuspid aortic heart valve fiber structure, that demonstrated the efficiency and robustness of the present approach. In summary, the present approach that integrates HOST and NN material model provides an efficient computational analysis framework with increased physical and functional realism for the simulation of native and replacement tri-leaflet heart valves. This article is protected by copyright. All rights reserved.

  • Isogeometric finite element‐based simulation of the aortic heart valve: Integration of neural network Structural material model and Structural Tensor fiber architecture representations
    International journal for numerical methods in biomedical engineering, 2021
    Co-Authors: Wenbo Zhang, Giovanni Rossini, David Kamensky, Tan Bui-thanh, Michael S Sacks
    Abstract:

    The functional complexity of native and replacement aortic heart valves are well known, incorporating such physical phenomenons as time-varying non-linear anisotropic soft tissue mechanical behavior, geometric non-linearity, complex multi-surface time varying contact, and fluid-structure interactions to name a few. It is thus clear that computational simulations are critical in understanding AV function and for the rational basis for design of their replacements. However, such approaches continued to be limited by ad-hoc approaches for incorporating tissue fibrous structure, high-fidelity material models, and valve geometry. To this end, we developed an integrated tri-leaflet valve pipeline built upon an isogeometric analysis (IGA) framework. A high-order Structural Tensor (HOST) based method was developed for efficient storage and mapping the two-dimensional fiber Structural data onto the valvular 3D geometry. We then developed a neural network (NN) material model that learned the responses of a detailed mesoStructural model for exogenously cross-linked planar soft tissues. The NN material model not only reproduced the full anisotropic mechanical responses but also demonstrated a considerable efficiency improvement, as it was trained over a range of realizable fibrous structures. Results of parametric simulations were then performed, as well as population based bicuspid aortic heart valve fiber structure, that demonstrated the efficiency and robustness of the present approach. In summary, the present approach that integrates HOST and NN material model provides an efficient computational analysis framework with increased physical and functional realism for the simulation of native and replacement tri-leaflet heart valves. This article is protected by copyright. All rights reserved.