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Approximation Kernel

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Karen Egiazarian – One of the best experts on this subject based on the ideXlab platform.

  • local feature descriptor based on 2d local polynomial Approximation Kernel indices
    Proceedings of SPIE, 2014
    Co-Authors: A I Sherstobitov, Vladimir I Marchuk, Dmitriy V Timofeev, Viacheslav V Voronin, Karen Egiazarian
    Abstract:

    A texture descriptor based on a set of indices of degrees of local approximating polynomials is proposed in this paper. First, a method to construct 2D local polynomial Approximation Kernels (k-LPAp) for arbitrary polynomials of degree p is presented. An image is split into non-overlapping patches, reshaped into one-dimensional source vectors and convolved with the polynomial Approximation Kernels of various degrees. As a result, a set of Approximations is obtained. For each element of the source vector, these Approximations are ranked according to the difference between the original and approximated values. A set of indices of polynomial degrees form a local feature. This procedure is repeated for each pixel. Finally, a proposed texture descriptor is obtained from the frequency histogram of all obtained local features. A nearest neighbor classifier utilizing Chi-square distance metric is used to evaluate a performance of the introduced descriptor. An accuracy of texture classification is evaluated on the following datasets: Brodatz, KTH-TIPS, KTH-TIPS2b and Columbia-Utrecht (CUReT) with respect to different methods of texture analysis and classification. The results of this comparison show that the proposed method is competitive with the recent statistical approaches such as local binary patterns (LBP), local ternary patterns, completed LBP, Weber’s local descriptor, and VZ algorithms (VZMR8 and VZ-Joint). At the same time, on KTH-TIPS2-b and KTH-TIPS datasets, the proposed method is slightly inferior to some of the state-of-the-art methods.

  • Image Processing: Algorithms and Systems – Local feature descriptor based on 2D local polynomial Approximation Kernel indices
    Proceedings of SPIE, 2014
    Co-Authors: A I Sherstobitov, Vladimir I Marchuk, Dmitriy V Timofeev, Viacheslav V Voronin, Karen Egiazarian
    Abstract:

    A texture descriptor based on a set of indices of degrees of local approximating polynomials is proposed in this paper. First, a method to construct 2D local polynomial Approximation Kernels (k-LPAp) for arbitrary polynomials of degree p is presented. An image is split into non-overlapping patches, reshaped into one-dimensional source vectors and convolved with the polynomial Approximation Kernels of various degrees. As a result, a set of Approximations is obtained. For each element of the source vector, these Approximations are ranked according to the difference between the original and approximated values. A set of indices of polynomial degrees form a local feature. This procedure is repeated for each pixel. Finally, a proposed texture descriptor is obtained from the frequency histogram of all obtained local features. A nearest neighbor classifier utilizing Chi-square distance metric is used to evaluate a performance of the introduced descriptor. An accuracy of texture classification is evaluated on the following datasets: Brodatz, KTH-TIPS, KTH-TIPS2b and Columbia-Utrecht (CUReT) with respect to different methods of texture analysis and classification. The results of this comparison show that the proposed method is competitive with the recent statistical approaches such as local binary patterns (LBP), local ternary patterns, completed LBP, Weber’s local descriptor, and VZ algorithms (VZMR8 and VZ-Joint). At the same time, on KTH-TIPS2-b and KTH-TIPS datasets, the proposed method is slightly inferior to some of the state-of-the-art methods.

Carlo Pierpaoli – One of the best experts on this subject based on the ideXlab platform.

  • Medical Imaging: Image Processing – Estimating intensity variance due to noise in registered images
    Medical Imaging 2005: Image Processing, 2005
    Co-Authors: Gustavo K. Rohde, Alan S. Barnett, Peter J. Basser, Carlo Pierpaoli
    Abstract:

    Image registration refers to the process of finding the spatial correspondence between two or more images. This is usually done by applying a spatial transformation, computed automatic or manually, to a given image using a continuous image model computed either with interpolation or Approximation methods. We show that noise induced signal variance in interpolated images differs significantly from the signal variance of the original images in native space. We describe a simple approach to compute the signal variance in registered images based on the signal variance and covariance of the original images, the spatial transformations computed by the registration procedure, and the interpolation or Approximation Kernel chosen. Our approach is applied to diffusion tensor (DT) MRI data. We show that incorrect noise variance estimates in registered diffusion weighted images can affect the estimated DT parameters, their estimated uncertainty, as well as indices of goodness of fit such as chi-square maps. In addition to DT-MRI, we believe that this methodology would be useful any time parameter extrextraction methods are applied to registered or interpolated data.

  • Estimating intensity variance due to noise in registered images: Applications to diffusion tensor MRI
    NeuroImage, 2005
    Co-Authors: Gustavo K. Rohde, Alan S. Barnett, Peter J. Basser, Carlo Pierpaoli
    Abstract:

    Image registration techniques which require image inteinterpolation are widely used in neuroimaging research. We show that signal variance in interpolated images differs significantly from the signal variance of the original images in native space. We describe a simple approach to compute the signal variance in registered images based on the signal variance and covariance of the original images, the spatial transformations computed by the registration procedure, and the interpolation or Approximation Kernel chosen. The method is general and could handle various sources of signal variability, such as thermal noise and physiological noise, provided that their effects can be assessed in the original images. Our approach is applied to diffusion tensor (DT) MRI data, assuming only thermal noise as the source of variability in the data. We show that incorrect noise variance estimates in registered diffusion-weighted images can affect DT parameters, as well as indices of goodness of fit such as chi-square maps. In addition to DT-MRI, we believe that this methodology would be useful any time parameter extrextraction methods are applied to registered or interpolated data, such as in relaxometry and functional MRI studies.

A I Sherstobitov – One of the best experts on this subject based on the ideXlab platform.

  • local feature descriptor based on 2d local polynomial Approximation Kernel indices
    Proceedings of SPIE, 2014
    Co-Authors: A I Sherstobitov, Vladimir I Marchuk, Dmitriy V Timofeev, Viacheslav V Voronin, Karen Egiazarian
    Abstract:

    A texture descriptor based on a set of indices of degrees of local approximating polynomials is proposed in this paper. First, a method to construct 2D local polynomial Approximation Kernels (k-LPAp) for arbitrary polynomials of degree p is presented. An image is split into non-overlapping patches, reshaped into one-dimensional source vectors and convolved with the polynomial Approximation Kernels of various degrees. As a result, a set of Approximations is obtained. For each element of the source vector, these Approximations are ranked according to the difference between the original and approximated values. A set of indices of polynomial degrees form a local feature. This procedure is repeated for each pixel. Finally, a proposed texture descriptor is obtained from the frequency histogram of all obtained local features. A nearest neighbor classifier utilizing Chi-square distance metric is used to evaluate a performance of the introduced descriptor. An accuracy of texture classification is evaluated on the following datasets: Brodatz, KTH-TIPS, KTH-TIPS2b and Columbia-Utrecht (CUReT) with respect to different methods of texture analysis and classification. The results of this comparison show that the proposed method is competitive with the recent statistical approaches such as local binary patterns (LBP), local ternary patterns, completed LBP, Weber’s local descriptor, and VZ algorithms (VZMR8 and VZ-Joint). At the same time, on KTH-TIPS2-b and KTH-TIPS datasets, the proposed method is slightly inferior to some of the state-of-the-art methods.

  • Image Processing: Algorithms and Systems – Local feature descriptor based on 2D local polynomial Approximation Kernel indices
    Proceedings of SPIE, 2014
    Co-Authors: A I Sherstobitov, Vladimir I Marchuk, Dmitriy V Timofeev, Viacheslav V Voronin, Karen Egiazarian
    Abstract:

    A texture descriptor based on a set of indices of degrees of local approximating polynomials is proposed in this paper. First, a method to construct 2D local polynomial Approximation Kernels (k-LPAp) for arbitrary polynomials of degree p is presented. An image is split into non-overlapping patches, reshaped into one-dimensional source vectors and convolved with the polynomial Approximation Kernels of various degrees. As a result, a set of Approximations is obtained. For each element of the source vector, these Approximations are ranked according to the difference between the original and approximated values. A set of indices of polynomial degrees form a local feature. This procedure is repeated for each pixel. Finally, a proposed texture descriptor is obtained from the frequency histogram of all obtained local features. A nearest neighbor classifier utilizing Chi-square distance metric is used to evaluate a performance of the introduced descriptor. An accuracy of texture classification is evaluated on the following datasets: Brodatz, KTH-TIPS, KTH-TIPS2b and Columbia-Utrecht (CUReT) with respect to different methods of texture analysis and classification. The results of this comparison show that the proposed method is competitive with the recent statistical approaches such as local binary patterns (LBP), local ternary patterns, completed LBP, Weber’s local descriptor, and VZ algorithms (VZMR8 and VZ-Joint). At the same time, on KTH-TIPS2-b and KTH-TIPS datasets, the proposed method is slightly inferior to some of the state-of-the-art methods.

Hannes Nickisch – One of the best experts on this subject based on the ideXlab platform.

  • ICML – Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)
    , 2015
    Co-Authors: Andrew Gordon Wilson, Hannes Nickisch
    Abstract:

    We introduce a new structured Kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce Kernel Approximations for fast computations through Kernel interpolation. The SKI framework clarifies how the quality of an inducing point approach depends on the number of inducing (aka interpolation) points, interpolation strategy, and GP covariance Kernel. SKI also provides a mechanism to create new scalable Kernel methods, through choosing different Kernel interpolation strategies. Using SKI, with local cubic Kernel interpolation, we introduce KISSGP, which is 1) more scalable than inducing point alternatives, 2) naturally enables Kronecker and Toeplitz algebra for substantial additional gains in scalability, without requiring any grid data, and 3) can be used for fast and expressive Kernel learning. KISS-GP costs O(n) time and storage for GP inference. We evaluate KISS-GP for Kernel matrix Approximation, Kernel learning, and natural sound modelling.

  • Kernel Interpolation for Scalable Structured Gaussian Processes (KISS-GP)
    arXiv: Learning, 2015
    Co-Authors: Andrew Gordon Wilson, Hannes Nickisch
    Abstract:

    We introduce a new structured Kernel interpolation (SKI) framework, which generalises and unifies inducing point methods for scalable Gaussian processes (GPs). SKI methods produce Kernel Approximations for fast computations through Kernel interpolation. The SKI framework clarifies how the quality of an inducing point approach depends on the number of inducing (aka interpolation) points, interpolation strategy, and GP covariance Kernel. SKI also provides a mechanism to create new scalable Kernel methods, through choosing different Kernel interpolation strategies. Using SKI, with local cubic Kernel interpolation, we introduce KISS-GP, which is 1) more scalable than inducing point alternatives, 2) naturally enables Kronecker and Toeplitz algebra for substantial additional gains in scalability, without requiring any grid data, and 3) can be used for fast and expressive Kernel learning. KISS-GP costs O(n) time and storage for GP inference. We evaluate KISS-GP for Kernel matrix Approximation, Kernel learning, and natural sound modelling.

Gustavo K. Rohde – One of the best experts on this subject based on the ideXlab platform.

  • Medical Imaging: Image Processing – Estimating intensity variance due to noise in registered images
    Medical Imaging 2005: Image Processing, 2005
    Co-Authors: Gustavo K. Rohde, Alan S. Barnett, Peter J. Basser, Carlo Pierpaoli
    Abstract:

    Image registration refers to the process of finding the spatial correspondence between two or more images. This is usually done by applying a spatial transformation, computed automatic or manually, to a given image using a continuous image model computed either with interpolation or Approximation methods. We show that noise induced signal variance in interpolated images differs significantly from the signal variance of the original images in native space. We describe a simple approach to compute the signal variance in registered images based on the signal variance and covariance of the original images, the spatial transformations computed by the registration procedure, and the interpolation or Approximation Kernel chosen. Our approach is applied to diffusion tensor (DT) MRI data. We show that incorrect noise variance estimates in registered diffusion weighted images can affect the estimated DT parameters, their estimated uncertainty, as well as indices of goodness of fit such as chi-square maps. In addition to DT-MRI, we believe that this methodology would be useful any time parameter extraction methods are applied to registered or interpolated data.

  • Estimating intensity variance due to noise in registered images: Applications to diffusion tensor MRI
    NeuroImage, 2005
    Co-Authors: Gustavo K. Rohde, Alan S. Barnett, Peter J. Basser, Carlo Pierpaoli
    Abstract:

    Image registration techniques which require image interpolation are widely used in neuroimaging research. We show that signal variance in interpolated images differs significantly from the signal variance of the original images in native space. We describe a simple approach to compute the signal variance in registered images based on the signal variance and covariance of the original images, the spatial transformations computed by the registration procedure, and the interpolation or Approximation Kernel chosen. The method is general and could handle various sources of signal variability, such as thermal noise and physiological noise, provided that their effects can be assessed in the original images. Our approach is applied to diffusion tensor (DT) MRI data, assuming only thermal noise as the source of variability in the data. We show that incorrect noise variance estimates in registered diffusion-weighted images can affect DT parameters, as well as indices of goodness of fit such as chi-square maps. In addition to DT-MRI, we believe that this methodology would be useful any time parameter extraction methods are applied to registered or interpolated data, such as in relaxometry and functional MRI studies.