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Approximation Kernel

The Experts below are selected from a list of 81 Experts worldwide ranked by ideXlab platform

Karen Egiazarian – 1st expert 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 – 2nd expert 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.

A I Sherstobitov – 3rd expert 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.