Regular Grid

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Rodney A Kennedy - One of the best experts on this subject based on the ideXlab platform.

  • spherical harmonic transform for minimum dimensionality Regular Grid sampling on the sphere
    International Conference on Acoustics Speech and Signal Processing, 2015
    Co-Authors: Zubair Khalid, Rodney A Kennedy
    Abstract:

    We develop a method to compute spherical harmonic transform (SHT) of a band-limited signal on the sphere discretized over a minimum dimensionality Regular sampling Grid on the sphere. For the computation of SHT of a signal band-limited at L, the proposed method requires L2 number of samples on a Regular Grid composed of L iso-latitude rings of samples with only L samples in each ring along longitude. Since a signal band-limited at L is represented by L2 degrees of freedom in the spectral (spherical harmonic) domain, the proposed method requires the minimal number of samples for the computation of SHT. In comparison to the other schemes that require 2L − 1 samples along each iso-latitude ring, we show that the SHT can be computed, by exploiting the structure of spectral domain, from only L samples in each iso-latitude ring. We also analyse the numerical accuracy and the computational complexity of our proposed SHT for a Regular Grid with equiangular sampling. We demonstrate, through numerical experiments, that the proposed SHT is sufficiently accurate for band-limits of interest in diffusion magnetic resonance imaging.

  • ICASSP - Spherical harmonic transform for minimum dimensionality Regular Grid sampling on the sphere
    2015 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2015
    Co-Authors: Zubair Khalid, Rodney A Kennedy
    Abstract:

    We develop a method to compute spherical harmonic transform (SHT) of a band-limited signal on the sphere discretized over a minimum dimensionality Regular sampling Grid on the sphere. For the computation of SHT of a signal band-limited at L, the proposed method requires L2 number of samples on a Regular Grid composed of L iso-latitude rings of samples with only L samples in each ring along longitude. Since a signal band-limited at L is represented by L2 degrees of freedom in the spectral (spherical harmonic) domain, the proposed method requires the minimal number of samples for the computation of SHT. In comparison to the other schemes that require 2L − 1 samples along each iso-latitude ring, we show that the SHT can be computed, by exploiting the structure of spectral domain, from only L samples in each iso-latitude ring. We also analyse the numerical accuracy and the computational complexity of our proposed SHT for a Regular Grid with equiangular sampling. We demonstrate, through numerical experiments, that the proposed SHT is sufficiently accurate for band-limits of interest in diffusion magnetic resonance imaging.

Masatoshi Okutomi - One of the best experts on this subject based on the ideXlab platform.

  • direct generation of Regular Grid ground surface map from in vehicle stereo image sequences
    International Conference on Computer Vision, 2013
    Co-Authors: Shigeki Sugimoto, Kouma Motooka, Masatoshi Okutomi
    Abstract:

    We propose a direct method for incrementally estimating a Regular-Grid ground surface map from stereo image sequences captured by nearly front-looking stereo cameras, taking illumination changes on all images into consideration. At each frame, we simultaneously estimate a camera motion and vertex heights of the Regular mesh, composed of piecewise triangular patches, drawn on a level plane in the ground coordinate system, by minimizing a cost representing the differences of the photo metrically transformed pixel values in homography-related projective triangular patches over three image pairs in a two-frame stereo image sequence. The data term is formulated by the Inverse Compositional trick for high computational efficiency. The main difficulty of the problem formulation lies in the instability of the height estimation for the vertices distant from the cameras. We first develop a stereo ground surface reconstruction method where the stability is effectively improved by the combinational use of three complementary techniques, the use of a smoothness term, update constraint term, and a hierarchical meshing approach. Then we extend the stereo method for incremental ground surface map generation. The validity of the proposed method is demonstrated through experiments using real images.

  • ICCV Workshops - Direct Generation of Regular-Grid Ground Surface Map from In-Vehicle Stereo Image Sequences
    2013 IEEE International Conference on Computer Vision Workshops, 2013
    Co-Authors: Shigeki Sugimoto, Kouma Motooka, Masatoshi Okutomi
    Abstract:

    We propose a direct method for incrementally estimating a Regular-Grid ground surface map from stereo image sequences captured by nearly front-looking stereo cameras, taking illumination changes on all images into consideration. At each frame, we simultaneously estimate a camera motion and vertex heights of the Regular mesh, composed of piecewise triangular patches, drawn on a level plane in the ground coordinate system, by minimizing a cost representing the differences of the photo metrically transformed pixel values in homography-related projective triangular patches over three image pairs in a two-frame stereo image sequence. The data term is formulated by the Inverse Compositional trick for high computational efficiency. The main difficulty of the problem formulation lies in the instability of the height estimation for the vertices distant from the cameras. We first develop a stereo ground surface reconstruction method where the stability is effectively improved by the combinational use of three complementary techniques, the use of a smoothness term, update constraint term, and a hierarchical meshing approach. Then we extend the stereo method for incremental ground surface map generation. The validity of the proposed method is demonstrated through experiments using real images.

Zubair Khalid - One of the best experts on this subject based on the ideXlab platform.

  • spherical harmonic transform for minimum dimensionality Regular Grid sampling on the sphere
    International Conference on Acoustics Speech and Signal Processing, 2015
    Co-Authors: Zubair Khalid, Rodney A Kennedy
    Abstract:

    We develop a method to compute spherical harmonic transform (SHT) of a band-limited signal on the sphere discretized over a minimum dimensionality Regular sampling Grid on the sphere. For the computation of SHT of a signal band-limited at L, the proposed method requires L2 number of samples on a Regular Grid composed of L iso-latitude rings of samples with only L samples in each ring along longitude. Since a signal band-limited at L is represented by L2 degrees of freedom in the spectral (spherical harmonic) domain, the proposed method requires the minimal number of samples for the computation of SHT. In comparison to the other schemes that require 2L − 1 samples along each iso-latitude ring, we show that the SHT can be computed, by exploiting the structure of spectral domain, from only L samples in each iso-latitude ring. We also analyse the numerical accuracy and the computational complexity of our proposed SHT for a Regular Grid with equiangular sampling. We demonstrate, through numerical experiments, that the proposed SHT is sufficiently accurate for band-limits of interest in diffusion magnetic resonance imaging.

  • ICASSP - Spherical harmonic transform for minimum dimensionality Regular Grid sampling on the sphere
    2015 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2015
    Co-Authors: Zubair Khalid, Rodney A Kennedy
    Abstract:

    We develop a method to compute spherical harmonic transform (SHT) of a band-limited signal on the sphere discretized over a minimum dimensionality Regular sampling Grid on the sphere. For the computation of SHT of a signal band-limited at L, the proposed method requires L2 number of samples on a Regular Grid composed of L iso-latitude rings of samples with only L samples in each ring along longitude. Since a signal band-limited at L is represented by L2 degrees of freedom in the spectral (spherical harmonic) domain, the proposed method requires the minimal number of samples for the computation of SHT. In comparison to the other schemes that require 2L − 1 samples along each iso-latitude ring, we show that the SHT can be computed, by exploiting the structure of spectral domain, from only L samples in each iso-latitude ring. We also analyse the numerical accuracy and the computational complexity of our proposed SHT for a Regular Grid with equiangular sampling. We demonstrate, through numerical experiments, that the proposed SHT is sufficiently accurate for band-limits of interest in diffusion magnetic resonance imaging.

Shigeki Sugimoto - One of the best experts on this subject based on the ideXlab platform.

  • direct generation of Regular Grid ground surface map from in vehicle stereo image sequences
    International Conference on Computer Vision, 2013
    Co-Authors: Shigeki Sugimoto, Kouma Motooka, Masatoshi Okutomi
    Abstract:

    We propose a direct method for incrementally estimating a Regular-Grid ground surface map from stereo image sequences captured by nearly front-looking stereo cameras, taking illumination changes on all images into consideration. At each frame, we simultaneously estimate a camera motion and vertex heights of the Regular mesh, composed of piecewise triangular patches, drawn on a level plane in the ground coordinate system, by minimizing a cost representing the differences of the photo metrically transformed pixel values in homography-related projective triangular patches over three image pairs in a two-frame stereo image sequence. The data term is formulated by the Inverse Compositional trick for high computational efficiency. The main difficulty of the problem formulation lies in the instability of the height estimation for the vertices distant from the cameras. We first develop a stereo ground surface reconstruction method where the stability is effectively improved by the combinational use of three complementary techniques, the use of a smoothness term, update constraint term, and a hierarchical meshing approach. Then we extend the stereo method for incremental ground surface map generation. The validity of the proposed method is demonstrated through experiments using real images.

  • ICCV Workshops - Direct Generation of Regular-Grid Ground Surface Map from In-Vehicle Stereo Image Sequences
    2013 IEEE International Conference on Computer Vision Workshops, 2013
    Co-Authors: Shigeki Sugimoto, Kouma Motooka, Masatoshi Okutomi
    Abstract:

    We propose a direct method for incrementally estimating a Regular-Grid ground surface map from stereo image sequences captured by nearly front-looking stereo cameras, taking illumination changes on all images into consideration. At each frame, we simultaneously estimate a camera motion and vertex heights of the Regular mesh, composed of piecewise triangular patches, drawn on a level plane in the ground coordinate system, by minimizing a cost representing the differences of the photo metrically transformed pixel values in homography-related projective triangular patches over three image pairs in a two-frame stereo image sequence. The data term is formulated by the Inverse Compositional trick for high computational efficiency. The main difficulty of the problem formulation lies in the instability of the height estimation for the vertices distant from the cameras. We first develop a stereo ground surface reconstruction method where the stability is effectively improved by the combinational use of three complementary techniques, the use of a smoothness term, update constraint term, and a hierarchical meshing approach. Then we extend the stereo method for incremental ground surface map generation. The validity of the proposed method is demonstrated through experiments using real images.

Kouma Motooka - One of the best experts on this subject based on the ideXlab platform.

  • direct generation of Regular Grid ground surface map from in vehicle stereo image sequences
    International Conference on Computer Vision, 2013
    Co-Authors: Shigeki Sugimoto, Kouma Motooka, Masatoshi Okutomi
    Abstract:

    We propose a direct method for incrementally estimating a Regular-Grid ground surface map from stereo image sequences captured by nearly front-looking stereo cameras, taking illumination changes on all images into consideration. At each frame, we simultaneously estimate a camera motion and vertex heights of the Regular mesh, composed of piecewise triangular patches, drawn on a level plane in the ground coordinate system, by minimizing a cost representing the differences of the photo metrically transformed pixel values in homography-related projective triangular patches over three image pairs in a two-frame stereo image sequence. The data term is formulated by the Inverse Compositional trick for high computational efficiency. The main difficulty of the problem formulation lies in the instability of the height estimation for the vertices distant from the cameras. We first develop a stereo ground surface reconstruction method where the stability is effectively improved by the combinational use of three complementary techniques, the use of a smoothness term, update constraint term, and a hierarchical meshing approach. Then we extend the stereo method for incremental ground surface map generation. The validity of the proposed method is demonstrated through experiments using real images.

  • ICCV Workshops - Direct Generation of Regular-Grid Ground Surface Map from In-Vehicle Stereo Image Sequences
    2013 IEEE International Conference on Computer Vision Workshops, 2013
    Co-Authors: Shigeki Sugimoto, Kouma Motooka, Masatoshi Okutomi
    Abstract:

    We propose a direct method for incrementally estimating a Regular-Grid ground surface map from stereo image sequences captured by nearly front-looking stereo cameras, taking illumination changes on all images into consideration. At each frame, we simultaneously estimate a camera motion and vertex heights of the Regular mesh, composed of piecewise triangular patches, drawn on a level plane in the ground coordinate system, by minimizing a cost representing the differences of the photo metrically transformed pixel values in homography-related projective triangular patches over three image pairs in a two-frame stereo image sequence. The data term is formulated by the Inverse Compositional trick for high computational efficiency. The main difficulty of the problem formulation lies in the instability of the height estimation for the vertices distant from the cameras. We first develop a stereo ground surface reconstruction method where the stability is effectively improved by the combinational use of three complementary techniques, the use of a smoothness term, update constraint term, and a hierarchical meshing approach. Then we extend the stereo method for incremental ground surface map generation. The validity of the proposed method is demonstrated through experiments using real images.