The Experts below are selected from a list of 4311 Experts worldwide ranked by ideXlab platform

Erwan Deriaz - One of the best experts on this subject based on the ideXlab platform.

  • Wavelet Helmholtz Decomposition for weak lensing mass map reconstruction
    Astronomy & Astrophysics, 2012
    Co-Authors: Erwan Deriaz, J L Starck, S Pires
    Abstract:

    Laboratoire AIM, UMR CEA-CNRS-Paris 7, Irfu, SEDI-SAP, Service d’Astrophysique, CEA Saclay, F-91191GIF-Sur-YVETTE CEDEX, FranceJanuary 26, 2012Abstract To derive the convergence eld from the gravitational shear of the background galaxy images, theclassical methods require a convolution of the shear to be performed over the entire sky, usually expressed thanksto the Fast Fourier transform (FFT). However, it is not optimal for an imperfect geometry survey. Furthermore,FFT implicitly uses periodic conditions that introduce errors to the reconstruction. A method has been proposedthat relies on computation of an intermediate eld uthat combines the derivatives of and on convolution with aGreen kernel. In this paper, we study the wavelet Helmholtz Decomposition as a new approach to reconstructingthe dark matter mass map. We show that a link exists between the Helmholtz Decomposition and the E/B modeseparation. We introduce a new wavelet construction, that has a property that gives us more exibility in handlingthe border problem, and we propose a new method of reconstructing the dark matter mass map in the waveletspace. A set of experiments based on noise-free images illustrates that this Wavelet Helmholtz Decompositionreconstructs the borders better than all other existing methods.

  • wavelet Helmholtz Decomposition for weak lensing mass map reconstruction
    arXiv: Cosmology and Nongalactic Astrophysics, 2012
    Co-Authors: Erwan Deriaz, J L Starck, S Pires
    Abstract:

    To derive the convergence field from the gravitational shear (gamma) of the background galaxy images, the classical methods require a convolution of the shear to be performed over the entire sky, usually expressed thanks to the Fast Fourier transform (FFT). However, it is not optimal for an imperfect geometry survey. Furthermore, FFT implicitly uses periodic conditions that introduce errors to the reconstruction. A method has been proposed that relies on computation of an intermediate field u that combines the derivatives of gamma and on convolution with a Green kernel. In this paper, we study the wavelet Helmholtz Decomposition as a new approach to reconstructing the dark matter mass map. We show that a link exists between the Helmholtz Decomposition and the E/B mode separation. We introduce a new wavelet construction, that has a property that gives us more flexibility in handling the border problem, and we propose a new method of reconstructing the dark matter mass map in the wavelet space. A set of experiments based on noise-free images illustrates that this Wavelet Helmholtz Decomposition reconstructs the borders better than all other existing methods.

  • Orthogonal Helmholtz Decomposition in arbitrary dimension using divergence-free and curl-free wavelets
    Applied and Computational Harmonic Analysis, 2009
    Co-Authors: Erwan Deriaz, Valérie Perrier
    Abstract:

    Abstract We present tensor-product divergence-free and curl-free wavelets, and define associated projectors. These projectors enable the construction of an iterative algorithm to compute the Helmholtz Decomposition of any vector field, in wavelet domain. This Decomposition is localized in space, in contrast to the Helmholtz Decomposition calculated by Fourier transform. Then we prove the convergence of the algorithm in dimension two for any kind of wavelets, and in larger dimension for the particular case of Shannon wavelets. We also present a modification of the algorithm by using quasi-isotropic divergence-free and curl-free wavelets. Finally, numerical tests show the validity of this approach for a large class of wavelets.

  • Décomposition de Helmholtz par ondelettes : convergence d'un algorithme itératif
    2007
    Co-Authors: Erwan Deriaz, Kai Bittner, Valérie Perrier
    Abstract:

    In what follows, we present tensor-product divergence-free and curl-free wavelets, and we define associated projectors. These projectors permit the construction of an iterative algorithm for the computation of the Helmholtz Decomposition in terms of wavelets. This Helmholtz Decomposition is localized in space, in contrast to a Helmholtz Decomposition calculated by the Fourier transform. Finally, we show the convergence of the algorithm in 2 and 3 dimensions for the particular case of Shannon wavelets.

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

  • Wavelet Helmholtz Decomposition for weak lensing mass map reconstruction
    Astronomy & Astrophysics, 2012
    Co-Authors: Erwan Deriaz, J L Starck, S Pires
    Abstract:

    Laboratoire AIM, UMR CEA-CNRS-Paris 7, Irfu, SEDI-SAP, Service d’Astrophysique, CEA Saclay, F-91191GIF-Sur-YVETTE CEDEX, FranceJanuary 26, 2012Abstract To derive the convergence eld from the gravitational shear of the background galaxy images, theclassical methods require a convolution of the shear to be performed over the entire sky, usually expressed thanksto the Fast Fourier transform (FFT). However, it is not optimal for an imperfect geometry survey. Furthermore,FFT implicitly uses periodic conditions that introduce errors to the reconstruction. A method has been proposedthat relies on computation of an intermediate eld uthat combines the derivatives of and on convolution with aGreen kernel. In this paper, we study the wavelet Helmholtz Decomposition as a new approach to reconstructingthe dark matter mass map. We show that a link exists between the Helmholtz Decomposition and the E/B modeseparation. We introduce a new wavelet construction, that has a property that gives us more exibility in handlingthe border problem, and we propose a new method of reconstructing the dark matter mass map in the waveletspace. A set of experiments based on noise-free images illustrates that this Wavelet Helmholtz Decompositionreconstructs the borders better than all other existing methods.

  • wavelet Helmholtz Decomposition for weak lensing mass map reconstruction
    arXiv: Cosmology and Nongalactic Astrophysics, 2012
    Co-Authors: Erwan Deriaz, J L Starck, S Pires
    Abstract:

    To derive the convergence field from the gravitational shear (gamma) of the background galaxy images, the classical methods require a convolution of the shear to be performed over the entire sky, usually expressed thanks to the Fast Fourier transform (FFT). However, it is not optimal for an imperfect geometry survey. Furthermore, FFT implicitly uses periodic conditions that introduce errors to the reconstruction. A method has been proposed that relies on computation of an intermediate field u that combines the derivatives of gamma and on convolution with a Green kernel. In this paper, we study the wavelet Helmholtz Decomposition as a new approach to reconstructing the dark matter mass map. We show that a link exists between the Helmholtz Decomposition and the E/B mode separation. We introduce a new wavelet construction, that has a property that gives us more flexibility in handling the border problem, and we propose a new method of reconstructing the dark matter mass map in the wavelet space. A set of experiments based on noise-free images illustrates that this Wavelet Helmholtz Decomposition reconstructs the borders better than all other existing methods.

Christoph Schnorr - One of the best experts on this subject based on the ideXlab platform.

  • Scale-Space - Variational dense motion estimation using the Helmholtz Decomposition
    Scale Space Methods in Computer Vision, 2003
    Co-Authors: Timo Kohlberger, Etienne Memin, Christoph Schnorr
    Abstract:

    We present a novel variational approach to dense motion estimation of highly non-rigid structures in image sequences. Our representation of the motion vector field is based on the extended Helmholtz Decomposition into its principal constituents: The laminar flow and two potential functions related to the solenoidal and irrotational flow, respectively. The potential functions, which are of primary interest for flow pattern analysis in numerous application fields like remote sensing or fluid mechanics, are directly estimated from image sequences with a variational approach. We use regularizers with derivatives up to third order to obtain unbiased high-quality solutions. Computationally, the approach is made tractable by means of auxiliary variables. The performance of the approach is demonstrated with ground-truth experiments and real-world data.

  • variational dense motion estimation using the Helmholtz Decomposition
    Lecture Notes in Computer Science, 2003
    Co-Authors: Timo Kohlberger, Etienne Memin, Christoph Schnorr
    Abstract:

    We present a novel variational approach to dense motion estimation of highly non-rigid structures in image sequences. Our representation of the motion vector field is based on the extended Helmholtz Decomposition into its principal constituents: The laminar flow and two potential functions related to the solenoidal and irrotational flow, respectively. The potential functions, which are of primary interest for flow pattern analysis in numerous application fields like remote sensing or fluid mechanics, are directly estimated from image sequences with a variational approach. We use regularizers with derivatives up to third order to obtain unbiased high-quality solutions. Computationally, the approach is made tractable by means of auxiliary variables. The performance of the approach is demonstrated with ground-truth experiments and real-world data.

Timo Kohlberger - One of the best experts on this subject based on the ideXlab platform.

  • Scale-Space - Variational dense motion estimation using the Helmholtz Decomposition
    Scale Space Methods in Computer Vision, 2003
    Co-Authors: Timo Kohlberger, Etienne Memin, Christoph Schnorr
    Abstract:

    We present a novel variational approach to dense motion estimation of highly non-rigid structures in image sequences. Our representation of the motion vector field is based on the extended Helmholtz Decomposition into its principal constituents: The laminar flow and two potential functions related to the solenoidal and irrotational flow, respectively. The potential functions, which are of primary interest for flow pattern analysis in numerous application fields like remote sensing or fluid mechanics, are directly estimated from image sequences with a variational approach. We use regularizers with derivatives up to third order to obtain unbiased high-quality solutions. Computationally, the approach is made tractable by means of auxiliary variables. The performance of the approach is demonstrated with ground-truth experiments and real-world data.

  • variational dense motion estimation using the Helmholtz Decomposition
    Lecture Notes in Computer Science, 2003
    Co-Authors: Timo Kohlberger, Etienne Memin, Christoph Schnorr
    Abstract:

    We present a novel variational approach to dense motion estimation of highly non-rigid structures in image sequences. Our representation of the motion vector field is based on the extended Helmholtz Decomposition into its principal constituents: The laminar flow and two potential functions related to the solenoidal and irrotational flow, respectively. The potential functions, which are of primary interest for flow pattern analysis in numerous application fields like remote sensing or fluid mechanics, are directly estimated from image sequences with a variational approach. We use regularizers with derivatives up to third order to obtain unbiased high-quality solutions. Computationally, the approach is made tractable by means of auxiliary variables. The performance of the approach is demonstrated with ground-truth experiments and real-world data.

Mrinal Mandal - One of the best experts on this subject based on the ideXlab platform.

  • singular point detection using discrete hodge Helmholtz Decomposition in fingerprint images
    International Conference on Acoustics Speech and Signal Processing, 2010
    Co-Authors: Hengzhen Gao, Mrinal Mandal, Gencheng Guo, Jianwei Wan
    Abstract:

    Identification of singular points in the ridge structure is an important problem in fingerprint matching. This paper presents a fingerprint singular point detection method that is applicable to various fingerprint images regardless of their resolutions. Using the Discrete Hodge Helmholtz Decomposition (DHHD) method, potential structures of singular points can be extracted. We also calculate Poincare Index (PI) of the image. Then we combine DHHD and PI to detect singular points. The result of the experiment on the public databases with different images demonstrates that the proposed method has high accuracy in locating singular points.

  • ICASSP - Singular point detection using Discrete Hodge Helmholtz Decomposition in fingerprint images
    2010 IEEE International Conference on Acoustics Speech and Signal Processing, 2010
    Co-Authors: Hengzhen Gao, Mrinal Mandal, Gencheng Guo, Jianwei Wan
    Abstract:

    Identification of singular points in the ridge structure is an important problem in fingerprint matching. This paper presents a fingerprint singular point detection method that is applicable to various fingerprint images regardless of their resolutions. Using the Discrete Hodge Helmholtz Decomposition (DHHD) method, potential structures of singular points can be extracted. We also calculate Poincare Index (PI) of the image. Then we combine DHHD and PI to detect singular points. The result of the experiment on the public databases with different images demonstrates that the proposed method has high accuracy in locating singular points.

  • applications of the discrete hodge Helmholtz Decomposition to image and video processing
    Pattern Recognition and Machine Intelligence, 2005
    Co-Authors: Biswaroop Palit, Anup Basu, Mrinal Mandal
    Abstract:

    The Discrete Hodge Helmholtz Decomposition (DHHD) is able to locate critical points in a vector field. We explore two novel applications of this technique to image processing problems, viz., hurricane tracking and fingerprint analysis. The eye of the hurricane represents a rotational center, which is shown to be robustly detected using DHHD. This is followed by an automatic segmentation and tracking of the hurricane eye, which does not require manual initializations. DHHD is also used for identification of reference points in fingerprints. The new technique for reference point detection is relatively insensitive to noise in the orientation field. The DHHD based method is shown to detect reference points correctly for 96.25% of the images in the database used.

  • efficient hodge Helmholtz Decomposition of motion fields
    Pattern Recognition Letters, 2005
    Co-Authors: Qinghong Guo, Mrinal Mandal
    Abstract:

    Motion analysis is an active but challenging research area. In this paper, we propose a simplified implementation of the recently developed discrete Hodge-Helmholtz field Decomposition (DHHFD) using the finite element method. The DHHFD can decompose an arbitrary flow field into three components: a curl-free component, a divergence-free component, and a harmonic remainder. Experimental results show that the proposed implementation provides an excellent motion field Decomposition performance.

  • PReMI - Applications of the discrete hodge Helmholtz Decomposition to image and video processing
    Lecture Notes in Computer Science, 2005
    Co-Authors: Biswaroop Palit, Anup Basu, Mrinal Mandal
    Abstract:

    The Discrete Hodge Helmholtz Decomposition (DHHD) is able to locate critical points in a vector field. We explore two novel applications of this technique to image processing problems, viz., hurricane tracking and fingerprint analysis. The eye of the hurricane represents a rotational center, which is shown to be robustly detected using DHHD. This is followed by an automatic segmentation and tracking of the hurricane eye, which does not require manual initializations. DHHD is also used for identification of reference points in fingerprints. The new technique for reference point detection is relatively insensitive to noise in the orientation field. The DHHD based method is shown to detect reference points correctly for 96.25% of the images in the database used.