Auxiliary Function

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Kenjiro Yanagi - One of the best experts on this subject based on the ideXlab platform.

Ken Kuriyama - One of the best experts on this subject based on the ideXlab platform.

Mady Elias - One of the best experts on this subject based on the ideXlab platform.

  • Skin color modeling using the radiative transfer equation solved by the Auxiliary Function method: inverse problem
    Journal of the Optical Society of America. A Optics Image Science and Vision, 2008
    Co-Authors: Caroline Magnain, Mady Elias, Jean-marc Frigerio
    Abstract:

    In a previous article [J. Opt. Soc. Am. A 24, 2196 (2007)] we have modeled skin color using the radiative transfer equation, solved by the Auxiliary Function method. Three main parameters have been determined as being predominant in the diversity of skin color: the concentrations of melanosomes and of red blood cells and the oxygen saturation of blood. From the reflectance spectrum measured on real Caucasian skin, these parameters are now evaluated by minimizing the standard deviation on the adjusted wavelength range between the experimental spectrum and simulated spectra gathered in a database. (C) 2008 Optical Society of America.

  • Color modeling of stratified pictorial layers using the radiative transfer equation solved by the Auxiliary Function method
    Journal of the Optical Society of America. A Optics Image Science and Vision, 2007
    Co-Authors: Gael Latour, Mady Elias, Jean-marc Frigerio
    Abstract:

    The diffuse reflectance spectra and the trichromatic coordinates of diffusing stratified paints are modeled. Each layer contains its own pigments, and their optical properties are first determined from experiments. The radiative transfer equation is then solved by the Auxiliary Function method for modeling the total light scattered by the stratified systems. The results are in good agreement with experimental spectra and validate the modeling. The calculations are then applied on the same stratified systems to study the influence of the observation angle in a bidirectional configuration and to study the influence of the thickness of the layers in a given configuration. In both cases, the reflectance spectra and the trichromatic coordinates are calculated and compared.

  • skin color modeling using the radiative transfer equation solved by the Auxiliary Function method
    Journal of The Optical Society of America A-optics Image Science and Vision, 2007
    Co-Authors: Caroline Magnain, Mady Elias, Jean-marc Frigerio
    Abstract:

    The Auxiliary Function method is an efficient technique for solving the radiative tranfer equation without adding any assumption and was applied until now only for theoretical stratified media. The first application (to our knowledge) of the method to a real case, the human skin, is presented. This makes it possible to validate the method by comparing model results with experimental reflectance spectra of real skin. An excellent agreement is obtained for a multilayer model of the skin made of 22 sublayers and taking into account the anisotropic phase Function of the scatterers. Thus there is the opportunity to develop interest in such models by quantitatively evaluating the influence of the parameters commonly used in the literature that modify skin color, such as the concentration of the scatterers and the thickness of each sublayer.

  • special visual effect of art glazes explained by the radiative transfer equation
    Applied Optics, 2004
    Co-Authors: Lionel Simonot, Mady Elias, Eric Charron
    Abstract:

    We present the first modeling of the light scattered by a paint layer in a bidirectional configuration. The studied medium is composed of small concentrated pigments embedded in an oil binder. The color is modulated by changing the number of paint layers, called glazes. The radiative transfer equation is established for incoherent light scattered by the pigments with use of a collimated illumination. The equation is solved by use of the Auxiliary Function method. This new method, applied here for the first time to a practical case, allows for exact computations of the scattered flux for any incident and collected directions. Spectroscopic and goniometric measurements are implemented in bidirectional and backscattered configurations. The excellent agreement between the measurement and the simulation validates the assumptions used for the glaze model and proves the effectiveness of the Auxiliary Function method.

  • radiative transfer in inhomogeneous stratified scattering media with use of the Auxiliary Function method
    Journal of The Optical Society of America A-optics Image Science and Vision, 2004
    Co-Authors: Mady Elias, Georges Elias
    Abstract:

    The Auxiliary Function method consists of taking full advantage of the expansion of the phase Function on spherical harmonics in order to deduce an integral equation from the radiative transfer equation. In contrast to the discrete-ordinate method, it is free of the channel concept, the unknowns being a Function only of the optical depth. After presenting the method, we show that it is very accurate and particularly well fitted when the scattering medium is continuously inhomogeneous in albedo and phase Function and also for sublayers with different refractive index.

Jean-marc Frigerio - One of the best experts on this subject based on the ideXlab platform.

  • Skin color modeling using the radiative transfer equation solved by the Auxiliary Function method: inverse problem
    Journal of the Optical Society of America. A Optics Image Science and Vision, 2008
    Co-Authors: Caroline Magnain, Mady Elias, Jean-marc Frigerio
    Abstract:

    In a previous article [J. Opt. Soc. Am. A 24, 2196 (2007)] we have modeled skin color using the radiative transfer equation, solved by the Auxiliary Function method. Three main parameters have been determined as being predominant in the diversity of skin color: the concentrations of melanosomes and of red blood cells and the oxygen saturation of blood. From the reflectance spectrum measured on real Caucasian skin, these parameters are now evaluated by minimizing the standard deviation on the adjusted wavelength range between the experimental spectrum and simulated spectra gathered in a database. (C) 2008 Optical Society of America.

  • Color modeling of stratified pictorial layers using the radiative transfer equation solved by the Auxiliary Function method
    Journal of the Optical Society of America. A Optics Image Science and Vision, 2007
    Co-Authors: Gael Latour, Mady Elias, Jean-marc Frigerio
    Abstract:

    The diffuse reflectance spectra and the trichromatic coordinates of diffusing stratified paints are modeled. Each layer contains its own pigments, and their optical properties are first determined from experiments. The radiative transfer equation is then solved by the Auxiliary Function method for modeling the total light scattered by the stratified systems. The results are in good agreement with experimental spectra and validate the modeling. The calculations are then applied on the same stratified systems to study the influence of the observation angle in a bidirectional configuration and to study the influence of the thickness of the layers in a given configuration. In both cases, the reflectance spectra and the trichromatic coordinates are calculated and compared.

  • skin color modeling using the radiative transfer equation solved by the Auxiliary Function method
    Journal of The Optical Society of America A-optics Image Science and Vision, 2007
    Co-Authors: Caroline Magnain, Mady Elias, Jean-marc Frigerio
    Abstract:

    The Auxiliary Function method is an efficient technique for solving the radiative tranfer equation without adding any assumption and was applied until now only for theoretical stratified media. The first application (to our knowledge) of the method to a real case, the human skin, is presented. This makes it possible to validate the method by comparing model results with experimental reflectance spectra of real skin. An excellent agreement is obtained for a multilayer model of the skin made of 22 sublayers and taking into account the anisotropic phase Function of the scatterers. Thus there is the opportunity to develop interest in such models by quantitatively evaluating the influence of the parameters commonly used in the literature that modify skin color, such as the concentration of the scatterers and the thickness of each sublayer.

Nobutaka Ono - One of the best experts on this subject based on the ideXlab platform.

  • Auxiliary Function approach to independent component analysis and independent vector analysis
    Independent Component Analyses Compressive Sampling Large Data Analyses (LDA) Neural Networks Biosystems and Nanoengineering XIII, 2015
    Co-Authors: Nobutaka Ono
    Abstract:

    In this paper, we review an Auxiliary Function approach to independent component analysis (ICA) and independent vector analysis (IVA). The derived algorithm consists of two alternative updates: 1) weighted covariance matrix update and 2) demixing matrix update, which include no tuning parameters such as a step size in the gradient descent method. The monotonic decrease of the objective Function is guaranteed by the principle of the Auxiliary Function method. The experimental evaluation shows that the derived update rules yield faster convergence and better results than natural gradient updates. An efficient implementation on a mobile phone is also presented.

  • ICASSP - Fast DNN training based on Auxiliary Function technique
    2015 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2015
    Co-Authors: Dung T. Tran, Nobutaka Ono, Emmanuel Vincent
    Abstract:

    Deep neural networks (DNN) are typically optimized with stochastic gradient descent (SGD) using a fixed learning rate or an adaptive learning rate approach (ADAGRAD). In this paper, we introduce a new learning rule for neural networks that is based on an Auxiliary Function technique without parameter tuning. Instead of minimizing the objective Function, a quadratic Auxiliary Function is recursively introduced layer by layer which has a closed-form optimum. We prove the monotonic decrease of the new learning rule. Our experiments show that the proposed algorithm converges faster and to a better local minimum than SGD. In addition, we propose a combination of the proposed learning rule and ADAGRAD which further accelerates convergence. Experimental evaluation on the MNIST database shows the benefit of the proposed approach in terms of digit recognition accuracy.

  • an Auxiliary Function approach to online independent vector analysis for real time blind source separation
    2014 4th Joint Workshop on Hands-free Speech Communication and Microphone Arrays (HSCMA), 2014
    Co-Authors: Toru Taniguchi, Nobutaka Ono, Akinori Kawamura, Shigeki Sagayama
    Abstract:

    This paper proposes online independent vector analysis (IVA) based on an Auxiliary-Function approach for real-time blind speech separation. A batch Auxiliary-Function approach is naturally extended with autoregressive approximation of an Auxiliary variable. Experimental evaluations show that the proposed online algorithm works in real time and attains relatively high signal-to-interference ratios without environment-sensitive tuning parameters such as step size under both spatially stationary and dynamic conditions compared to usual real-time IVAs using natural gradient updates or block-wise updates. Our implementation of the proposed algorithm works in real-time for four-channel observations on PCs and worked stably over 7 hours in realistic noisy environments.

  • Auxiliary Function based independent vector analysis with power of vector norm type weighting Functions
    Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, 2012
    Co-Authors: Nobutaka Ono
    Abstract:

    In this paper, we present an Auxiliary-Function-based independent vector analysis (AuxIVA) based on the Generalized super Gaussian source model or Gaussian source model with time-varying variance. AuxIVA is a convergence-guaranteed iterative algorithm for independent vector analysis (IVA) with a spherical and super Gaussian source model, and the source model can be characterized by a weighting Function. We show that both of the generalized Gaussian source models with the shape parameter 0 < β ≤ 2 and the Gaussian source model with time-varying variance unifiedly yield a power of vector-norm type weighting Functions. A scaling and a clipping technique for numerical stability are discussed. The dependency of the separation performance on the source model is also investigated.

  • stable and fast update rules for independent vector analysis based on Auxiliary Function technique
    Workshop on Applications of Signal Processing to Audio and Acoustics, 2011
    Co-Authors: Nobutaka Ono
    Abstract:

    This paper presents stable and fast update rules for independent vector analysis (IVA) based on Auxiliary Function technique. The algorithm consists of two alternative updates: 1) weighted covariance matrix updates and 2) demixing matrix updates, which include no tuning parameters such as step size. The monotonic decrease of the objective Function at each update is guaranteed. The experimental evaluation shows that the derived update rules yield faster convergence and better results than natural gradient updates.