Robust Factorization Methods Using a Gaussian/Uniform Mixture Model

Zaharescu, Andrei; Horaud, Radu

doi:10.1007/s11263-008-0169-x

Cited by 16 publications

(6 citation statements)

References 40 publications

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“…In order to assess the performance of GStudent-EM, we compared it with the use of a Gaussian distribution and with a Gaussian-uniform mixture (GUM) distribution with a single Gaussian component [56]. The use of a uniform component in addition to Gaussian components in a mixture was initially proposed in [5].…”

Section: Performance Analysismentioning

confidence: 99%

Robust Face Frontalization For Visual Speech Recognition

Kang

Horaud

Sadeghi

2021

2021 IEEE/CVF International Conference on Computer Vision Workshops (ICCVW)

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Face frontalization consists of synthesizing a frontallyviewed face from an arbitrarily-viewed one. The main contribution of this paper is a robust frontalization method that preserves non-rigid facial deformations, i.e. expressions, to perform lip reading. The method iteratively estimates the rigid transformation (scale, rotation, and translation) and the non-rigid deformation between 3D landmarks extracted from an arbitrarily-viewed face, and 3D vertices parameterized by a deformable shape model. An important merit of the method is its ability to deal with large Gaussian and non-Gaussian errors in the data. For that purpose, we use the generalized Student-t distribution. The associated EM algorithm assigns a weight to each observed landmark, the higher the weight the more important the landmark, thus favoring landmarks that are only affected by rigid head movements. We propose to use the zero-mean normalized cross-correlation (ZNCC) score to evaluate the ability to preserve facial expressions. We show that the method, when incorporated into a deep lipreading pipeline, considerably improves the word classification score on an in-the-wild benchmark. An extended version with supplemental materials can be found at https: //team.inria.fr/robotlearn/rff-vsr/ * This work has been partially supported by MIAI@Grenoble Alpes (ANR-19-P3IA-0003).

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Section: Performance Analysismentioning

confidence: 99%

Robust Face Frontalization For Visual Speech Recognition

Kang

Horaud

Sadeghi

2021

2021 IEEE/CVF International Conference on Computer Vision Workshops (ICCVW)

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“…We refer to [1,14,18,8,7] and references therein for other, mostly iterative approaches to solve this low-rank SfM problem.…”

Section: Application To Projective Sfmmentioning

confidence: 99%

The generalized trace-norm and its application to structure-from-motion problems

Angst

Zach

Pollefeys

2011

2011 International Conference on Computer Vision

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In geometric computer vision, the structure from motion (SfM) problem can be formulated as a optimization problem with a rank constraint. It is well known that the trace norm of a matrix can act as a convex proxy for a low rank constraint. Hence, in recent work [7], the trace-norm relaxation has been applied to the SfM problem. However, SfM problems often exhibit a certain structure, for example a smooth camera path. Unfortunately, the trace norm relaxation can not make use of this additional structure. This observation motivates the main contribution of this paper. We present the so-called generalized trace norm which allows to encode prior knowledge about a specific problem into a convex regularization term which enforces a low rank solution while at the same time taking the problem structure into account.While deriving the generalized trace norm and stating its different formulations, we draw interesting connections to other fields, most importantly to the field of compressive sensing. Even though the generalized trace norm is a very general concept with a wide area of potential applications we are ultimately interested in applying it to SfM problems. Therefore, we also present an efficient algorithm to optimize the resulting generalized trace norm regularized optimization problems. Results show that the generalized trace norm indeed achieves its goals in providing a problem-dependent regularization.

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“…Xu et al 12 used robust linear regression and analyzed the association between DNA copy number and gene expression in tumor cells from metastatic lymph nodes in patients with oral squamous cell carcinoma. In computer vision, robust regression methods have been used extensively to estimate surface model parameters in small image regions and imaging geometry of multiple cameras (see Stewart 13 and the more recent work of Zaharescu and Horaud 14 ). In the analysis of gene microarrays, Ahdesmäki et al 15 proposed use of robust M estimation of regression when dealing with biological time series models.…”

Section: Introductionmentioning

confidence: 99%

TELBS robust linear regression method

Tabatabai¹,

Wm²,

Li³

et al. 2012

OAMS

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Ordinary least squares estimates can behave badly when outliers are present. An alternative is to use a robust regression technique that can handle outliers and influential observations. We introduce a new robust estimation method called TELBS robust regression method. We also introduce a new measurement called S h (i) for detecting influential observations. In addition, a new measure for goodness of fit, called R 2 RFPR , is introduced. We provide an algorithm to perform the TELBS estimation of regression parameters. Real and simulated data sets are used to assess the performance of this new estimator. In simulated data with outliers, the TELBS estimator of regression parameters performs better in comparison with least squares, M and MM estimators, with respect to both bias and mean squared error. For rat liver weights data, none of the estimators (least squares, M, and MM) are able to estimate the parameters accurately. However, TELBS does give an accurate estimate. Using real data for brain imaging, the TELBS and MM methods were equally accurate. In both of these real data sets, the S h (i) measure was very effective in identifying influential observations. The robustness and simplicity of computations of TELBS model parameters make this method an appropriate one for analysis of linear regression. Algorithms and programs have been provided for ease in implementation, including all relevant statistics necessary to perform a complete analysis of linear regression.

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Robust Factorization Methods Using a Gaussian/Uniform Mixture Model

Cited by 16 publications

References 40 publications

Robust Face Frontalization For Visual Speech Recognition

Robust Face Frontalization For Visual Speech Recognition

The generalized trace-norm and its application to structure-from-motion problems

TELBS robust linear regression method

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