A Penalized Likelihood Approach to Image Warping

Glasbey, C. A.; Mardia, Kanti V.

doi:10.1111/1467-9868.00295

Cited by 86 publications

(78 citation statements)

References 103 publications

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“…This generative model is commonly used in Computational anatomy in diverse frameworks, for instance with currents [11,12], varifolds [13], LDDMM on images [14] but also in functional data analysis [1]. All these works are applied in different spaces, for instance, the varifold builds an embedding of the surfaces into an Hilbert space, and a group of diffeomorphisms have the ability of deform these surfaces.…”

Section: Settings and Notationmentioning

confidence: 99%

Inconsistency of Template Estimation by Minimizing of the Variance/Pre-Variance in the Quotient Space

Devilliers¹,

Allassonnière

Trouvé

et al. 2017

Entropy

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Abstract:We tackle the problem of template estimation when data have been randomly deformed under a group action in the presence of noise. In order to estimate the template, one often minimizes the variance when the influence of the transformations have been removed (computation of the Fréchet mean in the quotient space). The consistency bias is defined as the distance (possibly zero) between the orbit of the template and the orbit of one element which minimizes the variance. In the first part, we restrict ourselves to isometric group action, in this case the Hilbertian distance is invariant under the group action. We establish an asymptotic behavior of the consistency bias which is linear with respect to the noise level. As a result the inconsistency is unavoidable as soon as the noise is enough. In practice, template estimation with a finite sample is often done with an algorithm called "max-max". In the second part, also in the case of isometric group finite, we show the convergence of this algorithm to an empirical Karcher mean. Our numerical experiments show that the bias observed in practice can not be attributed to the small sample size or to a convergence problem but is indeed due to the previously studied inconsistency. In a third part, we also present some insights of the case of a non invariant distance with respect to the group action. We will see that the inconsistency still holds as soon as the noise level is large enough. Moreover we prove the inconsistency even when a regularization term is added.

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Section: Settings and Notationmentioning

confidence: 99%

Inconsistency of Template Estimation by Minimizing of the Variance/Pre-Variance in the Quotient Space

Devilliers¹,

Allassonnière

Trouvé

et al. 2017

Entropy

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show abstract

“…Applications of warping techniques abound in the statistical, medical imaging, and computer vision literature. Examples include warping by elastic deformations [16], [17], optical or fluid flow [18], [19], [20], diffusion processes [21], Bayesian prior distributions [22], [23], and thin-plate splines (TPS) [24], [25], [26]. Only recently have warping techniques based on deformation models been used to describe distortions in fingerprint images for the purpose of matching [14], [9].…”

Section: The Fingerprint Warping Modelmentioning

confidence: 99%

Fingerprint warping using ridge curve correspondences

Ross

Dass

Jain

2006

IEEE Trans. Pattern Anal. Machine Intell.

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Abstract-The performance of a fingerprint matching system is affected by the nonlinear deformation introduced in the fingerprint impression during image acquisition. This nonlinear deformation causes fingerprint features such as minutiae points and ridge curves to be distorted in a complex manner. A technique is presented to estimate the nonlinear distortion in fingerprint pairs based on ridge curve correspondences. The nonlinear distortion, represented using the thin-plate spline (TPS) function, aids in the estimation of an "average" deformation model for a specific finger when several impressions of that finger are available. The estimated average deformation is then utilized to distort the template fingerprint prior to matching it with an input fingerprint. The proposed deformation model based on ridge curves leads to a better alignment of two fingerprint images compared to a deformation model based on minutiae patterns. An index of deformation is proposed for selecting the "optimal" deformation model arising from multiple impressions associated with a finger. Results based on experimental data consisting of 1,600 fingerprints corresponding to 50 different fingers collected over a period of two weeks show that incorporating the proposed deformation model results in an improvement in the matching performance.

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“…where f is the monotonic warp to align Y and m. For a review of image warping methods, see Glasbey and Mardia [6,7]. The least squares solution can be obtained by dynamic time warping, further details for which will be given in Section 2.2.…”

Section: Model Formulationmentioning

confidence: 99%

A statistical model for unwarping of 1-D electrophoresis gels

2005

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A statistical model is proposed which relates density profiles in 1-D electrophoresis gels, such as those produced by pulsed-field gel electrophoresis (PFGE), to databases of profiles of known genotypes. The warp in each gel lane is described by a trend that is linear in its parameters plus a first-order autoregressive process, and density differences are modelled by a mixture of two normal distributions. Maximum likelihood estimates are computed efficiently by a recursive algorithm that alternates between dynamic time warping to align individual lanes and generalised-least-squares regression to ensure that the warp is smooth between lanes. The method, illustrated using PFGE of Escherichia coli O157 strains, automatically unwarps and classifies gel lanes, and facilitates manual identification of new genotypes.

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A Penalized Likelihood Approach to Image Warping

Cited by 86 publications

References 103 publications

Inconsistency of Template Estimation by Minimizing of the Variance/Pre-Variance in the Quotient Space

Inconsistency of Template Estimation by Minimizing of the Variance/Pre-Variance in the Quotient Space

Fingerprint warping using ridge curve correspondences

A statistical model for unwarping of 1-D electrophoresis gels

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