Conservative Adaptation in Metric Spaces

International audienceConservative adaptation consists in a minimal change on a source case to be consistent with the target case, given the domain knowledge. It has been formalised in a previous work thanks to the AGM theory of belief revision applied to propositional logic. However, this formalism is rarely used in case-based reasoning systems. In this paper, conservative adaptation is extended to a more general representation framework, that includes also attribute-value formalisms. In this framework, a case is a class of case instances, which are elements of a metric space. Conservative adaptation is formalised in this framework and is extended to α-conservative adaptation, that relaxes the conservativeness. These approaches to adaptation in a metric space transform adaptation problems to well-formulated optimization problems. A running example in the cooking domain is used to illustrate the notions that are introduced

Wasserstein model reduction approach for parametrized flow problems in porous media

The aim of this work is to build a reduced order model for parametrized porous media equations. The main challenge of this type of problems is that the Kolmogorov width of the solution manifold typically decays quite slowly and thus makes usual linear model order reduction methods inappropriate. In this work, we investigate an adaptation of the methodology proposed in [Ehrlacher et al., Nonlinear model reduction on metric spaces. Application to one-dimensional conservative PDEs in Wasserstein spaces, ESAIM: Mathematical Modelling and Numerical Analysis (2020)], based on the use of Wasserstein barycenters [Agueh & Carlier, Barycenters in the Wasserstein Space, SIAM Journal on Mathematical Analysis (2011)], to the case of non-conservative problems. Numerical examples in one-dimensional test cases illustrate the advantages and limitations of this approach and suggest further research directions that we intend to explore in the future

Lip segmentation using adaptive color space training

In audio-visual speech recognition (AVSR), it is beneficial to use lip boundary information in addition to texture-dependent features. In this paper, we propose an automatic lip segmentation method that can be used in AVSR systems. The algorithm consists of the following steps: face detection, lip corners extraction, adaptive color space training for lip and non-lip regions using Gaussian mixture models (GMMs), and curve evolution using level-set formulation based on region and image gradients fields. Region-based fields are obtained using adapted GMM likelihoods. We have tested the proposed algorithm on a database (SU-TAV) of 100 facial images and obtained objective performance results by comparing automatic lip segmentations with hand-marked ground truth segmentations. Experimental results are promising and much work has to be done to improve the robustness of the proposed method