Parametric approaches for modelling local structure tensor fields with applications to texture analysis

Abstract : This thesis proposes and evaluates parametric frameworks for modelling local structure tensor (LST) fields computed on textured images. A texture’s underlying geometry is described in terms of orientation and anisotropy, estimated in each pixel by the LST. Defined as symmetric non-negative definite matrices, LSTs cannot be handled using the classical tools of Euclidean geometry. In this work, two complete Riemannian statistical frameworks are investigated to address the representation of symmetric positive definite matrices. They rely on the a ne-invariant (AI) and log-Euclidean (LE) metric spaces. For each framework, a Gaussian distribution and its corresponding mixture models are considered for statistical modelling. Solutions for parameter estimation are provided and parametric dissimilarity measures between statistical models are proposed as well. The proposed statistical frameworks are first considered for characterising LST fields computed on textured images. Both AI and LE models are first employed to handle marginal LST distributions. Then, LE models are extended to describe joint LST distributions with the purpose of characterising both spatial and multiscale dependencies. The theoretical models’ fit to empirical LST distributions is experimentally assessed for a texture set composed of a large diversity of patterns. The descriptive potential of the proposed statistical models are then assessed in two applications. A first application consists of texture recognition. It deals with very high resolution remote sensing images and carbonaceous material images issued from high resolution transmission electron microscopy technology. The LST statistical modelling based approaches for texture characterisation outperform, in most cases, the state of the art methods. Competitive texture classification performances are obtained when modelling marginal LST distributions on both AI and LE metric spaces. When modelling joint LST distributions, a slight gain in performance is obtained with respect to the case when marginal distributions are modelled. In addition, the LST based methods’ intrinsic ability to address the rotation invariance prerequisite that arises in many classification tasks dealing with anisotropic textures is experimentally validated as well. In contrast, state of the art methods achieve a rather pseudo rotation invariance. A second application concerns LST field synthesis. To this purpose, monoscale and multiscale pyramidal approaches relying on a Markovian hypothesis are developed. Experiments are carried out on toy LST field examples and on real texture LST fields. The successful synthesis results obtained when optimal parameter configurations are employed, are a proof of the real descriptive potential of the proposed statistical models. However, the experiments have also shown a high sensitivity to the parameters’ choice, that may be due to statistical inference limitations in high dimensional spaces.
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Roxana Gabriela Rosu. Parametric approaches for modelling local structure tensor fields with applications to texture analysis. Computer science. Université de Bordeaux, 2018. English. ⟨NNT : 2018BORD0102⟩. ⟨tel-01897833⟩

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