Регуляризация дифференцирования с использованием репагулярного вейвлет-преобразования

В статье рассматривается проблема регуляризации дифференцирования изображений с помощью репагулярного вейвлет-преобразования, для решения которой выполняется представление этого преобразования с помощью интегрирования дробного порядка.У статті розглядається проблема регуляризації диференціювання зображень за допомогою репагулярного вейвлет-перетворення, для вирішення якої виконується представлення цього перетворення за допомогою інтегрування дробового порядку.The paper is devoted to the problem of regularization of image differentiation by repagular wavelet transform for the decision of which this transform is expressed based on integration of fractional order

Codomain scale space and regularization for high angular resolution diffusion imaging

Regularization is an important aspect in high angular resolution diffusion imaging (HARDI), since, unlike with classical diffusion tensor imaging (DTI), there is no a priori regularity of raw data in the co-domain, i.e. considered as a multispectral signal for fixed spatial position. HARDI preprocessing is therefore a crucial step prior to any subsequent analysis, and some insight in regularization paradigms and their interrelations is compulsory. In this paper we posit a codomain scale space regularization paradigm that has hitherto not been applied in the context of HARDI. Unlike previous (first and second order) schemes it is based on infinite order regularization, yet can be fully operationalized. We furthermore establish a closed-form relation with first order Tikhonov regularization via the Laplace transform

Scale-Space Properties of Nonstationary Iterative Regularization Methods

Most scale-space concepts have been expressed as parabolic or hyperbolic partial differential equations (PDEs). In this paper we extend our work on scale-space properties of elliptic PDEs arising from regularization methods: we study linear and nonlinear regularization methods that are applied iteratively and with different regularization parameters. For these so-called nonstationary iterative regularization techniques we clarify their relations to both isotropic diffusion filters with a scalar-valued diffusivity and anisotropic diffusion filters with a diffusion tensor. We establish scale-space properties for iterative regularization methods that are in complete accordance with those for diffusion filtering. In particular, we show that nonstationary iterative regularization satisfies a causality property in terms of a maximum-minimum principle, possesses a large class of Lyapunov functionals, and converges to a constant image as the regularization parameters tend to infinity. We also establish continuous dependence of the result with respect to the sequence of regularization parameters. Numerical experiments in two and three space dimensions are presented that illustrate the scale-space behavior of regularization methods

Shape Calculus for Shape Energies in Image Processing

Many image processing problems are naturally expressed as energy minimization or shape optimization problems, in which the free variable is a shape, such as a curve in 2d or a surface in 3d. Examples are image segmentation, multiview stereo reconstruction, geometric interpolation from data point clouds. To obtain the solution of such a problem, one usually resorts to an iterative approach, a gradient descent algorithm, which updates a candidate shape gradually deforming it into the optimal shape. Computing the gradient descent updates requires the knowledge of the first variation of the shape energy, or rather the first shape derivative. In addition to the first shape derivative, one can also utilize the second shape derivative and develop a Newton-type method with faster convergence. Unfortunately, the knowledge of shape derivatives for shape energies in image processing is patchy. The second shape derivatives are known for only two of the energies in the image processing literature and many results for the first shape derivative are limiting, in the sense that they are either for curves on planes, or developed for a specific representation of the shape or for a very specific functional form in the shape energy. In this work, these limitations are overcome and the first and second shape derivatives are computed for large classes of shape energies that are representative of the energies found in image processing. Many of the formulas we obtain are new and some generalize previous existing results. These results are valid for general surfaces in any number of dimensions. This work is intended to serve as a cookbook for researchers who deal with shape energies for various applications in image processing and need to develop algorithms to compute the shapes minimizing these energies

Anisotropic Diffusion Partial Differential Equations in Multi-Channel Image Processing : Framework and Applications

We review recent methods based on diffusion PDE's (Partial Differential Equations) for the purpose of multi-channel image regularization. Such methods have the ability to smooth multi-channel images anisotropically and can preserve then image contours while removing noise or other undesired local artifacts. We point out the pros and cons of the existing equations, providing at each time a local geometric interpretation of the corresponding processes. We focus then on an alternate and generic tensor-driven formulation, able to regularize images while specifically taking the curvatures of local image structures into account. This particular diffusion PDE variant is actually well suited for the preservation of thin structures and gives regularization results where important image features can be particularly well preserved compared to its competitors. A direct link between this curvature-preserving equation and a continuous formulation of the Line Integral Convolution technique (Cabral and Leedom, 1993) is demonstrated. It allows the design of a very fast and stable numerical scheme which implements the multi-valued regularization method by successive integrations of the pixel values along curved integral lines. Besides, the proposed implementation, based on a fourth-order Runge Kutta numerical integration, can be applied with a subpixel accuracy and preserves then thin image structures much better than classical finite-differences discretizations, usually chosen to implement PDE-based diffusions. We finally illustrate the efficiency of this diffusion PDE's for multi-channel image regularization - in terms of speed and visual quality - with various applications and results on color images, including image denoising, inpainting and edge-preserving interpolation

Learning a Probabilistic Model for Diffeomorphic Registration

International audienceWe propose to learn a low-dimensional probabilistic deformation model from data which can be used for registration and the analysis of deformations. The latent variable model maps similar deformations close to each other in an encoding space. It enables to compare deformations, generate normal or pathological deformations for any new image or to transport deformations from one image pair to any other image. Our unsupervised method is based on variational inference. In particular, we use a conditional variational autoencoder (CVAE) network and constrain transformations to be symmetric and diffeomorphic by applying a differentiable exponentiation layer with a symmetric loss function. We also present a formulation that includes spatial regularization such as diffusion-based filters. Additionally, our framework provides multi-scale velocity field estimations. We evaluated our method on 3-D intra-subject registration using 334 cardiac cine-MRIs. On this dataset, our method showed state-of-the-art performance with a mean DICE score of 81.2% and a mean Hausdorff distance of 7.3mm using 32 latent dimensions compared to three state-of-the-art methods while also demonstrating more regular deformation fields. The average time per registration was 0.32s. Besides, we visualized the learned latent space and show that the encoded deformations can be used to transport deformations and to cluster diseases with a classification accuracy of 83% after applying a linear projection

Learning a Probabilistic Model for Diffeomorphic Registration

International audienceWe propose to learn a low-dimensional probabilistic deformation model from data which can be used for registration and the analysis of deformations. The latent variable model maps similar deformations close to each other in an encoding space. It enables to compare deformations, generate normal or pathological deformations for any new image or to transport deformations from one image pair to any other image. Our unsupervised method is based on variational inference. In particular, we use a conditional variational autoencoder (CVAE) network and constrain transformations to be symmetric and diffeomorphic by applying a differentiable exponentiation layer with a symmetric loss function. We also present a formulation that includes spatial regularization such as diffusion-based filters. Additionally, our framework provides multi-scale velocity field estimations. We evaluated our method on 3-D intra-subject registration using 334 cardiac cine-MRIs. On this dataset, our method showed state-of-the-art performance with a mean DICE score of 81.2% and a mean Hausdorff distance of 7.3mm using 32 latent dimensions compared to three state-of-the-art methods while also demonstrating more regular deformation fields. The average time per registration was 0.32s. Besides, we visualized the learned latent space and show that the encoded deformations can be used to transport deformations and to cluster diseases with a classification accuracy of 83% after applying a linear projection

PORTR: Pre-Operative and Post-Recurrence Brain Tumor Registration

We propose a new method for deformable registration of pre-operative and post-recurrence brain MR scans of glioma patients. Performing this type of intra-subject registration is challenging as tumor, resection, recurrence, and edema cause large deformations, missing correspondences, and inconsistent intensity profiles between the scans. To address this challenging task, our method, called PORTR, explicitly accounts for pathological information. It segments tumor, resection cavity, and recurrence based on models specific to each scan. PORTR then uses the resulting maps to exclude pathological regions from the image-based correspondence term while simultaneously measuring the overlap between the aligned tumor and resection cavity. Embedded into a symmetric registration framework, we determine the optimal solution by taking advantage of both discrete and continuous search methods. We apply our method to scans of 24 glioma patients. Both quantitative and qualitative analysis of the results clearly show that our method is superior to other state-of-the-art approaches

Le recalage robuste d’images médicales et la modélisation du mouvement basée sur l’apprentissage profond

This thesis presents new computational tools for quantifying deformations and motion of anatomical structures from medical images as required by a large variety of clinical applications. Generic deformable registration tools are presented that enable deformation analysis useful for improving diagnosis, prognosis and therapy guidance. These tools were built by combining state-of-the-art medical image analysis methods with cutting-edge machine learning methods.First, we focus on difficult inter-subject registration problems. By learning from given deformation examples, we propose a novel agent-based optimization scheme inspired by deep reinforcement learning where a statistical deformation model is explored in a trial-and-error fashion showing improved registration accuracy. Second, we develop a diffeomorphic deformation model that allows for accurate multiscale registration and deformation analysis by learning a low-dimensional representation of intra-subject deformations. The unsupervised method uses a latent variable model in form of a conditional variational autoencoder (CVAE) for learning a probabilistic deformation encoding that is useful for the simulation, classification and comparison of deformations.Third, we propose a probabilistic motion model derived from image sequences of moving organs. This generative model embeds motion in a structured latent space, the motion matrix, which enables the consistent tracking of structures and various analysis tasks. For instance, it leads to the simulation and interpolation of realistic motion patterns allowing for faster data acquisition and data augmentation.Finally, we demonstrate the importance of the developed tools in a clinical application where the motion model is used for disease prognosis and therapy planning. It is shown that the survival risk for heart failure patients can be predicted from the discriminative motion matrix with a higher accuracy compared to classical image-derived risk factors.Cette thèse présente de nouveaux outils informatiques pour quantifier les déformations et le mouvement de structures anatomiques à partir d’images médicales dans le cadre d’une grande variété d’applications cliniques. Des outils génériques de recalage déformable sont présentés qui permettent l’analyse de la déformation de tissus anatomiques pour améliorer le diagnostic, le pronostic et la thérapie. Ces outils combinent des méthodes avancées d’analyse d’images médicales avec des méthodes d’apprentissage automatique performantes.Dans un premier temps, nous nous concentrons sur les problèmes de recalages inter-sujets difficiles. En apprenant à partir d’exemples de déformation donnés, nous proposons un nouveau schéma d’optimisation basé sur un agent inspiré de l’apprentissage par renforcement profond dans lequel un modèle de déformation statistique est exploré de manière itérative montrant une précision améliorée de recalage. Dans un second temps, nous développons un modèle de déformation difféomorphe qui permet un recalage multi-échelle précis et une analyse de déformation en apprenant une représentation de faible dimension des déformations intra-sujet. La méthode non supervisée utilise un modèle de variable latente sous la forme d’un autoencodeur variationnel conditionnel (CVAE) pour apprendre une représentation probabiliste des déformations qui est utile pour la simulation, la classification et la comparaison des déformations. Troisièmement, nous proposons un modèle de mouvement probabiliste dérivé de séquences d’images d’organes en mouvement. Ce modèle génératif décrit le mouvement dans un espace latent structuré, la matrice de mouvement, qui permet le suivi cohérent des structures ainsi que l’analyse du mouvement. Ainsi cette approche permet la simulation et l’interpolation de modèles de mouvement réalistes conduisant à une acquisition et une augmentation des données plus rapides.Enfin, nous démontrons l’intérêt des outils développés dans une application clinique où le modèle de mouvement est utilisé pour le pronostic de maladies et la planification de thérapies. Il est démontré que le risque de survie des patients souffrant d’insuffisance cardiaque peut être prédit à partir de la matrice de mouvement discriminant avec une précision supérieure par rapport aux facteurs de risque classiques dérivés de l’image

Invariant encoding schemes for visual recognition

Many encoding schemes, such as the Scale Invariant Feature Transform (SIFT) and Histograms of Oriented Gradients (HOG), make use of templates of histograms to enable a loose encoding of the spatial position of basic features such as oriented gradients. Whilst such schemes have been successfully applied, the use of a template may limit the potential as it forces the histograms to conform to a rigid spatial arrangement. In this work we look at developing novel schemes making use of histograms, without the need for a template, which offer good levels of performance in visual recognition tasks. To do this, we look at the way the basic feature type changes across scale at individual locations. This gives rise to the notion of column features, which capture this change across scale by concatenating feature types at a given scale separation. As well as applying this idea to oriented gradients, we make wide use of Basic Image Features (BIFs) and oriented Basic Image Features (oBIFs) which encode local symmetry information. This resulted in a range of encoding schemes. We then tested these schemes on problems of current interest in three application areas. First, the recognition of characters taken from natural images, where our system outperformed existing methods. For the second area we selected a texture problem, involving the discrimination of quartz grains using surface texture, where the system achieved near perfect performance on the first task, and a level of performance comparable to an expert human on the second. In the third area, writer identification, the system achieved a perfect score and outperformed other methods when tested using the Arabic handwriting dataset as part of the ICDAR 2011 Competition