New Convex Relaxations and Global Optimality in Variational Imaging

Variational methods constitute the basic building blocks for solving many image analysis tasks, be it segmentation, depth estimation, optical flow, object detection etc. Many of these problems can be expressed in the framework of Markov Random Fields (MRF) or as continuous labelling problems. Finding the Maximum A-Posteriori (MAP) solutions of suitably constructed MRFs or the optimizers of the labelling problems give solutions to the aforementioned tasks. In either case, the associated optimization problem amounts to solving structured energy minimization problems. In this thesis we study novel extensions applicable to Markov Random Fields and continuous labelling problems through which we are able to incorporate statistical global constraints. To this end, we devise tractable relaxations of the resulting energy minimization problem and efficient algorithms to tackle them. Second, we propose a general mechanism to find partial optimal solutions to the problem of finding a MAP-solution of an MRF, utilizing only standard relxations

Co-segmentation non-supervisée d'images utilisant les distances de Sinkhorn

National audienceIn this work, a convex and robust formulation of the unsupervised co-segmentation problem is introduced for pair of images. The proposed model relies on the optimal transport theory to asset the statistical similarity of the segmented regions’ features (color histograms in this work). The optimal transport cost is approximated by Sinkhorn distance to reduce the optimization complexity. A primal-dual algorithm is used to solve the problem efficiently, without making use of sub-iterative routines.Nous proposons une formulation convexe et robuste du problème de co-segmentation non supervisée de paire d'images. Ce modèle définit l'adéquation statistique des régions segmentées dans le cadre du transport optimal, en mesurant le coût de transport entre les histogrammes de descripteurs (ici la couleur). Afin de réduire la complexité de mise en oeuvre de ce modèle, les coûts de transport optimaux sont approchés par les distances de Sinkhorn, qui sont formulées comme la régularisation entropique du transport optimal. Un algorithme itératif exploitant la formulation primale-duale du problème est utilisé pour résoudre le problème de manière efficace et exacte

Generalized Zero Shot Learning For Medical Image Classification

In many real world medical image classification settings we do not have access to samples of all possible disease classes, while a robust system is expected to give high performance in recognizing novel test data. We propose a generalized zero shot learning (GZSL) method that uses self supervised learning (SSL) for: 1) selecting anchor vectors of different disease classes; and 2) training a feature generator. Our approach does not require class attribute vectors which are available for natural images but not for medical images. SSL ensures that the anchor vectors are representative of each class. SSL is also used to generate synthetic features of unseen classes. Using a simpler architecture, our method matches a state of the art SSL based GZSL method for natural images and outperforms all methods for medical images. Our method is adaptable enough to accommodate class attribute vectors when they are available for natural images

Automated Segmentation of Left and Right Ventricles in MRI and Classification of the Myocarfium Abnormalities

A fundamental step in diagnosis of cardiovascular diseases, automated left and right ventricle (LV and RV) segmentation in cardiac magnetic resonance images (MRI) is still acknowledged to be a difficult problem. Although algorithms for LV segmentation do exist, they require either extensive training or intensive user inputs. RV segmentation in MRI has yet to be solved and is still acknowledged a completely unsolved problem because its shape is not symmetric and circular, its deformations are complex and varies extensively over the cardiac phases, and it includes papillary muscles. In this thesis, I investigate fast detection of the LV endo- and epi-cardium surfaces (3D) and contours (2D) in cardiac MRI via convex relaxation and distribution matching. A rapid 3D segmentation of the RV in cardiac MRI via distribution matching constraints on segment shape and appearance is also investigated. These algorithms only require a single subject for training and a very simple user input, which amounts to one click. The solution is sought following the optimization of functionals containing probability product kernel constraints on the distributions of intensity and geometric features. The formulations lead to challenging optimization problems, which are not directly amenable to convex-optimization techniques. For each functional, the problem is split into a sequence of sub-problems, each of which can be solved exactly and globally via a convex relaxation and the augmented Lagrangian method. Finally, an information-theoretic based artificial neural network (ANN) is proposed for normal/abnormal LV myocardium motion classification. Using the LV segmentation results, the LV cavity points is estimated via a Kalman filter and a recursive dynamic Bayesian filter. However, due to the similarities between the statistical information of normal and abnormal points, differentiating between distributions of abnormal and normal points is a challenging problem. The problem was investigated with a global measure based on the Shannon\u27s differential entropy (SDE) and further examined with two other information-theoretic criteria, one based on Renyi entropy and the other on Fisher information. Unlike the existing information-theoretic studies, the approach addresses explicitly the overlap between the distributions of normal and abnormal cases, thereby yielding a competitive performance. I further propose an algorithm based on a supervised 3-layer ANN to differentiate between the distributions farther. The ANN is trained and tested by five different information measures of radial distance and velocity for points on endocardial boundary

Potentials and caveats of AI in Hybrid Imaging

State-of-the-art patient management frequently mandates the investigation of both anatomy and physiology of the patients. Hybrid imaging modalities such as the PET/MRI, PET/CT and SPECT/CT have the ability to provide both structural and functional information of the investigated tissues in a single examination. With the introduction of such advanced hardware fusion, new problems arise such as the exceedingly large amount of multi-modality data that requires novel approaches of how to extract a maximum of clinical information from large sets of multi-dimensional imaging data. Artificial intelligence (AI) has emerged as one of the leading technologies that has shown promise in facilitating highly integrative analysis of multi-parametric data. Specifically, the usefulness of AI algorithms in the medical imaging field has been heavily investigated in the realms of (1) image acquisition and reconstruction, (2) post-processing and (3) data mining and modelling. Here, we aim to provide an overview of the challenges encountered in hybrid imaging and discuss how AI algorithms can facilitate potential solutions. In addition, we highlight the pitfalls and challenges in using advanced AI algorithms in the context of hybrid imaging and provide suggestions for building robust AI solutions that enable reproducible and transparent research

Multisensory Imagery Cues for Object Separation, Specularity Detection and Deep Learning based Inpainting

Multisensory imagery cues have been actively investigated in diverse applications in the computer vision community to provide additional geometric information that is either absent or difficult to capture from mainstream two-dimensional imaging. The inherent features of multispectral polarimetric light field imagery (MSPLFI) include object distribution over spectra, surface properties, shape, shading and pixel flow in light space. The aim of this dissertation is to explore these inherent properties to exploit new structures and methodologies for the tasks of object separation, specularity detection and deep learning-based inpainting in MSPLFI. In the first part of this research, an application to separate foreground objects from the background in both outdoor and indoor scenes using multispectral polarimetric imagery (MSPI) cues is examined. Based on the pixel neighbourhood relationship, an on-demand clustering technique is proposed and implemented to separate artificial objects from natural background in a complex outdoor scene. However, due to indoor scenes only containing artificial objects, with vast variations in energy levels among spectra, a multiband fusion technique followed by a background segmentation algorithm is proposed to separate the foreground from the background. In this regard, first, each spectrum is decomposed into low and high frequencies using the fast Fourier transform (FFT) method. Second, principal component analysis (PCA) is applied on both frequency images of the individual spectrum and then combined with the first principal components as a fused image. Finally, a polarimetric background segmentation (BS) algorithm based on the Stokes vector is proposed and implemented on the fused image. The performance of the proposed approaches are evaluated and compared using publicly available MSPI datasets and the dice similarity coefficient (DSC). The proposed multiband fusion and BS methods demonstrate better fusion quality and higher segmentation accuracy compared with other studies for several metrics, including mean absolute percentage error (MAPE), peak signal-to-noise ratio (PSNR), Pearson correlation coefficient (PCOR) mutual information (MI), accuracy, Geometric Mean (G-mean), precision, recall and F1-score. In the second part of this work, a twofold framework for specular reflection detection (SRD) and specular reflection inpainting (SRI) in transparent objects is proposed. The SRD algorithm is based on the mean, the covariance and the Mahalanobis distance for predicting anomalous pixels in MSPLFI. The SRI algorithm first selects four-connected neighbouring pixels from sub-aperture images and then replaces the SRD pixel with the closest matched pixel. For both algorithms, a 6D MSPLFI transparent object dataset is captured from multisensory imagery cues due to the unavailability of this kind of dataset. The experimental results demonstrate that the proposed algorithms predict higher SRD accuracy and better SRI quality than the existing approaches reported in this part in terms of F1-score, G-mean, accuracy, the structural similarity index (SSIM), the PSNR, the mean squared error (IMMSE) and the mean absolute deviation (MAD). However, due to synthesising SRD pixels based on the pixel neighbourhood relationship, the proposed inpainting method in this research produces artefacts and errors when inpainting large specularity areas with irregular holes. Therefore, in the last part of this research, the emphasis is on inpainting large specularity areas with irregular holes based on the deep feature extraction from multisensory imagery cues. The proposed six-stage deep learning inpainting (DLI) framework is based on the generative adversarial network (GAN) architecture and consists of a generator network and a discriminator network. First, pixels’ global flow in the sub-aperture images is calculated by applying the large displacement optical flow (LDOF) method. The proposed training algorithm combines global flow with local flow and coarse inpainting results predicted from the baseline method. The generator attempts to generate best-matched features, while the discriminator seeks to predict the maximum difference between the predicted results and the actual results. The experimental results demonstrate that in terms of the PSNR, MSSIM, IMMSE and MAD, the proposed DLI framework predicts superior inpainting quality to the baseline method and the previous part of this research

Connected Attribute Filtering Based on Contour Smoothness

A new attribute measuring the contour smoothness of 2-D objects is presented in the context of morphological attribute filtering. The attribute is based on the ratio of the circularity and non-compactness, and has a maximum of 1 for a perfect circle. It decreases as the object boundary becomes irregular. Computation on hierarchical image representation structures relies on five auxiliary data members and is rapid. Contour smoothness is a suitable descriptor for detecting and discriminating man-made structures from other image features. An example is demonstrated on a very-high-resolution satellite image using connected pattern spectra and the switchboard platform

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal