A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representations in image processing and computer vision challenging. The latter observation has not prevented the design of image representations, which trade off between efficiency and complexity, while achieving accurate rendering of smooth regions as well as reproducing faithful contours and textures. The most recent ones, proposed in the past decade, share an hybrid heritage highlighting the multiscale and oriented nature of edges and patterns in images. This paper presents a panorama of the aforementioned literature on decompositions in multiscale, multi-orientation bases or dictionaries. They typically exhibit redundancy to improve sparsity in the transformed domain and sometimes its invariance with respect to simple geometric deformations (translation, rotation). Oriented multiscale dictionaries extend traditional wavelet processing and may offer rotation invariance. Highly redundant dictionaries require specific algorithms to simplify the search for an efficient (sparse) representation. We also discuss the extension of multiscale geometric decompositions to non-Euclidean domains such as the sphere or arbitrary meshed surfaces. The etymology of panorama suggests an overview, based on a choice of partially overlapping "pictures". We hope that this paper will contribute to the appreciation and apprehension of a stream of current research directions in image understanding.Comment: 65 pages, 33 figures, 303 reference

Applications of Physically Accurate Deep Learning for Processing Digital Rock Images

Digital rock analysis aims to improve our understanding of the fluid flow properties of reservoir rocks, which are important for enhanced oil recovery, hydrogen storage, carbonate dioxide storage, and groundwater management. X-ray microcomputed tomography (micro-CT) is the primary approach to capturing the structure of porous rock samples for digital rock analysis. Initially, the obtained micro-CT images are processed using image-based techniques, such as registration, denoising, and segmentation depending on various requirements. Numerical simulations are then conducted on the digital models for petrophysical prediction. The accuracy of the numerical simulation highly depends on the quality of the micro-CT images. Therefore, image processing is a critical step for digital rock analysis. Recent advances in deep learning have surpassed conventional methods for image processing. Herein, the utility of convolutional neural networks (CNN) and generative adversarial networks (GAN) are assessed in regard to various applications in digital rock image processing, such as segmentation, super-resolution, and denoising. To obtain training data, different sandstone and carbonate samples were scanned using various micro-CT facilities. After that, validation images previously unseen by the trained neural networks are utilised to evaluate the performance and robustness of the proposed deep learning techniques. Various threshold scenarios are applied to segment the reconstructed digital rock images for sensitivity analyses. Then, quantitative petrophysical analyses, such as porosity, absolute/relative permeability, and pore size distribution, are implemented to estimate the physical accuracy of the digital rock data with the corresponding ground truth data. The results show that both CNN and GAN deep learning methods can provide physically accurate digital rock images with less user bias than traditional approaches. These results unlock new pathways for various applications related to the reservoir characterisation of porous reservoir rocks