Covariance matrices outperform first-order features in many tasks, attracting considerable attention from the computer vision research community. Covariance matrices encode second-order statistics between features, at the same time it is robust to noise. Based on this, we propose representing images by covariance matrices and defining a loss function that measures the distance between them through the Riemannian distance. Motivated by the robustness and invariance properties of the affine invariant Riemannian metric the proposed method was validated in printer-proof data transmission, which is a challenging task due to the trade-off between image quality and message recovery capabilities after printing and digitization procedures. The effectiveness of this approach was systematically assessed using MS COCO and IMM Face datasets. The results demon-strated that the proposed approach outperforms conventional methods that use Euclidean distance, generating encoded images with better quality and achieving higher recovery accuracy in printed images. Additionally, a broader application of the proposed loss was successfully tested in image generation tasks, using generative adversarial networks (GANs).

Lithological characterization plays a crucial role in geological studies, and outcrops serve as the primary source of geological information. Automatic identification of lithologies enhances geological mapping and reduces costs and risks associated with mapping less accessible outcrops. These outcrops are typically imaged using remote sensing techniques, enabling the identification of geological structures and lithologies through computer vision and machine learning (ML) approaches. In this context, convolutional neural networks (CNNs) have significantly contributed to lithological characterization in outcrop images. Recent advancements include novel architectures based on residual and attention blocks, which improve upon base CNN models. In addition, transformer-based architectures have surpassed CNNs in various tasks. Taking a step further, we propose a novel architecture that incorporates Fourier operators. Our proposed architecture builds upon the Transformer model, utilizing a sequential combination of Fourier neural operators (FNOs) and channelwise self-attention layers. To train our model, we adopt a transfer learning strategy, initially training it on a texture dataset with 47 classes. Subsequently, we fine-tune the same model to classify five specific lithologies in our custom dataset. These lithologies include sandstone, gray and brownish-gray shale, limestone, and laminated limestone images from the Tres Irmãos quarry within the Araripe Basin—an outcrop analogous to oil exploration reservoirs. The proposed architecture achieved an F1-score of up to 98%, performing better than reference CNN and ResNet models. This advancement holds promise for accurate lithological characterization, benefiting geological research and exploration efforts.

This work investigates the use of smooth neural networks for modeling dynamic variations of implicit surfaces under the level set equation (LSE). For this, it extends the representation of neural implicit surfaces to the space-time ℝ3× ℝ, which opens up mechanisms for continuous geometric transformations. Examples include evolving an initial surface towards general vector fields, smoothing and sharpening using the mean curvature equation, and interpolations of initial conditions.The network training considers two constraints. A data term is responsible for fitting the initial condition to the corresponding time instant, usually ℝ3× {0}. Then, a LSE term forces the network to approximate the underlying geometric evolution given by the LSE, without any supervision. The network can also be initialized based on previously trained initial conditions, resulting in faster convergence compared to the standard approach.

Finding concepts considering their meaning and semantic relations in a document corpus is an important and challenging task. In this paper, we present our contributions on how to understand unstructured data present in one or multiple documents. Generally, the current literature concentrates efforts in structuring knowledge by identifying semantic entities in the data. In this paper, we test our hypothesis that hyperknowledge specifications are capable of defining rich relations among documents and extracted facts. The main evidence supporting this hypothesis is the fact that hyperknowledge was built on top of hypermedia fundamentals, easing the specification of rich relationships between different multimodal components (i.e. multimedia content and knowledge entities). The key challenge tackled in this paper is how to structure and correlate these components considering their meaning and semantic relations.