U-Nets are a go-to neural architecture across numerous tasks for continuous signals on a square such as images and Partial Differential Equations (PDE), however their design and architecture is understudied. In this paper, we provide a framework for designing and analysing general U-Net architectures.

U-Net architectures are ubiquitous in state-of-the-art deep learning, however their regularisation properties and relationship to wavelets are understudied. In this paper, we formulate a multi-resolution framework which identifies U-Nets as finite-dimensional truncations of models on an infinite-dimensional function space. We provide theoretical results which prove that average pooling corresponds to projection within the space of square-integrable functions and show that U-Nets with average pooling implicitly learn a Haar wavelet basis representation of the data. We then leverage our framework to identify state-of-the-art hierarchical VAEs (HVAEs), which have a U-Net architecture, as a type of two-step forward Euler discretisation of multi-resolution diffusion processes which flow from a point mass, introducing sampling instabilities. We also demonstrate that HVAEs learn a representation of time which allows for improved parameter efficiency through weight-sharing. We use this observation to achieve state-of-the-art HVAE performance with half the number of parameters of existing models, exploiting the properties of our continuous-time formulation.

In this paper, we provide a framework for designing and analysing general U-Net architectures.

Abstract--This paper presents a novel approach for enabling robust robotic perception in dark environments using infrared (IR) stream. IR stream is less susceptible to noise than RGB in low-light conditions. However, it is dominated by active emitter patterns that hinder high-level tasks such as object detection, tracking and localisation. T o address this, a U-Net-based architecture is proposed that reconstructs clean IR images from emitter-populated input, improving both image quality and downstream robotic performance. This approach outperforms existing enhancement techniques and enables reliable operation of vision-driven robotic systems across illumination conditions from well-lit to extreme low-light scenes. Lighting-invariant vision systems are desirable for enabling robots to operate robustly across diverse and unpredictable environments without requiring modifications to the underlying perception pipeline. In order to support high-level tasks such as object detection, semantic segmentation, and image classification, the vision system must remain reliable even in low light or completely dark scenes. Such capabilities are critical in domains like mine shaft exploration, post-disaster victim identification, nuclear facility inspection, and visual loop closure in feature-deprived environments using aruco markers.

Liver cancer is one of the most prevalent and lethal forms of cancer, making early detection crucial for effective treatment. This paper introduces a novel approach for automated liver tumor segmentation in computed tomography (CT) images by integrating a 3D U-Net architecture with the Bat Algorithm for hyperparameter optimization. The method enhances segmentation accuracy and robustness by intelligently optimizing key parameters like the learning rate and batch size. Evaluated on a publicly available dataset, our model demonstrates a strong ability to balance precision and recall, with a high F1-score at lower prediction thresholds. This is particularly valuable for clinical diagnostics, where ensuring no potential tumors are missed is paramount. Our work contributes to the field of medical image analysis by demonstrating that the synergy between a robust deep learning architecture and a metaheuristic optimization algorithm can yield a highly effective solution for complex segmentation tasks.

Incomplete satellite-based precipitation presents a significant challenge in global monitoring. For example, the Global Satellite Mapping of Precipitation (GSMaP) from JAXA suffers from substantial missing regions due to the orbital characteristics of satellites that have microwave sensors, and its current interpolation methods often result in spatial discontinuities. In this study, we formulate the completion of the precipitation map as a video inpainting task and propose a machine learning approach based on conditional diffusion models. Our method employs a 3D U-Net with a 3D condition encoder to reconstruct complete precipitation maps by leveraging spatio-temporal information from infrared images, latitude-longitude grids, and physical time inputs. Training was carried out on ERA5 hourly precipitation data from 2020 to 2023. We generated a pseudo-GSMaP dataset by randomly applying GSMaP masks to ERA maps. Performance was evaluated for the calendar year 2024, and our approach produces more spatio-temporally consistent inpainted precipitation maps compared to conventional methods. These results indicate the potential to improve global precipitation monitoring using the conditional diffusion models.

This study investigates the effectiveness of U-Net architectures integrated with various convolutional neural network (CNN) backbones for automated lung cancer detection and segmentation in chest CT images, addressing the critical need for accurate diagnostic tools in clinical settings. A balanced dataset of 832 chest CT images (416 cancerous and 416 non-cancerous) was preprocessed using Contrast Limited Adaptive Histogram Equalization (CLAHE) and resized to 128x128 pixels. U-Net models were developed with three CNN backbones: ResNet50, VGG16, and Xception, to segment lung regions. After segmentation, CNN-based classifiers and hybrid models combining CNN feature extraction with traditional machine learning classifiers (Support Vector Machine, Random Forest, and Gradient Boosting) were evaluated using 5-fold cross-validation. Metrics included accuracy, precision, recall, F1-score, Dice coefficient, and ROC-AUC. U-Net with ResNet50 achieved the best performance for cancerous lungs (Dice: 0.9495, Accuracy: 0.9735), while U-Net with VGG16 performed best for non-cancerous segmentation (Dice: 0.9532, Accuracy: 0.9513). For classification, the CNN model using U-Net with Xception achieved 99.1 percent accuracy, 99.74 percent recall, and 99.42 percent F1-score. The hybrid CNN-SVM-Xception model achieved 96.7 percent accuracy and 97.88 percent F1-score. Compared to prior methods, our framework consistently outperformed existing models. In conclusion, combining U-Net with advanced CNN backbones provides a powerful method for both segmentation and classification of lung cancer in CT scans, supporting early diagnosis and clinical decision-making.