Variational and learning models for image and time series inverse problems

Inverse problems are at the core of many challenging applications. Variational and learning models provide estimated solutions of inverse problems as the outcome of specific reconstruction maps. In the variational approach, the result of the reconstruction map is the solution of a regularized minimization problem encoding information on the acquisition process and prior knowledge on the solution. In the learning approach, the reconstruction map is a parametric function whose parameters are identified by solving a minimization problem depending on a large set of data. In this thesis, we go beyond this apparent dichotomy between variational and learning models and we show they can be harmoniously merged in unified hybrid frameworks preserving their main advantages. We develop several highly efficient methods based on both these model-driven and data-driven strategies, for which we provide a detailed convergence analysis. The arising algorithms are applied to solve inverse problems involving images and time series. For each task, we show the proposed schemes improve the performances of many other existing methods in terms of both computational burden and quality of the solution. In the first part, we focus on gradient-based regularized variational models which are shown to be effective for segmentation purposes and thermal and medical image enhancement. We consider gradient sparsity-promoting regularized models for which we develop different strategies to estimate the regularization strength. Furthermore, we introduce a novel gradient-based Plug-and-Play convergent scheme considering a deep learning based denoiser trained on the gradient domain. In the second part, we address the tasks of natural image deblurring, image and video super resolution microscopy and positioning time series prediction, through deep learning based methods. We boost the performances of supervised, such as trained convolutional and recurrent networks, and unsupervised deep learning strategies, such as Deep Image Prior, by penalizing the losses with handcrafted regularization terms.

A Semantic-based Framework for Digital Survey of Architectural Heritage

The research aims at developing a framework for semantic-based digital survey of architectural heritage. Rooted in knowledge-based modeling which extracts mathematical constraints of geometry from architectural treatises, as-built information of architecture obtained from image-based modeling is integrated with the ideal model in BIM platform. The knowledge-based modeling transforms the geometry and parametric relation of architectural components from 2D printings to 3D digital models, and create large amount variations based on shape grammar in real time thanks to parametric modeling. It also provides prior knowledge for semantically segmenting unorganized survey data. The emergence of SfM (Structure from Motion) provides access to reconstruct large complex architectural scenes with high flexibility, low cost and full automation, but low reliability of metric accuracy. We solve this problem by combing photogrammetric approaches which consists of camera configuration, image enhancement, and bundle adjustment, etc. Experiments show the accuracy of image-based modeling following our workflow is comparable to that from range-based modeling. We also demonstrate positive results of our optimized approach in digital reconstruction of portico where low-texture-vault and dramatical transition of illumination bring huge difficulties in the workflow without optimization. Once the as-built model is obtained, it is integrated with the ideal model in BIM platform which allows multiple data enrichment. In spite of its promising prospect in AEC industry, BIM is developed with limited consideration of reverse-engineering from survey data. Besides representing the architectural heritage in parallel ways (ideal model and as-built model) and comparing their difference, we concern how to create as-built model in BIM software which is still an open area to be addressed. The research is supposed to be fundamental for research of architectural history, documentation and conservation of architectural heritage, and renovation of existing buildings.

Mind the gaps: cognitive-inspired AI for high-level visual sensemaking. Towards abstract concept image classification

The abundance of visual data and the push for robust AI are driving the need for automated visual sensemaking. Computer Vision (CV) faces growing demand for models that can discern not only what images "represent," but also what they "evoke." This is a demand for tools mimicking human perception at a high semantic level, categorizing images based on concepts like freedom, danger, or safety. However, automating this process is challenging due to entropy, scarcity, subjectivity, and ethical considerations. These challenges not only impact performance but also underscore the critical need for interoperability. This dissertation focuses on abstract concept-based (AC) image classification, guided by three technical principles: situated grounding, performance enhancement, and interpretability. We introduce ART-stract, a novel dataset of cultural images annotated with ACs, serving as the foundation for a series of experiments across four key domains: assessing the effectiveness of the end-to-end DL paradigm, exploring cognitive-inspired semantic intermediaries, incorporating cultural and commonsense aspects, and neuro-symbolic integration of sensory-perceptual data with cognitive-based knowledge. Our results demonstrate that integrating CV approaches with semantic technologies yields methods that surpass the current state of the art in AC image classification, outperforming the end-to-end deep vision paradigm. The results emphasize the role semantic technologies can play in developing both effective and interpretable systems, through the capturing, situating, and reasoning over knowledge related to visual data. Furthermore, this dissertation explores the complex interplay between technical and socio-technical factors. By merging technical expertise with an understanding of human and societal aspects, we advocate for responsible labeling and training practices in visual media. These insights and techniques not only advance efforts in CV and explainable artificial intelligence but also propel us toward an era of AI development that harmonizes technical prowess with deep awareness of its human and societal implications.