Mathematical Imaging and Surface Processing

Within the last decade image and geometry processing have become increasingly rigorous with solid foundations in mathematics. Both areas are research fields at the intersection of different mathematical disciplines, ranging from geometry and calculus of variations to PDE analysis and numerical analysis. The workshop brought together scientists from all these areas and a fruitful interplay took place. There was a lively exchange of ideas between geometry and image processing applications areas, characterized in a number of ways in this workshop. For example, optimal transport, first applied in computer vision is now used to define a distance measure between 3d shapes, spectral analysis as a tool in image processing can be applied in surface classification and matching, and so on. We have also seen the use of Riemannian geometry as a powerful tool to improve the analysis of multivalued images. This volume collects the abstracts for all the presentations covering this wide spectrum of tools and application domains

Foundations and Recent Trends in Multimodal Machine Learning: Principles, Challenges, and Open Questions

Multimodal machine learning is a vibrant multi-disciplinary research field that aims to design computer agents with intelligent capabilities such as understanding, reasoning, and learning through integrating multiple communicative modalities, including linguistic, acoustic, visual, tactile, and physiological messages. With the recent interest in video understanding, embodied autonomous agents, text-to-image generation, and multisensor fusion in application domains such as healthcare and robotics, multimodal machine learning has brought unique computational and theoretical challenges to the machine learning community given the heterogeneity of data sources and the interconnections often found between modalities. However, the breadth of progress in multimodal research has made it difficult to identify the common themes and open questions in the field. By synthesizing a broad range of application domains and theoretical frameworks from both historical and recent perspectives, this paper is designed to provide an overview of the computational and theoretical foundations of multimodal machine learning. We start by defining two key principles of modality heterogeneity and interconnections that have driven subsequent innovations, and propose a taxonomy of 6 core technical challenges: representation, alignment, reasoning, generation, transference, and quantification covering historical and recent trends. Recent technical achievements will be presented through the lens of this taxonomy, allowing researchers to understand the similarities and differences across new approaches. We end by motivating several open problems for future research as identified by our taxonomy

LOOKING INTO ACTORS, OBJECTS AND THEIR INTERACTIONS FOR VIDEO UNDERSTANDING

Automatic video understanding is critical for enabling new applications in video surveillance, augmented reality, and beyond. Powered by deep networks that learn holistic representations of video clips, and large-scale annotated datasets, modern systems are capable of accurately recognizing hundreds of human activity classes. However, their performance significantly degrades as the number of actors in the scene or the complexity of the activities increases. Therefore, most of the research thus far has focused on videos that are short and/or contain a few activities performed only by adults. Furthermore, most current systems require expensive, spatio-temporal annotations for training. These limitations prevent the deployment of such systems in real-life applications, such as detecting activities of people and vehicles in an extended surveillance videos. To address these limitations, this thesis focuses on developing data-driven, compositional, region-based video understanding models motivated by the observation that actors, objects and their spatio-temporal interactions are the building blocks of activities and the main content of video descriptions provided by humans. This thesis makes three main contributions. First, we propose a novel Graph Neural Network for representation learning on heterogeneous graphs that encode spatio-temporal interactions between actor and object regions in videos. This model can learn context-aware representations for detected actors and objects, which we leverage for detecting complex activities. Second, we propose an attention-based deep conditional generative model of sentences, whose latent variables correspond to alignments between words in textual descriptions of videos and object regions. Building upon the framework of Conditional Variational Autoencoders, we train this model using only textual descriptions without bounding box annotations, and leverage its latent variables for localizing the actors and objects that are mentioned in generated or ground-truth descriptions of videos. Finally, we propose an actor-centric framework for real-time activity detection in videos that are extended both in space and time. Our framework leverages object detections and tracking to generate actor-centric tubelets, capturing all relevant spatio-temporal context for a single actor, and detects activities per tubelet based on contextual region embeddings. The models described have demonstrably improved the ability to temporally detect activities, as well as ground words in visual inputs