Objects and concepts underlying our environments are frequently defined in relation to one another as well as to other entities. Encoding various kinds of relationships, graphs offer a unifying, natural representation for many forms of data. As such, they sit at the heart of modern computer vision. For instance, scene graphs, correspondence graphs, pose graphs or part graphs are all relational structures heavily used in computer vision. To work with these relational structures, modern, data-driven computer vision methods emerged and are gathered under the umbrella of geometric deep learning. Especially, graph neural networks aim to make learning native to these graph data structures.

Unfortunately, summarising our complex environments and interactions with a simple bag of pairwise relationships (e.g. graphs) is an oversimplification. Oftentimes, data would involve multi-way (n-ary) connections that relate not just pairs of concepts / objects but rather families or groups of nodes. In such cases, we are rather interested in higher-order relationships. Examples include 3D triangular or tetrahedral meshes, multi-agent trajectories, and hierarchical, semantic correspondences. Additionally, such higher-order relationships not only naturally emerge in our everyday environments, but also within the computational graphs of neural networks, in the intricacies of road traffic, between the neurons in our brain, as well as in the structure of molecules or proteins. Topology (and related fields of mathematics) offers a principled, novel way to work with higher-order relations within the data under interrogation. Based on the principles of topology, Topological Deep Learning (TDL) is becoming a rapidly growing frontier that leverages generalisation of graphs, such as simplicial complexes, cell complexes, and hypergraphs, to extract more global information from data, generalising most data domains encountered in scientific computations. Deep learning models developed to learn from data supported on these topological domains constitute the essence of TDL, which facilitates the analysis of higher-order network data, enabling the representation of relations between multiple entities. Consequently, computational models supported on these higher-order domains offer the possibility to tackle novel applications across various fields, such as computer vision. On the other hand, TDL also encapsulates tools of topology that are used to characterise deep neural networks. For instance, it is known that the topology of training dynamics is highly correlated to generalisation performance.

What is topological deep learning?

Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. TDL may complement graph representation learning and geometric deep learning by incorporating topological concepts, and can thus provide a natural choice for various machine learning settings, especially in computer vision. TDL focuses on learning directly on topological spaces. In the domains of vision and graphics, these spaces often manifest naturally as 3D point clouds, graphs, or meshes, either acquired in the real world through 3D sensors or designed in computer-aided design software. To date, the field has distinctly differentiated between these data representations, with the optimal choice often remaining elusive and highly dependent on the specific application. The lack of a unifying representation has led vision and graphics researchers to develop specialized architectures for different data types. Examples include PointNet for point clouds, MeshCNN for meshes and 3D GCNs for spatial graphs. Limited efforts have been made to consider a unified domain approach.

Why organize TDLCV now?

We believe that going forward we need to rethink how we model relationships intrinsic in data we use. We are confronted everyday with the fact that state-of-the-art methods neglect this important bit. Hence we like to bring attention to higher-oder modeling and its potential in computer vision.

What will the workshop aim, briefly?

We will introduce TDL and its current state. We will discuss open problems and promising research avenues in TDL, ranging from practical benefits in computer vision to theoretical foundations. Thereby, we will invite the scientific community to actively participate in TDL research to unlock the potential of this emerging field.

Feb 15, 2024: TDLCV is live! 🎉

Topics

The first of its kind, our workshop, TDLCV, will be dedicated to bringing together industry experts, academic researchers, and practitioners from computer vision and machine learning communities into a lively environment for discussing methodologies and challenges raised in exploiting these new learning machines. TDLCV aims to foster fruitful interactions and cross-pollination of ideas, contributing to the advancement of TDL and opening up new vistas for computer vision. As a targeted topic venue, this workshop will offer participants a unique opportunity to network with a diverse but focused research community, around the following focus areas: The goal of this workshop is to introduce topological deep learning to the realm of computer vision and foster the formation of a community dedicated to advancing computer vision via this new machinery of learning. A concrete summary of the aims are as follows:

• Define and introduce Topological Deep Learning in connection to computer vision
• Identify computer vision problems that can be benefit from the premises of topological deep learning such as modelling higher order relations
• Showcase recent and ongoing progress in TDL and its applications
• Explore and discuss current landscape of available datasets facilitating the modelling of higher order relations in TDL
• Address and discuss the current state-of-the art, limitations therein, expected progress and its impact on the computer vision world
• Enlighten the community to attract further researchers in this direction

Focal points for discussions and talks include but are not limited to:

• Applications of topological neural networks in (3D) computer vision
• Topological neural network architectures
• Higher-order network datasetsL
• Generative topological neural networks
• Topological representation learning
• Probabilistic topological deep learning models
• Theoretical foundations of topological deep learning
• Data-driven topological analysis for computer vision.

We collected recent papers that target the computer vision community and are relevant to the field.