Related papers: Localized Shape Modelling with Global Coherence: A…
Currently, prominent Transformer architectures applied on graphs and meshes for shape analysis tasks employ traditional attention layers that heavily utilize spectral features requiring costly eigenvalue decomposition-based methods. To…
Recent research has tried to extend the concept of renormalization, which is naturally defined for geometric objects, to more general networks with arbitrary topology. The current attempts do not naturally apply to directed networks, for…
Mathematically representing the shape of an object is a key ingredient for solving inverse rendering problems. Explicit representations like meshes are efficient to render in a differentiable fashion but have difficulties handling topology…
We introduce LOGAN, a deep neural network aimed at learning general-purpose shape transforms from unpaired domains. The network is trained on two sets of shapes, e.g., tables and chairs, while there is neither a pairing between shapes from…
Unsupervised localization and segmentation are long-standing computer vision challenges that involve decomposing an image into semantically-meaningful segments without any labeled data. These tasks are particularly interesting in an…
We consider object detection using a generic model for natural shapes. A common approach for object recognition involves matching object models directly to images. Another approach involves building intermediate representations via a…
We propose a regularization scheme for image reconstruction that leverages the power of deep learning while hinging on classic sparsity-promoting models. Many deep-learning-based models are hard to interpret and cumbersome to analyze…
Metric networks are network-shaped, one-dimensional structures on which one can solve differential equations to simulate a wide range of physical systems including conjugated molecules, photonic crystals, quantum mechanics in waveguide…
We describe and analyze algorithms for shape-constrained symbolic regression, which allows the inclusion of prior knowledge about the shape of the regression function. This is relevant in many areas of engineering -- in particular whenever…
Although 3D shape matching and interpolation are highly interrelated, they are often studied separately and applied sequentially to relate different 3D shapes, thus resulting in sub-optimal performance. In this work we present a unified…
We discuss the local differential geometry of convex affine spheres in $\re^3$ and of minimal Lagrangian surfaces in Hermitian symmetric spaces. In each case, there is a natural metric and cubic differential holomorphic with respect to the…
Generative AI models provide a wide range of tools capable of performing complex tasks in a fraction of the time it would take a human. Among these, Large Language Models (LLMs) stand out for their ability to generate diverse texts, from…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
The Laplace-Beltrami operator has established itself in the field of non-rigid shape analysis due to its many useful properties such as being invariant under isometric transformation, having a countable eigensystem forming an orthornormal…
In this paper, we propose a novel fitting method that uses local image features to fit a 3D Morphable Model to 2D images. To overcome the obstacle of optimising a cost function that contains a non-differentiable feature extraction operator,…
Hyperuniformity refers to the suppression of density fluctuations at large scales. Typical for ordered systems, this property also emerges in several disordered physical and biological systems, where it is particularly relevant to…
Shape information is crucial for human perception and cognition, and should therefore also play a role in cognitive AI systems. We employ the interdisciplinary framework of conceptual spaces, which proposes a geometric representation of…
Alignment between non-rigid stretchable structures is one of the most challenging tasks in computer vision, as the invariant properties are hard to define, and there is no labeled data for real datasets. We present unsupervised neural…
Shapes of cognition is a new conceptual paradigm for the computational cognitive modeling of Language-Endowed Intelligent Agents (LEIAs). Shapes are remembered constellations of sensory, linguistic, conceptual, episodic, and procedural…
The motivation for using qualitative shape descriptions is as follows: qualitative shape descriptions can implicitly act as a schema for measuring the similarity of shapes, which has the potential to be cognitively adequate. Then, shapes…