相关论文: Tangent Space Backpropagation for 3D Transformatio…

Euclidean deep learning is often inadequate for addressing real-world signals where the representation space is irregular and curved with complex topologies. Interpreting the geometric properties of such feature spaces has become paramount…

We briefly describe how to introduce the basic notions of noncommutative differential geometry on the 3-dim quantum space covariant under the quantum group of rotations $SO_q(3)$.

Supervised 3D reconstruction has witnessed a significant progress through the use of deep neural networks. However, this increase in performance requires large scale annotations of 2D/3D data. In this paper, we explore inexpensive 2D…

Reconstructing complex 3D interfaces from indirect measurements remains a grand challenge in scientific computing, particularly for ill-posed inverse problems like Electrical Impedance Tomography (EIT). Traditional shape optimization…

The line geometric model of 3-D projective geometry has the nice property that the Lie algebra sl(4) of 3-D projective transformations is isomorphic to the bivector algebra of CL(3,3), and line geometry is closely related to the classical…

In recent years, skeleton-based action recognition has become a popular 3D classification problem. State-of-the-art methods typically first represent each motion sequence as a high-dimensional trajectory on a Lie group with an additional…

This paper looks at how changes of coordinates on a pseudo-Riemannian manifold induce homogeneous linear transformations on its tangent spaces. We see that a pseudo-orthonormal frame in a given tangent space is the basis for a set of…

Deep neural network architectures have recently produced excellent results in a variety of areas in artificial intelligence and visual recognition, well surpassing traditional shallow architectures trained using hand-designed features. The…

Objects' rigid motions in 3D space are described by rotations and translations of a highly-correlated set of points, each with associated $x,y,z$ coordinates that real-valued networks consider as separate entities, losing information.…

We introduce ProcGen3D, a new approach for 3D content creation by generating procedural graph abstractions of 3D objects, which can then be decoded into rich, complex 3D assets. Inspired by the prevalent use of procedural generators in…

We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…

There is a need for open-source libraries in emission tomography that (i) use modern and popular backend code to encourage community contributions and (ii) offer support for the multitude of reconstruction techniques available in recent…

Although theoretically compelling, Bayesian learning with modern machine learning models is computationally challenging since it requires approximating a high dimensional posterior distribution. In this work, we (i) introduce posteriors, an…

In spite of showing unreasonable effectiveness in modalities like Text and Image, Deep Learning has always lagged Gradient Boosting in tabular data - both in popularity and performance. But recently there have been newer models created…

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of…

Evolutionary computation is an important component within various fields such as artificial intelligence research, reinforcement learning, robotics, industrial automation and/or optimization, engineering design, etc. Considering the…

This paper considers a network referred to as SoftGroup for accurate and scalable 3D instance segmentation. Existing state-of-the-art methods produce hard semantic predictions followed by grouping instance segmentation results.…

3D pre-training is crucial to 3D perception tasks. Nevertheless, limited by the difficulties in collecting clean and complete 3D data, 3D pre-training has persistently faced data scaling challenges. In this work, we introduce a novel…

Three-dimensional (3D) point cloud analysis has become central to applications ranging from autonomous driving and robotics to forestry and ecological monitoring. Although numerous deep learning methods have been proposed for point cloud…

Deep generative networks have been widely used for learning mappings from a low-dimensional latent space to a high-dimensional data space. In many cases, data transformations are defined by linear paths in this latent space. However, the…