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Geometric Algebra (GA) presents challenges to learners due to its highly abstract mathematical structure and complex operational rules, as translating algebraic manipulations into concrete geometric interpretations is a non-intuitive…
Geometric rounding of a mesh is the task of approximating its vertex coordinates by floating point numbers while preserving mesh structure. Geometric rounding allows algorithms of computational geometry to interface with numerical…
Robotic grinding is widely used for shaping workpieces in manufacturing, but it remains difficult to automate this process efficiently. In particular, efficiently grinding workpieces of different shapes and material hardness is challenging…
This paper presents a new class of adaptive filters, namely Geometric-Algebra Adaptive Filters (GAAFs). They are generated by formulating the underlying minimization problem (a deterministic cost function) from the perspective of Geometric…
Depth completion is a key task in autonomous driving, aiming to complete sparse LiDAR depth measurements into high-quality dense depth maps through image guidance. However, existing methods usually treat depth maps as an additional channel…
Multi-view multi-instance feature association constitutes a crucial step in 3D reconstruction, facilitating the consistent grouping of object instances across various camera perspectives. The presence of multiple identical objects within a…
Images degraded by geometric distortions pose a significant challenge to imaging and computer vision tasks such as object recognition. Deep learning-based imaging models usually fail to give accurate performance for geometrically distorted…
We propose GALA, a novel representation of 3D shapes that (i) excels at capturing and reproducing complex geometry and surface details, (ii) is computationally efficient, and (iii) lends itself to 3D generative modelling with modern,…
Reconstructing 3D clothed human avatars from single images is a challenging task, especially when encountering complex poses and loose clothing. Current methods exhibit limitations in performance, largely attributable to their dependence on…
There is often variation in the shape and size of input data used for deep learning. In many cases, such data can be represented using tensors with non-uniform shapes, or ragged tensors. Due to limited and non-portable support for efficient…
Shape optimization is of great significance in structural engineering, as an efficient geometry leads to better performance of structures. However, the application of gradient-based shape optimization for structural and architectural design…
We present a simple yet effective general-purpose framework for modeling 3D shapes by leveraging recent advances in 2D image generation using CNNs. Using just a single depth image of the object, we can output a dense multi-view depth map…
A hard hadron-collider event is treated here as a single geometric object - the kinematics and the discrete object-type labels of all reconstructed final-state particles encoded in one multivector $\evMV\in\Cl(1,3)\otimes\Vflav$ - rather…
The ever-increasing complexity and operational diversity of modern Neural Networks (NNs) have caused the need for low-power and, at the same time, high-performance edge devices for AI applications. Coarse Grained Reconfigurable…
We propose the first general framework to automatically correct different types of geometric distortion in a single input image. Our proposed method employs convolutional neural networks (CNNs) trained by using a large synthetic distortion…
This paper addresses the limitations of neural rendering-based multi-view surface reconstruction methods, which require an additional mesh extraction step that is inconvenient and would produce poor-quality surfaces with mesh aliasing,…
This paper presents a Surface-Aligned Gaussian representation for creating animatable human avatars from monocular videos,aiming at improving the novel view and pose synthesis performance while ensuring fast training and real-time…
Generative machine learning models have revolutionized material discovery by capturing complex structure-property relationships, yet extending these approaches to the inverse design of three-dimensional metamaterials remains limited by…
High-fidelity reconstruction of dynamic scenes is an important yet challenging problem. While recent 4D Gaussian Splatting (4DGS) has demonstrated the ability to model temporal dynamics, it couples Gaussian motion and geometric attributes…
The spatial control of material placement afforded by metal additive manufacturing (AM) has enabled significant progress in the development and implementation of compositionally graded alloys (CGAs) for spatial property variation in…