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The paper presents a new model for single channel images low-level interpretation. The image is decomposed into a graph which captures a complete set of structural features. The description allows to accurately identify every edge location…
Recent developments in single-cell omics technologies have enabled the quantification of molecular profiles in individual cells at an unparalleled resolution. Deep learning, a rapidly evolving sub-field of machine learning, has instilled a…
The Geometric Algebra Transformer (GATr) is a versatile architecture for geometric deep learning based on projective geometric algebra. We generalize this architecture into a blueprint that allows one to construct a scalable transformer…
This article considers the problem of 3-dimensional genome reconstruction for single-cell data, and the uniqueness of such reconstructions in the setting of haploid organisms. We consider multiple graph models as representations of this…
The last two decades, since the seminal work of Selig, has seen projective geometric algebra (PGA) gain popularity as a modern coordinate-free framework for doing classical Euclidean geometry and other Cayley-Klein geometries. This…
Streamline-based quad meshing algorithms use smooth cross fields to partition surfaces into quadrilateral regions by tracing cross field separatrices. In practice, re-entrant corners and misalignment of singularities lead to small regions…
We develop the symplectic elimnation algorithm. This algorithm using simple row operations reduce a symplectic matrix to a diagonal matrix. This algorithm gives rise to a decomposition of an arbitrary matrix into a product of a symplectic…
The problem of decomposing non-manifold object has already been studied in solid modeling. However, the few proposed solutions are limited to the problem of decomposing solids described through their boundaries. In this thesis we study the…
Cylindrical algebraic decomposition is one of the most important tools for computing with semi-algebraic sets, while triangular decomposition is among the most important approaches for manipulating constructible sets. In this paper, for an…
Let $\mathcal C$ be a real plane algebraic curve defined by the resultant of two polynomials (resp. by the discriminant of a polynomial). Geometrically such a curve is the projection of the intersection of the surfaces $P(x,y,z)=Q(x,y,z)=0$…
We propose a novel Auto-Regressive (AR) image generation approach that models images as hierarchical compositions of interpretable visual layers. While AR models have achieved transformative success in language modeling, replicating this…
The manuscript describes efficient algorithms for the computation of the CUR and ID decompositions. The methods used are based on simple modifications to the classical truncated pivoted QR decomposition, which means that highly optimized…
Geometric Deep Learning techniques have become a transformative force in the field of Computer-Aided Design (CAD), and have the potential to revolutionize how designers and engineers approach and enhance the design process. By harnessing…
Parity compilation is the challenge of laying out the required constraints for the parity mapping in a local way. We present the first constructive compilation algorithm for the parity architecture using plaquettes for arbitrary…
In this paper, we revisit the long-standing problem of automatic reconstruction of 3D objects from single line drawings. Previous optimization-based methods can generate compact and accurate 3D models, but their success rates depend heavily…
A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding…
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…
Automated design of neural network architectures tailored for a specific task is an extremely promising, albeit inherently difficult, avenue to explore. While most results in this domain have been achieved on image classification and…
Classical approaches for one-class problems such as one-class SVM and isolation forest require careful feature engineering when applied to structured domains like images. State-of-the-art methods aim to leverage deep learning to learn…
From a single image, visual cues can help deduce intrinsic and extrinsic camera parameters like the focal length and the gravity direction. This single-image calibration can benefit various downstream applications like image editing and 3D…