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Deep learning with 3D data such as reconstructed point clouds and CAD models has received great research interests recently. However, the capability of using point clouds with convolutional neural network has been so far not fully explored.…
Gay and Kirby recently introduced the concept of a trisection for arbitrary smooth, oriented closed 4-manifolds, and with it a new topological invariant, called the trisection genus. This paper improves and implements an algorithm due to…
Current CNN-based algorithms for recovering the 3D pose of an object in an image assume knowledge about both the object category and its 2D localization in the image. In this paper, we relax one of these constraints and propose to solve the…
Point clouds are rich geometric data structures, where their three dimensional structure offers an excellent domain for understanding the representation learning and generative modeling in 3D space. In this work, we aim to improve the…
Navigation in complex 3D scenarios requires appropriate environment representation for efficient scene understanding and trajectory generation. We propose a highly efficient and extensible global navigation framework based on a tomographic…
Segmentation of a colour image composed of different kinds of texture regions can be a hard problem, namely to compute for an exact texture fields and a decision of the optimum number of segmentation areas in an image when it contains…
We explain how we computed equations for all genus 4 curves defined of the field with 2 elements, up-to-isomorphism, and some of the data we obtained. We give descriptions also of nice models for genus 4 curves over characteristic 2 fields,…
This work aims to define the concept of manifold, which has a very important place in the topology, on digital images. So, a general perspective is provided for two and three-dimensional imaging studies on digital curves and digital…
While recent generative models for 2D images achieve impressive visual results, they clearly lack the ability to perform 3D reasoning. This heavily restricts the degree of control over generated objects as well as the possible applications…
Over the years, scene understanding has attracted a growing interest in computer vision, providing the semantic and physical scene information necessary for robots to complete some particular tasks autonomously. In 3D scenes, rich spatial…
Inspired by the generation power of generative adversarial networks (GANs) in image domains, we introduce a novel hierarchical architecture for learning characteristic topological features from a single arbitrary input graph via GANs. The…
Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often…
The topology of artificial neural networks has a significant effect on their performance. Characterizing efficient topology is a field of promising research in Artificial Intelligence. However, it is not a trivial task and it is mainly…
We give a survey of algorithms for computing topological invariants of semi-algebraic sets with special emphasis on the more recent developments in designing algorithms for computing the Betti numbers of semi-algebraic sets. Aside from…
In this paper, we analyze embeddings of grid graphs on orientable surfaces. We determine the genus of a large class of k-dimensional grid graphs and effective two-sided bounds for the genus of any 3-dimensional grid graph, both in terms of…
Identifying disease genes from human genome is an important and fundamental problem in biomedical research. Despite many publications of machine learning methods applied to discover new disease genes, it still remains a challenge because of…
In this paper, three Computational Topology methods (namely effective homology, persistent homology and discrete vector fields) are mixed together to produce algorithms for homological digital image processing. The algorithms have been…
Engineering new glass compositions have experienced a sturdy tendency to move forward from (educated) trial-and-error to data- and simulation-driven strategies. In this work, we developed a computer program that combines data-driven…
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…
One of the biggest challenges in the research of generative adversarial networks (GANs) is assessing the quality of generated samples and detecting various levels of mode collapse. In this work, we construct a novel measure of performance…