Related papers: The 3D Motorcycle Complex for Structured Volume De…
Omnidirectional cameras are widely used in such areas as robotics and virtual reality as they provide a wide field of view. Their images are often processed with classical methods, which might unfortunately lead to non-optimal solutions as…
CNN-based volumetric methods that label individual voxels now dominate the field of biomedical segmentation. However, 3D surface representations are often required for proper analysis. They can be obtained by post-processing the labeled…
Generative models have attracted considerable attention for their ability to produce novel shapes. However, their application in mechanical design remains constrained due to the limited size and variability of available datasets. This study…
We propose a novel and flexible roof modeling approach that can be used for constructing planar 3D polygon roof meshes. Our method uses a graph structure to encode roof topology and enforces the roof validity by optimizing a simple but…
Most 3D shape analysis methods use triangular meshes to discretize both the shape and functions on it as piecewise linear functions. With this representation, shape analysis requires fine meshes to represent smooth shapes and geometric…
Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…
In this paper, we investigate the algebraic structure underlying the acyclic decomposition. This decomposition applies to directed metric ribbon graphs and enables the recursive computation of the volumes of their moduli spaces. Building on…
Geometry processing of 3D objects is of primary interest in many areas of computer vision and graphics, including robot navigation, 3D object recognition, classification, feature extraction, etc. The recent introduction of cheap range…
Recent work has demonstrated that volumetric scene representations combined with differentiable volume rendering can enable photo-realistic rendering for challenging scenes that mesh reconstruction fails on. However, these methods entangle…
The main goal of this paper is to present the application of structural sums, mathematical objects originating from the computational materials science, in construction of a feature space vector of 2D random composites simulated by…
We develop a cylindrical shape decomposition (CSD) algorithm to decompose an object, a union of several tubular structures, into its semantic components. We decompose the object using its curve skeleton and restricted translational sweeps.…
Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a…
Data with features of volume, velocity, variety, and veracity are challenging traditional tools to extract useful analysis for decision-making. By integrating high-dimensional analysis with visualization, this paper develops a 3D power-map…
The geometry of three-dimensional (3D) graphs, consisting of nodes and edges, plays a crucial role in many important applications. An excellent example is molecular graphs, whose geometry influences important properties of a molecule…
We present a new algorithm for computing motorcycle graphs that runs in O(n^(4/3+e)) time for any e>0, improving on all previously known algorithms. The main application of this result is to computing the straight skeleton of a polygon. It…
For a graph embedded into a surface, we relate many combinatorial parameters of the cycle matroid of the graph and the bond matroid of the dual graph with the topological parameters of the embedding. This will give an expression of the…
In a balanced graph decomposition, every vertex of the host graph appears in the same number of blocks. We propose the use of colored loops as a framework for unifying various other types of local balance conditions in graph decompositions.…
In previous works [physics/0204035, physics/0404052, physics/0509126] a procedure was described for dividing the $3 \times N$-dimensional conformational space of a molecular system into a number of discrete cells, this partition allowed the…
Understanding the global organization of complicated and high dimensional data is of primary interest for many branches of applied sciences. It is typically achieved by applying dimensionality reduction techniques mapping the considered…
A random matrix model to describe the coupling of m-fold symmetry in constructed. The particular threefold case is used to analyze data on eigenfrequencies of elastomechanical vibration of an anisotropic quartz block. It is suggested that…