Search
Search Results
-
Bin-scanning: Segmentation of X-ray CT volume of binned parts using Morse skeleton graph of distance transform
X-ray CT scanners, due to the transmissive nature of X-rays, have enabled the non-destructive evaluation of industrial products, even inside their...
-
Some Equivalence Relation between Persistent Homology and Morphological Dynamics
In mathematical morphology, connected filters based on dynamics are used to filter the extrema of an image. Similarly, persistence is a concept...
-
-
Persistent-homology-based machine learning: a survey and a comparative study
A suitable feature representation that can both preserve the data intrinsic information and reduce data complexity and dimensionality is key to the...
-
Gradient Vector Fields of Discrete Morse Functions and Watershed-Cuts
In this paper, we study a class of discrete Morse functions, coming from Discrete Morse Theory, that are equivalent to a class of simplicial stacks,...
-
Denoising with discrete Morse theory
Denoising noisy datasets is a crucial task in this data-driven world. In this paper, we develop a persistence-guided discrete Morse theoretic...
-
Parametrized topological complexity of collision-free motion planning in the plane
Parametrized motion planning algorithms have high degrees of universality and flexibility, as they are designed to work under a variety of external...
-
Terrain trees: a framework for representing, analyzing and visualizing triangulated terrains
We propose a family of spatial data structures for the representation and processing of Triangulated Irregular Networks (TINs). We call such data...
-
High-dimensional scalar function visualization using principal parameterizations
Insightful visualization of multidimensional scalar fields, in particular parameter spaces, is key to many computational science and engineering...
-
Coherent Topological Landscapes for Simulation Ensembles
The topological structure is an intrinsic feature of a scalar field of any spatial dimensionality. The dependence of the topology on the isovalue of...
-
High-Dimensional Dataset Simplification by Laplace-Beltrami Operator
With the development of the Internet and other digital technologies, the speed of data generation has become considerably faster than the speed of...
-
Exploring the Geometry and Topology of Neural Network Loss Landscapes
Recent work has established clear links between the generalization performance of trained neural networks and the geometry of their loss landscape...
-
Mathematical Foundations in Visualization
Mathematical concepts and tools have shaped the field of visualization in fundamental ways and played a key role in the development of a large...
-
Transformations, Map**s, and Data Summaries
Fundamentally, data visualization is the process of placing dabs of ink or color on a 2D plane. However, the complexity of data is increasing so that...
-
On the Space Between Critical Points
The vertices of the neighborhood graph of a digital picture P can be interpolated to form a 2-manifold M with critical points (maxima, minima,...
-
Congratulations! Dual Graphs Are Now Orientated!
A digital image can be perceived as a 2.5D surface consisting of pixel coordinates and the intensity of pixel as height of the point in the surface....
-
Partitioning 2D Images into Prototypes of Slope Region
A gray scale digital image can be represented as a 2.5D surface where the height of the surface corresponds to the gray value of the respective...
-
Persistent Homology Computation Using Combinatorial Map Simplification
We propose an algorithm for persistence homology computation of orientable 2-dimensional (2D) manifolds with or without boundary (meshes) represented...
-
Maximum spatial–temporal isometric cluster for dynamic surface correspondence
Isometric correspondence is an important technique for surface correspondence. Recently, numerous algorithms have been proposed to build isometric...
-
Retiling scheme: a novel approach of direct anisotropic quad-dominant remeshing
Remeshing has been an active research topic in Digital Geometry Processing. In this paper, a novel approach of direct anisotropic quad-dominant...
