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The quest for regular models of arithmetic surfaces allows different viewpoints and approaches: using valuations or a covering by charts. In this article, we sketch both approaches and then show in a concrete example, how surprisingly…
The generation of triangle meshes from point clouds, i.e. meshing, is a core task in computer graphics and computer vision. Traditional techniques directly construct a surface mesh using local decision heuristics, while some recent methods…
Incremental scene reconstruction is essential to the navigation in robotics. Most of the conventional methods typically make use of either TSDF (truncated signed distance functions) volume or neural networks to implicitly represent the…
Integration of scalar and vector visualization has been an interesting topic. This paper presents a technique to appropriately select and display multiple streamlines while overlaying with isosurfaces, aiming an integrated scalar and vector…
To recover the three dimensional (3D) volumetric distribution of matter in an object, images of the object are captured from multiple directions and locations. Using these images tomographic computations extract the distribution. In highly…
In this paper, we propose several mathematical models for 3D surface reconstruction and volume estimation from a set of scattered cloud data. Three meshless methods including the interpolation-based method by RBF, PDE-based approach by…
X-ray tomography is a powerful volumetric imaging technique, but detailed three dimensional (3D) imaging requires the acquisition of a large number of individual X-ray images, which is time consuming. For applications where spatial…
With the ever growing popularity of integral field unit (IFU) spectroscopy, countless observations are being performed over multiple object systems such as blank fields and galaxy clusters. With this, an increasing amount of time is being…
In the field of volumetric data processing and analysis, extracting mid-surfaces from thinly bounded compartments is crucial for tasks such as surface area estimation and accurate modeling of biological structures, yet it has lacked a…
Texture analysis and classification are some of the problems which have been paid much attention by image processing scientists since late 80s. If texture analysis is done accurately, it can be used in many cases such as object tracking,…
Sphericity and roundness are fundamental measures used for assessing object uniformity in 2D and 3D images. However, using their strict definition makes computation costly. As both 2D and 3D microscopy imaging datasets grow larger, there is…
Medical visualization is the use of computers to create 3D images from medical imaging data sets, almost all surgery and cancer treatment in the developed world relies on it.Volume visualization techniques includes iso-surface…
We describe a technique of image analysis providing the time resolved shape of a water surface simultaneously with the three-component velocity field on this surface. The method relies on a combination of stereoscopic surface mapping and…
Visual odometry techniques typically rely on feature extraction from a sequence of images and subsequent computation of optical flow. This point-to-point correspondence between two consecutive frames can be costly to compute and suffers…
A novel method for common and individual feature analysis from exceedingly large-scale data is proposed, in order to ensure the tractability of both the computation and storage and thus mitigate the curse of dimensionality, a major…
X-ray tomographic reconstruction typically uses voxel basis functions to represent volumetric images. Due to the structure in voxel basis representations, efficient ray-tracing methods exist allowing fast, GPU accelerated implementations.…
Neural implicit representations have become a popular choice for modeling surfaces due to their adaptability in resolution and support for complex topology. While previous works have achieved impressive reconstruction quality by training on…
We present and discuss different algorithms for converting rectangular imagery into elliptical regions. We mainly focus on methods that use mathematical mappings with explicit and invertible equations. The key idea is to start with…
Geometrical Volume-of-Fluid (VoF) methods mainly support structured meshes, and only a small number of contributions in the scientific literature report results with unstructured meshes and three spatial dimensions. Unstructured meshes are…
Displacement mapping is an important tool for modeling detailed geometric features. We explore the problem of authoring complex surfaces while ray tracing interactively. Current techniques for ray tracing displaced surfaces rely on…