Related papers: Detecting and visualizing 3-dimensional surgery
We introduce a type of surgery on metric spaces. This surgery, in some sense, seeks to replace a subspace $S$ of a metric space $X$ with another metric space $T$ via a function $f : S \to T$. When $T$ is a discrete space, this amounts to…
We propose an approach to 3D reconstruction via inverse procedural modeling and investigate two variants of this approach. The first option consists in the fitting set of input parameters using a genetic algorithm. We demonstrate the…
The three-dimensional topologies of the membrane of M-theory can be constructed by performing Dehn surgery along knot lines. We investigate membranes wrapped around a circle and the correponding subset of topologies (Seifert manifolds). The…
We present a novel methodology based on geometric approach to simulate magnification lens effects. Our aim is to promote new applications of powerful geometric modeling techniques in visual computing. Conventional image…
Many surface cues support three-dimensional shape perception, but people can sometimes still see shape when these features are missing -- in extreme cases, even when an object is completely occluded, as when covered with a draped cloth. We…
While 3D GANs have recently demonstrated the high-quality synthesis of multi-view consistent images and 3D shapes, they are mainly restricted to photo-realistic human portraits. This paper aims to extend 3D GANs to a different, but…
A human 3D avatar is one of the important elements in the metaverse, and the modeling effect directly affects people's visual experience. However, the human body has a complex topology and diverse details, so it is often expensive,…
Reconstruction of a 3D shape from a single 2D image is a classical computer vision problem, whose difficulty stems from the inherent ambiguity of recovering occluded or only partially observed surfaces. Recent methods address this challenge…
Three-dimensional (3D) ultrasound imaging can overcome the limitations of conventional two dimensional (2D) ultrasound imaging in structural observation and measurement. However, conducting volumetric ultrasound imaging for large-sized…
Computational knot theory and 3-manifold topology have seen significant breakthroughs in recent years, despite the fact that many key algorithms have complexity bounds that are exponential or greater. In this setting, experimentation is…
Gauging is a powerful operation on symmetries in quantum field theory (QFT), as it connects distinct theories and also reveals hidden structures in a given theory. We initiate a systematic investigation of gauging discrete generalized…
It is important to have fast and effective methods for simplifying 3-manifold triangulations without losing any topological information. In theory this is difficult: we might need to make a triangulation super-exponentially more complex…
We try to convince the reader that the categorical version of differential geometry, called Synthetic Differential Geometry (SDG), offers valuable tools which can be applied to work with some unsolved problems of general relativity. We do…
Recent advances in 3D human shape reconstruction from single images have shown impressive results, leveraging on deep networks that model the so-called implicit function to learn the occupancy status of arbitrarily dense 3D points in space.…
The cosmetic surgery conjecture predicts that for a non-trivial knot in the three-sphere, performing two different Dehn surgeries results in distinct oriented three-manifolds. Hanselman reduced the problem to $\pm 2$ or $\pm 1/n$ surgeries…
This paper introduces a deep neural network based method, i.e., DeepOrganNet, to generate and visualize high-fidelity 3D / 4D organ geometric models from single-view medical image in real time. Traditional 3D / 4D medical image…
Manifolds occur naturally as configuration spaces of robotic systems. They provide global descriptions of local coordinate systems that are common tools in expressing positions of robots. The purpose of this survey is threefold. Firstly, we…
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…
In this paper we address the task of the comparison and the classification of 3D shape sequences of human. The non-linear dynamics of the human motion and the changing of the surface parametrization over the time make this task very…
3D modeling is becoming a well-developed field of medicine, but its applicability can be limited due to the lack of software allowing for easy utilizations of generated 3D visualizations. By leveraging recent advances in virtual reality, we…