Related papers: Detecting and visualizing 3-dimensional surgery
For the purposes of this paper, Dehn surgery along a curve K in a 3-manifold M with slope r is `exceptional' if the resulting 3-manifold M_K(r) is reducible or a solid torus, or the core of the surgery solid torus has finite order in the…
An invariant of orientable 3-manifolds is defined by taking the minimum $n$ such that a given 3-manifold embeds in the connected sum of $n$ copies of $S^2 \times S^2$, and we call this $n$ the embedding number of the 3-manifold. We give…
In this paper, we introduce a novel parametric method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford-Shah and the Chan-Vese functionals and perform a region-based segmentation of 3D…
Given an acyclic map $X\to Y$ of closed manifolds dimension $d$, we study the relationship between the embeddings of $Y$ in $S^{n}$ with those of $X$ in $S^{n}$ when $n-d \ge 3$. The approach taken here is to first solve the Poincar\'e…
Reconstructing 3D human heads in low-view settings presents technical challenges, mainly due to the pronounced risk of overfitting with limited views and high-frequency signals. To address this, we propose geometry decomposition and adopt a…
Two of the basic questions in contact topology are which manifolds admit tight contact structures, and on those that do, can we classify such structures. We present the first such classification on an infinite family of (mostly) hyperbolic…
For a 3-manifold with torus boundary admitting an appropriate involution, we show that Khovanov homology provides obstructions to certain exceptional Dehn fillings. For example, given a strongly invertible knot in S^3, we give obstructions…
Estimating the 3D shape of an object from a single or multiple images has gained popularity thanks to the recent breakthroughs powered by deep learning. Most approaches regress the full object shape in a canonical pose, possibly…
Human ability to visualize an image is usually hindered by optical scattering. Recent extensive studies have promoted imaging technique through turbid materials to a reality where color image can be restored behind scattering media in real…
This paper introduces two-dimensional diagrams that are slight generalizations of moment map images for toric four-manifolds and catalogs techniques for reading topological and symplectic properties of a symplectic four-manifold from these…
We extend the correspondence between universal statistical features of large-$c$ 2d CFTs and surgery methods in pure AdS$_3$ quantum gravity. In particular, we introduce a method that we call RMT surgery, which relates a large class of…
3D visual illusion is a perceptual phenomenon where a two-dimensional plane is manipulated to simulate three-dimensional spatial relationships, making a flat artwork or object look three-dimensional in the human visual system. In this…
This survey focuses on the computational complexity of some of the fundamental decision problems in 3-manifold theory. The article discusses the wide variety of tools that are used to tackle these problems, including normal and almost…
We develop the details of a surgery theory for contact manifolds of arbitrary dimension via convex structures, extending the 3-dimensional theory developed by Giroux. The theory is analogous to that of Weinstein manifolds in symplectic…
Semantic segmentation in cataract surgery has a wide range of applications contributing to surgical outcome enhancement and clinical risk reduction. However, the varying issues in segmenting the different relevant structures in these…
Deep learning-based 3-dimensional (3D) shape reconstruction from 2-dimensional (2D) magnetic resonance imaging (MRI) has become increasingly important in medical disease diagnosis, treatment planning, and computational modeling. This review…
Usually, lesions are not isolated but are associated with the surrounding tissues. For example, the growth of a tumour can depend on or infiltrate into the surrounding tissues. Due to the pathological nature of the lesions, it is…
We present a system that allows users to visualize complex human motion via 3D motion sculptures---a representation that conveys the 3D structure swept by a human body as it moves through space. Given an input video, our system computes the…
3D printing of surfaces has become an established method for prototyping and visualisation. However, surfaces often contain certain degenerations, such as self-intersecting faces or non-manifold parts, which pose problems in obtaining a 3D…
We present in this paper a novel approach for 3D/2D intraoperative registration during neurosurgery via cross-modal inverse neural rendering. Our approach separates implicit neural representation into two components, handling anatomical…