Related papers: Detecting and visualizing 3-dimensional surgery
The necessity of renormalization arises from the infinite integrals which are caused by the discrepancy between the orders of differential and integral operators in the four dimensional QFTs. Therefore in view of the fact that finiteness…
We present a simple visual description of the topology of the space of three-dimensional rotations, requiring just intuition, imagination and no advanced math.
Face is one of the most important things for communication with the world around us. It also forms our identity and expressions. Estimating the face structure is a fundamental task in computer vision with applications in different areas…
In this paper, as a fundamental study on the theory of Morse functions and their higher dimensional versions or fold maps and applications to geometric theory of manifolds, which were started in 1950s by differential topologists such as…
Accurate and robust tracking and reconstruction of the surgical scene is a critical enabling technology toward autonomous robotic surgery. Existing algorithms for 3D perception in surgery mainly rely on geometric information, while we…
The theory of Morse functions and their higher dimensional versions or fold maps on manifolds and its application to geometric theory of manifolds is one of important branches of geometry and mathematics. Studies related to this was started…
Surgery exact triangles in various 3-manifold Floer homology theories provide an important tool in studying and computing the relevant Floer homology groups. These exact triangles relate the invariants of 3-manifolds, obtained by three…
Minimally invasive procedures have been advanced rapidly by the robotic laparoscopic surgery. The latter greatly assists surgeons in sophisticated and precise operations with reduced invasiveness. Nevertheless, it is still safety critical…
3D face reconstruction technology aims to generate a face stereo model naturally and realistically. Previous deep face reconstruction approaches are typically designed to generate convincing textures and cannot generalize well to multiple…
This paper considers an extension of origami geometry to the case of "folding" a three dimensional (3D) space along a plane. First, all possible incidence constraints between given points, lines and planes are analyzed by using the geometry…
Generative reconstruction methods compute the 3D configuration (such as pose and/or geometry) of a shape by optimizing the overlap of the projected 3D shape model with images. Proper handling of occlusions is a big challenge, since the…
Recent years have witnessed the emergence and increasing popularity of 3D medical imaging techniques with the development of 3D sensors and technology. However, achieving geometric invariance in the processing of 3D medical images is…
In this work, we present an automated workflow to bring human figures, one of the most frequently appearing entities on pictorial maps, to the third dimension. Our workflow is based on training data and neural networks for single-view 3D…
There are various results that frame left-orderability of a group as a geometric property. Indeed, the fundamental group of a 3-manifold is left-orderable whenever the first Betti number is positive; in the case that the first Betti number…
Three-dimensional (3D) images, such as CT, MRI, and PET, are common in medical imaging applications and important in clinical diagnosis. Semantic ambiguity is a typical feature of many medical image labels. It can be caused by many factors,…
Radiography is widely used in orthopedics for its affordability and low radiation exposure. 3D reconstruction from a single radiograph, so-called 2D-3D reconstruction, offers the possibility of various clinical applications, but achieving…
We review two different methods of calculating Witten's invariant: a stationary phase approximation and a surgery calculus. We give a detailed description of the 1-loop approximation formula for Witten's invariant and of the technics…
We study embedded spheres in 4-manifolds (2-knots) via doubly pointed trisection diagrams, showing that such descriptions are unique up to stabilization and handleslides, and we describe how to obtain trisection diagrams for certain…
It is shown that with finitely many exceptions, the fundamental group obtained by Dehn surgery on a one cusped hyperbolic 3-manifold contains the fundamental group of a closed surface.
We describe decomposition formulas for rotations of $R^3$ and $R^4$ that have special properties with respect to stereographic projection. We use the lower dimensional decomposition to analyze stereographic projections of great circles in…