Assessing unconstrained surgical cuttings in VR using CNNs
We present a Convolutional Neural Network (CNN) suitable to assess unconstrained surgical cuttings, trained on a dataset created with a data augmentation technique.
cs.CV↗
arXiv subjects
Manos Kamarianakis
Publications and source records attributed to Manos Kamarianakis.
"Deep Cut": An all-in-one Geometric Algorithm for Unconstrained Cut, Tear and Drill of Soft-bodies in Mobile VR
In this work, we present an integrated geometric framework: "deep- cut" that enables for the first time a user to geometrically and algorithmically cut, tear and drill the surface of a skinned model without prior constraints, layered on top of a custom soft body mesh deformation algorithm. Both layered algorithms in this frame- work yield real-time results and are amenable for mobile Virtual Reality, in order to be utilized in a variety of interactive application scenarios. Our framework dramatically improves real-time user experience and task performance in VR, without pre-calculated or artificially designed cuts, tears, drills or surface deformations via predefined rigged animations, which is the current state-of-the-art in mobile VR. Thus our framework improves user experience on one hand, on the other hand saves both time and costs from expensive, manual, labour-intensive design pre-calculation stages.
cs.GR↗
Decidability of the theory of addition and the Frobenius map in rings of rational functions
We prove model completeness for the theory of addition and the Frobenius map for certain subrings of rational functions in positive characteristic. More precisely: Let $p$ be a prime number, $\mathbb{F}_{p}$ the prime field with $p$ elements, $F$ a field algebraic over $\mathbb{F}_p$ and $z$ a variable. We show that the structures of rings $R$, which are generated over $F[z]$ by adjoining a finite set of inverses of irreducible polynomials of $F[z]$ (e.g., $R=\mathbb{F}_p[z, \frac{1}{z}]$), with addition, the Frobenius map $x\mapsto x^p$ and the predicate '$\in F$' - together with function symbols and constants that allow building all elements of $\mathbb{F}_p[z]$ - are model complete, i.e., each formula is equivalent to an existential formula. Further, we show that in these structures all questions, i.e., \emph{first order sentences}, about the rings $R$ may be, constructively, translated into questions about $F$.
math.LO↗
Never 'Drop the Ball' in the Operating Room: An efficient hand-based VR HMD controller interpolation algorithm, for collaborative, networked virtual environments
In this work, we propose two algorithms that can be applied in the context of a networked virtual environment to efficiently handle the interpolation of displacement data for hand-based VR HMDs. Our algorithms, based on the use of dual-quaternions and multivectors respectively, impact the network consumption rate and are highly effective in scenarios involving multiple users. We illustrate convincing results in a modern game engine and a medical VR collaborative training scenario.
cs.GR↗
An All-In-One Geometric Algorithm for Cutting, Tearing, and Drilling Deformable Models
Conformal Geometric Algebra (CGA) is a framework that allows the representation of objects, such as points, planes and spheres, and deformations, such as translations, rotations and dilations as uniform vectors, called multivectors. In this work, we demonstrate the merits of multivector usage with a novel, integrated rigged character simulation framework based on CGA. In such a framework, and for the first time, one may perform real-time cuts and tears as well as drill holes on a rigged 3D model. These operations can be performed before and/or after model animation, while maintaining deformation topology. Moreover, our framework permits generation of intermediate keyframes on-the-fly based on user input, apart from the frames provided in the model data. We are motivated to use CGA as it is the lowest-dimension extension of dual-quaternion algebra that amends the shortcomings of the majority of existing animation and deformation techniques. Specifically, we no longer need to maintain objects of multiple algebras and constantly transmute between them, such as matrices, quaternions and dual-quaternions, and we can effortlessly apply dilations. Using such an all-in-one geometric framework allows for better maintenance and optimization and enables easier interpolation and application of all native deformations. Furthermore, we present these three novel algorithms in a single CGA representation which enables cutting, tearing and drilling of the input rigged model, where the output model can be further re-deformed in interactive frame rates. These close to real-time cut,tear and drill algorithms can enable a new suite of applications, especially under the scope of a medical VR simulation.
cs.GR↗
Deform, Cut and Tear a skinned model using Conformal Geometric Algebra
In this work, we present a novel, integrated rigged character simulation framework in Conformal Geometric Algebra (CGA) that supports, for the first time, real-time cuts and tears, before and/or after the animation, while maintaining deformation topology. The purpose of using CGA is to lift several restrictions posed by current state-of-the-art character animation & deformation methods. Previous implementations originally required weighted matrices to perform deformations, whereas, in the current state-of-the-art, dual-quaternions handle both rotations and translations, but cannot handle dilations. CGA is a suitable extension of dual-quaternion algebra that amends these two major previous shortcomings: the need to constantly transmute between matrices and dual-quaternions as well as the inability to properly dilate a model during animation. Our CGA algorithm also provides easy interpolation and application of all deformations in each intermediate steps, all within the same geometric framework. Furthermore we also present two novel algorithms that enable cutting and tearing of the input rigged, animated model, while the output model can be further re-deformed. These interactive, real-time cut and tear operations can enable a new suite of applications, especially under the scope of a medical surgical simulation.
cs.GR↗
Predicates of the 3D Apollonius Diagram
In this thesis we study one of the fundamental predicates required for the construction of the 3D Apollonius diagram (also known as the 3D Additively Weighted Voronoi diagram), namely the EDGECONFLICT predicate: given five sites $S_i, S_j,S_k,S_l,S_m$ that define an edge $e_{ijklm}$ in the 3D Apollonius diagram, and a sixth query site $S_q$, the predicate determines the portion of $e_{ijklm}$ that will disappear in the Apollonius diagram of the six sites due to the insertion of $S_q$. Our focus is on the algorithmic analysis of the predicate with the aim to minimize its algebraic degree. We decompose the main predicate into sub-predicates, which are then evaluated with the aid of additional primitive operations. We show that the maximum algebraic degree required to answer any of the sub-predicates and primitives, and, thus, our main predicate is 10 in non-degenerate configurations when the trisector is of Hausdorff dimension 1. We also prove that all subpredicates developed can be evaluated using 10 or 8-degree demanding operations for degenerate input for these trisector types, depending on whether they require the evaluation of an intermediate INSPHERE predicate or not. Among the tools we use is the 3D inversion transformation and the so-called qualitative symbolic perturbation scheme. Most of our analysis is carried out in the inverted space, which is where our geometric observations and analysis is captured in algebraic terms.
cs.CG↗
MAGES 3.0: Tying the knot of medical VR
In this work, we present MAGES 3.0, a novel Virtual Reality (VR)-based authoring SDK platform for accelerated surgical training and assessment. The MAGES Software Development Kit (SDK) allows code-free prototyping of any VR psychomotor simulation of medical operations by medical professionals, who urgently need a tool to solve the issue of outdated medical training. Our platform encapsulates the following novel algorithmic techniques: a) collaborative networking layer with Geometric Algebra (GA) interpolation engine b) supervised machine learning analytics module for real-time recommendations and user profiling c) GA deformable cutting and tearing algorithm d) on-the-go configurable soft body simulation for deformable surfaces.
cs.HC↗