arXiv research

This short article aims at demonstrate that the Intersection over Union (or Jaccard index) is not a submodular function. This mistake has been made in an article which is cited and used as a foundation in another article. The Intersection of Union is widely used in machine learning as a cost function especially for imb…

YOLOv3 detects ships in real-time with high accuracy.

In medicine, visualizing chromosomes is important for medical diagnostics, drug development, and biomedical research. Unfortunately, chromosomes often overlap and it is necessary to identify and distinguish between the overlapping chromosomes. A segmentation solution that is fast and automated will enable scaling of co…

Algorithm generates adaptive confidence sets for instance segmentation with guaranteed coverage.

This paper introduces a very challenging dataset of historic German documents and evaluates Fully Convolutional Neural Network (FCNN) based methods to locate handwritten annotations of any kind in these documents. The handwritten annotations can appear in form of underlines and text by using various writing instruments…

Bayesian variational inference improves medical image segmentation confidence.

RankSEG-RMA improves semantic segmentation efficiency and applicability.

Deep Convolutional Neural Networks (DCNNs) are used extensively in medical image segmentation and hence 3D navigation for robot-assisted Minimally Invasive Surgeries (MISs). However, current DCNNs usually use down sampling layers for increasing the receptive field and gaining abstract semantic information. These down s…

Accurate volume segmentation from the Computed Tomography (CT) scan is a common prerequisite for pre-operative planning, intra-operative guidance and quantitative assessment of therapeutic outcomes in robot-assisted Minimally Invasive Surgery (MIS). 3D Deep Convolutional Neural Network (DCNN) is a viable solution for t…

In multimodal traffic monitoring, we gather traffic statistics for distinct transportation modes, such as pedestrians, cars and bicycles, in order to analyze and improve people's daily mobility in terms of safety and convenience. On account of its robustness to bad light and adverse weather conditions, and inherent spe…

AI tool automates blood segmentation from head CT scans after SAH.

TokenCut detects and segments objects in images and videos without supervision.

The following problem was proposed in 2010 by S. Lando. Let $M$ and $N$ be two unions of the same number of disjoint circles in a sphere. Do there always exist two spheres in 3-space such that their intersection is transversal and is a union of disjoint circles that is situated as $M$ in one sphere and as $N$ in the ot…

A new framework for consistent segmentation evaluation reduces operating losses.

In the semantic segmentation of street scenes the reliability of the prediction and therefore uncertainty measures are of highest interest. We present a method that generates for each input image a hierarchy of nested crops around the image center and presents these, all re-scaled to the same size, to a neural network …

The increasing size and complexity of scientific data could dramatically enhance discovery and prediction for basic scientific applications. Realizing this potential, however, requires novel statistical analysis methods that are both interpretable and predictive. We introduce Union of Intersections (UoI), a flexible, m…

Formula for volumes of odd strata of quadratic differentials using graph intersection numbers.

Accurate estimation of the positions and shapes of microscale objects is crucial for automated imaging-guided manipulation using a non-contact technique such as optical tweezers. Perception methods that use traditional computer vision algorithms tend to fail when the manipulation environments are crowded. In this paper…

The paper defines and proves stabilization for 3-manifold decompositions with multibranched surface intersections.

Let $X$ be a contractible $2$-complex which is a union of two contractible subcomplexes $Y$ and $Z.$ Is the intersection $Y\cap Z$ contractible as well? In this note, we prove that the inclusion-induced map $π_{1}(Y\cap Z)\rightarrow π_{1}(Z)$ is injective if $Y$ is $π_{1}$-injective subcomplex in a locally CAT(0) 2-co…

Motion is a dominant cue in automated driving systems. Optical flow is typically computed to detect moving objects and to estimate depth using triangulation. In this paper, our motivation is to leverage the existing dense optical flow to improve the performance of semantic segmentation. To provide a systematic study, w…

We study the way a strongly irreducible Heegaard surface $Σ$ intersects a knot exterior $X$ embedded in a 3-manifold, and show that if $Σ\cap \partial X$ consists of simple closed curves which are essential in both $Σ$ and $\partial X$, then the intersection $X \cap Σ$ consists of meridional annuli only. As an applicat…

Ancient solutions and translators identified for Lagrangian flow.

A benchmark evaluates ioUS-to-MR synthesis methods for brain tumor surgery.

We present a method that "meta" classifies whether seg-ments predicted by a semantic segmentation neural networkintersect with the ground truth. For this purpose, we employ measures of dispersion for predicted pixel-wise class probability distributions, like classification entropy, that yield heat maps of the input sce…

We prove a relative isoperimetric inequalities for Lagrangian half disks in $\mathbb{C}^2$ with respect to a Lagrangian plane, or a complex plane, or a union of any two of Lagrangian or complex planes that intersect transversally at the origin.

Study on geodesics proving index and intersection bounds, with examples of multiplicity.

SCENE-Net improves 3D point cloud segmentation with low resource usage and transparency.

Joyce's criterion for sLag smoothings extended to non-compact, non-transverse intersections.

We are interested in contractible n-manifolds M which "split" as M = A union B where A,B, and A intersect B are all homeomorphic to Euclidean n-space (such M are called open n-splitters) or A,B, and A intersect B are all homeomorphic to the n-dimensional unit ball (such M are called closed n-splitters). We introduce a …

Gay and Kirby introduced trisections which describe any closed oriented smooth 4-manifold $X$ as a union of three four-dimensional handlebodies. A trisection is encoded in a diagram, namely three collections of curves in a closed oriented surface $Σ$, guiding the gluing of the handlebodies. Any morphism $\varphi$ from …

This letter introduces an abstract learning problem called the "set embedding": The objective is to map sets into probability distributions so as to lose less information. We relate set union and intersection operations with corresponding interpolations of probability distributions. We also demonstrate a preliminary so…

Graph Laplacians adapt to different manifold dimensions, while Dirichlet energies converge to a tensorized Dirichlet energy.

The SO(3)-monopole program, initiated by Pidstrigatch and Tyurin [arXiv:dg-ga/9507004], yields a relationship between the Donaldson and Seiberg-Witten invariants through a cobordism between the moduli spaces defining these invariants. The main technical difficulty in this program lies in describing the links of singula…

CITE algorithm provides anytime-valid certification of model outputs.

We propose a novel approach for semantic segmentation that uses an encoder in the reverse direction to decode. Many semantic segmentation networks adopt a feedforward encoder-decoder architecture. Typically, an input is first downsampled by the encoder to extract high-level semantic features and continues to be fed for…

In this thesis, we consider semi-algebraic sets over a real closed field $R$ defined by quadratic polynomials. Semi-algebraic sets of $R^k$ are defined as the smallest family of sets in $R^k$ that contains the algebraic sets as well as the sets defined by polynomial inequalities, and which is also closed under the bool…

Study intersection homotopy groups in coarsenings of CS sets.

Same travelling times imply identical obstacles in Riemannian manifolds.

The analysis of scientific data of increasing size and complexity requires statistical machine learning methods that are both interpretable and predictive. Union of Intersections (UoI), a recently developed framework, is a two-step approach that separates model selection and model estimation. A linear regression algori…

Counting meanders on surfaces of arbitrary genus, with precise asymptotics.

Uniformly Euclidean metrics with isolated singularities on certain manifolds are Ricci flat and have nonnegative synthetic Ricci curvature.

The study explores convex unions and completions in simplicial pseudomanifolds, revealing unexpected behavior.

A knot K in 1-bridge position with respect to a genus-g Heegaard surface in a 3-manifold can be moved by isotopy through knots in 1-bridge position until it lies in a union of n parallel genus-g surfaces tubed together by n-1 straight tubes, with K intersecting each tube in two arcs connecting the ends. We prove that t…

Let G be a (real or complex) linear reductive algebraic group acting on an affine variety V. Let W be a subvariety. In this work we study how the G-orbits intersect W. We develop a criterion to determine when the intersection can be described as a finite union of orbits of a reductive subgroup. The conditions of the cr…

Study shows non-spectrality of certain curves and line segments.

We consider the "partial information decomposition" (PID) problem, which aims to decompose the information that a set of source random variables provide about a target random variable into separate redundant, synergistic, union, and unique components. In the first part of this paper, we propose a general framework for …

New characterization of geodesic currents via curve functionals.