CURL uses neural curves to enhance global image properties.
problem Global image enhancement using neural networks.
method CURL is a multi-colour space neural retouching block trained in HSV, CIELab, and RGB color spaces.
result CURL produces state-of-the-art image quality in RGB-to-RGB and RAW-to-RGB transformations.
New theory for curve-based 3D reconstruction and camera estimation.
problem Challenges in point feature extraction limit traditional methods.
method Differential geometry of general curves for image and space curves.
result Theoretical foundations for curve-based multiview reconstruction.
In this article, we investigate Bertrand curves corresponding to the spherical images of the tangent, binormal, principal normal and Darboux indicatrices of a space curve in Euclidean 3-space. As a result, in case of a space curve is a general helix, we show that the curves corresponding to the spherical images of its …
Enhances curve alignment for diverse data types.
problem Aligning curve data effectively.
method Developed nonlinear transformations for curve data.
result Successfully aligned synthetic and real curve data.
New method uses contours of segmented images for X-ray classification.
problem Classifying X-ray images of segmented radiography.
method Develops a new approach for image analysis of multivariate planar curves, addressing alignment issues.
result Demonstrates the robustness and appeal of the proposed method through detection of cardiomegaly and numerical experiments.
The paper studies hyperbolic phenomena on closed surfaces using bicorn curves.
problem Understanding hyperbolic phenomena on curve graphs of closed surfaces.
method Using the theory of bicorn curves to analyze the curve graphs of closed surfaces.
result Proves that the curve graph of any closed surface is 15-hyperbolic with one exception.
In this paper, we consider the intensity surface of a 2D image, we study the evolution of the symmetry sets (and medial axes) of 1-parameter families of iso-intensity curves. This extends the investigation done on 1-parameter families of smooth plane curves (Bruce and Giblin, Giblin and Kimia, etc.) to the general case…
Paper develops methods for curve matching in medical imaging.
problem Analyzing shape variation in medical images.
method Numerical discretization of Riemannian metrics, geodesic computation, and optimization.
result Computes Karcher mean for shape variation studies.
Study of curves and surfaces from single-direction projections.
problem Obtaining complete shape information from a single view.
method Theoretical study of differential geometric information from multiple orthogonal projections.
result Formulae for recovering certain information on curves or surfaces from their projections.
GDGAN improves medical image accuracy for rare diseases.
problem Poor accuracy for infrequent medical image classes.
method Serial GANs for general and detailed labels.
result GDGAN outperformed existing methods in AUC.
Uniform bound on geodesic images for surfaces using bicorn curves.
problem Bounding geodesic images on closed surfaces.
method Utilizing bicorn curves and properties of 1-slim triangles.
result Uniform bound of 44 for non-annular subsurfaces, 3 for specific cases.
An analytic approach and description are presented for the moduli cotangent sheaf for suitable stable curve families including noded fibers. For sections of the square of the relative dualizing sheaf, the residue map at a node gives rise to an exact sequence. The residue kernel defines the vanishing residue subsheaf. F…
We give a combinatorial proof, using the hyperbolicity of the curve graphs, of the bounded geodesic image theorem of Masur and Minsky. Recently it has been shown that curve graphs are uniformly hyperbolic, thus a universal bound can be given for the diameter of the geodesic image. We also generalize the theorem for pro…
Study of curves in Teichmüller discs and their geometry.
problem Understanding the geometry of curves in Teichmüller discs.
method Analysis of systole and cylinder sets, quasiconvexity, Hausdorff distance, nearest point projections.
result Sets of curves are quasiconvex and agree up to bounded distance.
Polygon solitons shrink and rotate under a curve shortening process.
problem Understanding the behavior of polygons under a specific curve shortening transformation.
method Analyzing smooth curves that solve a second-order differential equation to find solitons.
result A large class of solitons on spiral curves is described, showing how they shrink and rotate.
In this paper, we investigate a curve whose spherical image the tangent indicatrix and binormal indicatrix is slant helix and called it as a slant helix. We obtain that the spherical images are spherical slant helices defined by [3]. This notation is a generalization of a slant helix. Furthermore, we have given some ch…
Investigates the vertex curve of smooth surfaces in 3D space, connecting geometry and image analysis.
problem Understanding the geometry of smooth surfaces in 3D space.
method Analyzes the vertex curve, related to differential geometry and symmetry sets of isophote curves.
result Establishes connections between the vertex curve and other geometric curves like parabolic and flecnodal curves.
A stroke-based method reconstructs characters from noisy images.
problem Challenges in reconstructing characters from noisy images.
method Uses a weighted quadratic Bezier curve (WQBC) to represent strokes.
result Achieves excellent reconstruction in real scenes.
Square can fit inside curves close to smooth ones.
problem Finding inscribed squares in nearly smooth curves.
method Using curvature and a map to relate curves, proving existence of inscribed squares.
result Curves close to smooth ones contain inscribed squares.
Study symmetry groups and curves from sums of exponentials.
problem Understanding the geometry and symmetry of curves from sums of exponentials.
method Analysis of symmetry groups, winding numbers, and parametrization of the unit circle.
result Unified method for constructing curves with specific properties.
Computes the monodromy of cubic surfaces branching over smooth cubic curves.
problem Understanding the monodromy of cubic surfaces.
method Computational approach using the relationship between inflection points and lines on cubic surfaces.
result The monodromy map is surjective onto the centralizer of the image of a generator of the deck group.
New findings on non-congruent curves with identical signatures.
problem Identifying congruence of non-degenerate curves with non-simple signatures.
method Associated directed graphs to signatures and used paths to reflect global and local symmetries.
result Non-congruent, non-degenerate curves can have identical signatures.
We present a novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. The motivation comes from the problem of establishing a correspondence between an object and an image, taken by a camera with unknown posit…
Paper finds unique solutions for curved surfaces with specific gradient.
problem Existence of curved surfaces with specific gradient.
method Second boundary value problem of constant mean curvature equations.
result Unique convex solutions for constant mean curvature equations.
Study of special vector fields on curves on spacelike surfaces.
problem Characterizing vector fields on curves on spacelike surfaces.
method Introducing and analyzing five special vector fields associated with the Lorentzian Darboux frame.
result Investigated the singularities of the introduced vector fields.
If X is a compact set, a {\it topological contraction} is a self-embedding f such that the intersection of the successive images fk(X), k>0, consists of one point. In dimension 3, we prove that there are smooth topological contractions of the handlebodies of genus ≥2 whose image is essential. Our proof i…
In this work, we discuss graph like image of curves under moment maps and their relation with the Newton polygon of the curve, which has applications to Lagrangian torus fibration of Calabi-Yau manifolds.
Study on constraints of monodromy group for smooth plane curves.
problem Understanding constraints on the monodromy group of smooth plane curves.
method Combining algebro-geometric and mapping class group theory.
result Invariant constrains the monodromy group, especially for degree 5.
Study character varieties of tangles to map immersed curves in the pillowcase.
problem Characterizing holonomy-perturbed traceless SU(2) character varieties.
method Examining marked tangles as endomorphisms in the cobordism category and using holonomy-perturbed traceless character variety functor.
result Endomorphisms of immersed curves in the pillowcase have the same image.
Study calculates Gothic Teichmüller curves' Euler characteristics, differing from usual.
problem Computing Euler characteristics of Gothic Teichmüller curves.
method Construction of 'Gothic' Hilbert modular forms.
result Euler characteristic not proportional to ambient surfaces.
Machine learning classifies surface wave dispersion curves from ambient noise.
problem Classifying surface wave dispersion curves from ambient noise.
method Convolutional neural network (U-net) with transfer learning and supervised learning.
result Machine classification nearly identical to human-picked phases.
In this work, we studied the properties of the spherical indicatrices of a Bertrand curve and its mate curve and presented some characteristic properties in the cases that Bertrand curve and its mate curve are slant helices, spherical indicatrices are slant helices and we also researched that whether the spherical indi…
Algorithms compute the topology of hyperelliptic curves in 2D and 3D.
problem Computing the topology of hyperelliptic curves in higher dimensions.
method Birational mapping of the plane or space to compute the topology of the curve.
result Algorithms implemented in { t Maple} for computing the topology of hyperelliptic curves.
Researchers describe the Gromov boundary of a graph related to surfaces.
problem Understanding the Gromov boundary of a graph associated with surfaces.
method Described a dense subset of the Gromov boundary as geodesic laminations, proving the graph satisfies a bounded geodesic image theorem.
result The boundary is not compact.
Formula for analytic torsion forms in fibrations by projective curves.
problem Calculating analytic torsion forms for specific geometric structures.
method New description of Bismut's equivariant Bott-Chern current for isolated fixed points.
result Explicit formula for analytic torsion forms in fibrations by projective curves.
Paper disproves Wright's periodic map conjecture.
problem Existence of periodic maps on closed hyperbolic surfaces.
method Analyzes automorphisms and curve behavior on surfaces.
result No periodic map can fill every curve with its image.
Step 2 Carnot groups can approximate horizontal curves without error.
problem Approximating horizontal curves in step 2 Carnot groups.
method Verification of Lusin approximation for free Carnot groups of step 2 and preservation by homomorphisms.
result All step 2 Carnot groups admit Lusin approximation for horizontal curves.
Neural network improves aneurysm classification accuracy in MRI images.
problem Classifying aneurysm status in MRI images with varying radiologist expertise.
method Constructed neural network trained on radiologists' annotations, compared to a control model.
result Proposed model had a higher area under the curve (0.845 vs. 0.793).
This paper is devoted to the complete classification of space curves under affine transformations in the view of Cartan's theorem. Spivak has introduced the method but has not found the invariants. Furthermore, for the first time, we propound a necessary and sufficient condition for the invariants. Then, we study the s…
A Steiner deltoid maintains constant area across all boundary points of an ellipse.
problem Finding curves associated with ellipses with constant area.
method Negative Pedal Curve of the Ellipse with respect to a boundary point M.
result The Steiner deltoid has constant area over all boundary points.
New method identifies vanishing arcs for curve singularities.
problem Characterizing arcs sent to geometric vanishing cycles.
method Introducing geometric variation operator and vanishing arcsets.
result Existence of topological exceptional collections of arcsets.
Factor analysis improves PET image interpretation by considering non-standard noise distributions.
problem Improving interpretation of dynamic PET images with non-standard noise distributions.
method Proposes using β-divergence to fit factor models for different noise distributions. result Improves factor analysis results for various noise types in PET images.
The coamoeba of any complex algebraic plane curve V is its image in the real torus under the argument map. The area counted with multiplicity of the coamoeba of any algebraic curve in (C∗)2 is bounded in terms of the degree of the curve. We show in this Note that up to multiplication by a constant in $(\…
Study on curve shortening flow in 3D space curves, showing convexity preservation and avoidance principle.
problem Analyzing the behavior of space curves under curve shortening flow in R3. method Analysis of properties of space curves evolved by the curve shortening flow, including convexity preservation and avoidance principle.
result Orthogonal projections of space curves remain convex, and the Avoidance principle is shown for spherical curves.
The paper explores the existence of multiple curved foldings with a common crease pattern.
problem Determining the number of distinct curved foldings with a given crease and crease pattern.
method Analyzing origami maps and their singular sets, focusing on the crease and crease pattern.
result For a non-closed simple arc crease, there are exactly 4 distinct non-congruent curved foldings.
Green's functions and Biot-Savart operators on curved spaces quantify linking numbers.
problem Calculating linking numbers on curved spaces.
method Constructing radial fundamental solutions for differential form Laplacian.
result Green's functions and Biot-Savart operators link curved spaces' geometry to linking numbers.
The first part of this paper is a survey on Teichmueller curves and Veech groups, with emphasis on the special case of origamis where much stronger tools for the investigation are available than in the general case. In the second part we study a particular configuration of origami curves in genus 3: A "base" curve is i…
Study on the geometry of secant caustic of planar curves.
problem Analyzing the secant caustic of planar curves.
method Investigating the geometrical properties of secant caustic, including number of branches, cusps, and inflexion points.
result Detailed investigation of secant caustic properties, especially for rosettes.