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In order to study projections of smooth curves, we introduce multifiltrations obtained by combining flags of osculating spaces. We classify all configurations of singularities occurring for a projection of a smooth curve embedded by a…
A new analytical formulation is prescribed to solve the Helmholtz equation in 2D with arbitrary boundary. A suitable diffeomorphism is used to annul the asymmetries in the boundary by mapping it into an equivalent circle. This results in a…
Boundary representation (B-rep) is the industry standard for computer-aided design (CAD). While deep learning shows promise in processing B-rep models, existing methods suffer from a representation gap: continuous approaches offer…
In this paper, we propose a novel gradient-based method to optimize curvilinear masks in optical lithography. The mask pattern is represented by periodic B-spline curves. We apply Delaunay triangulation to discretize the domains circled by…
In this paper, we first summarize the existing algorithms for computing all the generalized asymptotes of a plane algebraic curve implicitly or parametrically defined. From these previous results, we derive a method that allows to easily…
In this paper we propose two proximal gradient algorithms for fractional programming problems in real Hilbert spaces, where the numerator is a proper, convex and lower semicontinuous function and the denominator is a smooth function, either…
Intrinsic random functions (IRF) provide a versatile approach when the assumption of second-order stationarity is not met. Here, we develop the IRF theory on the circle with its universal kriging application. Unlike IRF in Euclidean spaces,…
Collective coordinates are frequently employed in path integrals to manage divergences caused by fluctuations around saddle points that align with classical symmetries. These coordinates parameterize a manifold of zero modes and more…
We are introducing two methods for revealing the true inflection point of data that contains or not error. The starting point is a set of geometrical properties that follow the existence of an inflection point p for a smooth function. These…
Shape implicit neural representations (INRs) have recently shown to be effective in shape analysis and reconstruction tasks. Existing INRs require point coordinates to learn the implicit level sets of the shape. When a normal vector is…
We formulate as an inverse problem the construction of sparse parametric continuous curve models that fit a sequence of contour points. Our prior is incorporated as a regularization term that encourages rotation invariance and sparsity. We…
We develop a new general method for computing the decomposition type of the normal bundle to a projective rational curve. This method is then used to detect and explain an example of a Hilbert scheme that parametrizes all the rational…
It is shown that if a proper holomorphic map $f: \mathbb C^n \to \mathbb C^N$, $1<n\le N$, sends a pseudoconvex real analytic hypersurface of finite type into another such hypersurface, then any $n-1$ dimensional component of the critical…
Connected decision boundaries are useful in several tasks like image segmentation, clustering, alpha-shape or defining a region in nD-space. However, the machine learning literature lacks methods for generating connected decision boundaries…
Active contour models based on partial differential equations have proved successful in image segmentation, yet the study of their geometric formulation on arbitrary geometric graphs is still at an early stage. In this paper, we introduce…
Given a bounded n-connected domain in the plane bounded by non-intersecting Jordan curves, and given one point on each boundary curve, L. Bieberbach proved that there exists a proper holomorphic mapping of the domain onto the unit disc that…
We introduce a rotation-invariant representation of planar shapes. In particular, this representation encodes shapes as vectors such that the Euclidean distance between them serves as a valid shape distance. For standardized, star-shaped…
A space-filling function is a bijection from the unit line segment to the unit square, cube, or hypercube. The function from the unit line segment is continuous. The inverse function, while well-defined, is not continuous. Space-filling…
In this paper we introduce the notion of rational Hausdorff divisor, we analyze the dimension and irreducibility of its associated linear system of curves, and we prove that all irreducible real curves belonging to the linear system are…
A path integral formulation is developed to study the spectrum of radiation from a perfectly reflecting (conducting) surface. It allows us to study arbitrary deformations in space and time. The spectrum is calculated to second order in the…