Related papers: Surgery of spline-type and molecular frames
Boundary-induced pattern formation from a spatially uniform state is investigated using one-dimensional reaction-diffusion equations. The temporal oscillation is successively transformed into a spatially periodic pattern, triggered by…
Image segmentation is often performed on medical images for identifying diseases in clinical evaluation. Hence it has become one of the major research areas. Conventional image segmentation techniques are unable to provide satisfactory…
Deep learning approaches to accelerated MRI take a matrix of sampled Fourier-space lines as input and produce a spatial image as output. In this work we show that by careful choice of the offset used in the sampling procedure, the…
This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier…
In this paper we present a method for direct evaluation of generalized B-splines (GB-splines) via the local representation of these curves as piecewise functions. To accomplish this we introduce a local structure that makes GB-spline curves…
Due to their adaptive nature, empirical wavelets had several successes in many fields from engineering, science, medical signal/image processing. Recently, a general theoretical framework has been developed in the one-dimensional case,…
We used a collocation method in refinable spline space to solve a linear dynamical system having fractional derivative in time. The method takes advantage of an explicit derivation rule for the B-spline basis that allows us to efficiently…
Semialgebraic splines are functions that are piecewise polynomial with respect to a cell decomposition into sets defined by polynomial inequalities. We study bivariate semialgebraic splines, formulating spaces of semialgebraic splines in…
Box splines provide smooth spline spaces as shifts of a single generating function on a lattice and so generalize tensor-product splines. Their elegant theory is laid out in classical papers and a summarizing book. This compendium aims to…
In this work we use the deformation procedure and explore the route to obtain distinct field theory models that present similar stability potentials. Starting from systems that interact polynomially or hyperbolically, we use a deformation…
We propose a new model for pattern formation in peeling of an adhesive tape based on the equation of motion for the displacement of deformed adhesives in the peel front. The spatiotemporal patterns obtained from the model are consistent…
Optical wave packets that are localized in space and time, but nevertheless overcome diffraction and travel rigidly in free space, are a long sought-after field structure with applications ranging from microscopy and remote sensing, to…
In the same manner that free-space propagation and curved glass lenses are used to shape the spatial properties of light, a combination of chromatic dispersion and devices known as time lenses may be used to reshape its temporal properties.…
Machine learning has achieved impressive performance in tomographic reconstruction, but supervised training requires paired measurements and ground-truth images that are often unavailable. This has motivated self-supervised approaches,…
We propose a direct reconstruction algorithm for Computed Tomography, based on a local fusion of a few preliminary image estimates by means of a non-linear fusion rule. One such rule is based on a signal denoising technique which is…
In this paper we will look at the connection of frames and finite dimensionality. A main focus is to present simple algorithms and make them available online. The main result is a way to 'switch' between different frames, giving an…
Standard video frame interpolation methods first estimate optical flow between input frames and then synthesize an intermediate frame guided by motion. Recent approaches merge these two steps into a single convolution process by convolving…
We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane arrangements. Using our decomposition, we bound the number of…
In this paper we implement experimentally the spatial shape modelling of nondiffracting optical beams via computer generated holograms. The results reported here are the experimental confirmation of the so called Frozen Wave method,…
We demonstrate a different scheme to perform optical sectioning of a sample based on the concept of induced coherence [Zou et al., Phys. Rev. Lett. 67, 318 (1991)]. This can be viewed as a different type of optical coherence tomography…