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An Inner-Product Calculus for Periodic Functions and Curves

Related publications (37)

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Minimizing movements along a sequence of functionals and curves of maximal slope

Maria Colombo

We prove that a general condition introduced by Colombo and Gobbino to study limits of curves of maximal slope allows us to characterize also minimizing movements along a sequence of functionals as curves of maximal slope of a limit functional. ...

2016

Similarity-Based Shape Priors for 2D Spline Snakes

Michaël Unser, Daniel Andreas Schmitter

We present a new formulation of a shape space containing all continuously defined 2D spline curves up to a similarity transform of a reference shape. We are able to measure a distance between an arbitrary curve and the shape space itself. Our contribution ...

IEEE2015

A distance measure for colored curves

Seyed Mohsen Moosavi Dezfooli

In some computer vision applications, matching between shapes and colors are required. There are lots of similarity measures for shapes, especially curves, but as far as we know there are not many that deal with shapes and colors at the same time. In this ...

2015

Snakes with Tangent-Based Control and Energies for Bioimage Analysis

Michaël Unser, Ricard Delgado Gonzalo, Virginie Sophie Uhlmann

We propose a novel active contour for the analysis of filament-like structures and boundaries—features that traditional snakes based on closed curves have difficulties to delineate. Our method relies on a parametric representation of an open curve involvin ...

IEEE2014

Sampling Curves with Finite Rate of Innovation

Thierry Blu, Hanjie Pan, Pier Luigi Dragotti

In this paper, we extend the theory of sampling signals with finite rate of innovation (FRI) to a specific class of two-dimensional curves, which are defined implicitly as the zeros of a mask function. Here the mask function has a parametric representation ...

Institute of Electrical and Electronics Engineers2014

Constructing reparameterization invariant metrics on spaces of plane curves

Martins Bruveris, Martin Bauer

Metrics on shape spaces are used to describe deformations that take one shape to another, and to define a distance between shapes. We study a family of metrics on the space of curves, which includes several recently proposed metrics, for which the metrics ...

Elsevier2014

Geometric Variational Models for Inverse Problems in Imaging

Virginia Estellers Casas

This dissertation develops geometric variational models for different inverse problems in imaging that are ill-posed, designing at the same time efficient numerical algorithms to compute their solutions. Variational methods solve inverse problems by the fo ...

EPFL2013

G1 continuous approximate curves on NURBS surfaces

Bailin Deng, Wei Zeng

Curves on surfaces play an important role in computer aided geometric design. In this paper, we present a parabola approximation method based on the cubic reparameterization of rational Bezier surfaces, which generates G1 continuous approximate curves lyin ...

2012

Snakes With an Ellipse-Reproducing Property

Michaël Unser, Philippe Thévenaz, Ricard Delgado Gonzalo, Chandra Sekhar Seelamantula

We present a new class of continuously defined parametric snakes using a special kind of exponential splines as basis functions. We have enforced our bases to have the shortest possible support subject to some design constraints to maximize efficiency. Whi ...

IEEE2012

Special Curve Patterns for Freeform Architecture

Bailin Deng

In recent years, freeform shapes are gaining more and more popularity in architecture. Such shapes are often challenging to manufacture, and have motivated an active research field called architectural geometry. In this thesis, we investigate patterns of s ...

Vienna University of Technology2011