Splines are unifying mathematical objects that allow making the link between the real continuous world of physics and the digital world of computers. In the field of imaging, a whole class of problems are usually formulated in the continuous domain but call for a digital implementation, which can be efficiently achieved relying on splines. Spline models are advantageous not only computationally, but also conceptually as they allow drawing a number of fundamental connections between disciplines. This mini-symposium focuses on research topics that are relevant to image processing including but not limited to the development of novel spline tools for image processing, segmentation, and for the efficient resolution of inverse problems such as computed tomography. It will also explore the deep connection between splines and variational methods, including Bayesian estimation as well as sparsity-promoting schemes.

Optimality of splines for the resolution of linear inverse problems with Tikhonov or total-variation regularization

Michael Unser (EPFL, Lausanne)

Sparse Approximation for Few View Tomographic Reconstruction

Alireza Entezari (Department of Computer & Information Science & Engineering, University of Florida, Gainesville)

Recovery of piecewise smooth signals on manifolds using structured low-rank methods

Mathews Jacob (Department of Electrical and Computer Engineering, University of Iowa)

Hermite-like representation of images in terms of samples with local tangents

Costanza Conti (University of Firenze)

Statistical optimality of Hermite splines for the reconstruction of self-similar signals

Virginie Uhlmann (EPFL, Lausanne)

The Role of Discretization in X-Ray CT Reconstruction

Michael McCann (EPFL)

Subdivision-based Active Contours

Anaïs Badoual (EPFL, Lausanne)

Sparse Approximation of Images by Adaptive Thinning

Armin Iske (Dept. Mathematics, University of Hamburg)

Applications of nonstationary wavelet filters in image processing

Vittoria Bruni (Dept. of Basic and Applied Sciences for Engineering, University of Rome “La Sapienza”)

Acceleration of B-spline based nonrigid image registration

Stefan Klein (Biomedical Imaging Group Rotterdam, Erasmus MC)

High-dimensional and accurate MRF dictionary-based fitting with spline interpolation

Willem van Valenberg (Quantitative Imaging Group, Delft University of Technology, Biomedical Imaging Group Rotterdam, Erasmus MC)

DTHB3D_Reg: Dynamic Truncated Hierarchical B-Spline Based 3D Nonrigid Image Registration

Aishwarya Pawar (Department of Mechanical Engineering, Carnagie Mellon University, Pittsburgh)

Organizers:

Carolina Beccari (Dept. Mathematics, University of Bologna)

Virginie Uhlmann (EPFL, Lausanne)

Michael Unser (EPFL, Lausanne)

Keywords:

bayesian methods, computed tomography, image registration, image representation, image segmentation, inverse problems