Biomedical Imaging Group

Seminars

CONTENTS |

Seminars |

Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems30 Jan 2018

Fast Piecewise-Affine Motion Estimation Without Segmentation19 Dec 2017

Continuous Representations in Bioimage Analysis: a Bridge from Pixels to the Real World12 Dec 2017

Steer&Detect on Images 14 Nov 2017

Fundamental computational barriers in inverse problems and the mathematics of information27 Oct 2017

Variational use of B-splines and Kernel Based Functions27 Oct 2017

Kernel Based Functions are generalizations of spline functions and radial basis functions. These R^d to R functions are in the form f = \sum_{i=1}^n λi φ(x−xi) or \sum_{i=1}^n λi φ(x−xi)+pk(x) where φ is called the kernel, (xi)_{i=1:n} ∈ (R^d)^n are the so called centers of f, (λi)_{i=1:n} are real coefficients, and pk is some degree k polynomial. When φ is a bell shaped function meeting some property (such as, in particular \sum_{i=1}^n φ(x) = 1 for any x ∈ R^d), we write it B and call it, for short, B-spline. In this talk we present two particular uses of these Kernel Based Functions, and a property of a specific polynomial interpolation. First, hierarchical B-splines: using B-splines of different scales, and a mean square optimization, we show how to approximate scattered data with possibility of zoom on some regions, adaptively from the data. We so obtain locally tensor product functions, where the grid of the centers is finer in some regions and coarser in other regions. Second, in a CAGD aim and using modified (variational) Bézier curves or surfaces, we show that it is possible to derive B-spline curves or surfaces being closer to (or further from) the control polygon, while being in the same vectorial space. This gives more flexibility to easily derive new forms. Third we present variational polynomial interpolation, which is true polynomial interpolation of any given data, and so obtain a polynomial interpolation without the famous Runge oscillations. These interpolating polynomials converge towards the interpolating polynomial spline of the data.

Deep learning based data manifold projection - a new regularization for inverse problems17 Oct 2017

GlobalBioIm Lib - v2: new tools, more flexibility, and improved composition rules.03 Oct 2017

Fractional Integral transforms and Time-Frequency Representations02 Jun 2017

First steps toward fast PET reconstruction30 May 2017

Lipid membranes and surface reconstruction - a biologically inspired method for 3D segmentation16 May 2017

Optical Diffraction Tomography: Principles and Algorithms09 May 2017

Compressed Sensing for Dose Reduction in STEM Tomography11 Apr 2017

Chasing Mycobacteria10 Apr 2017

Multifractal analysis for signal and image classification23 Mar 2017

Inverse problems and multimodality for biological imaging28 Feb 2017

A unified reconstruction framework for coherent imaging24 Jan 2017

BPConvNet for compressed sensing recovery in bioimaging10 Jan 2017

Steerable template detection based on maximum correlation: preliminary results13 Dec 2016

Opportunities in Computational Imaging for Biomicroscopy06 Dec 2016

A multiple scattering approach to diffraction tomography30 Nov 2016

Learning Optimal Shrinkage Splines for ADMM Algorithms22 Nov 2016

SIGGRAPH ASIA 201601 Nov 2016

Lévy's Persian summers18 Oct 2016

High-quality parallel-ray X-ray CT back projection using optimized interpolation11 Oct 2016

Algorithmic Aspects of Compressive Sensing03 Oct 2016

ICIP 201620 Sep 2016

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