Publications by Michaël Unser

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We propose a general approach for the design of 2D feature detectors from a class of steerable functions based on the optimization of a Canny-like criterion. In contrast with previous computational designs, our approach is truly 2D and provides filters that have closed-form expressions. It also yields operators that have a better orientation selectivity than the classical gradient or Hessian-based detectors. We illustrate the method with the design of operators for edge and ridge detection. We present some

We review the normal-based interpolating subdivision scheme proposed in [1]. We show that it allows the user to exactly represent circles/spheres whenever suitable initial data are provided, and we also prove that it enjoys the property of similarity invar ...

Every now and then, a new design of an interpolation kernel shows up in the literature. While interesting results have emerged, the traditional design methodology proves laborious and is riddled with very large systems of linear equations that must be solved analytically. In this paper, we propose to ease this burden by providing an explicit formula that will generate every possible piecewise-polynomial kernel given its degree, its support, its regularity, and its order of approximation. This formula contai

We provide a complete pipeline for the detection of patterns of interest in an image. In our approach, the patterns are assumed to be adequately modeled by a known template, and are located at unknown positions and orientations that we aim at retrieving. W ...

Differential phase contrast imaging using grating interferometer is a promising alternative to conventional X-ray radiographic methods. It provides the absorption, differential phase and scattering information of the underlying sample simultaneously. Phase ...

Microscopy imaging often suffers from limited depth-of-focus. However, the specimen can be “optically sectioned” by moving the object along the optical axis; different areas appear in focus in different images. Extended depth-of-focus is a fusion algorithm that combines those images into one single sharp composite. One promising method is based on the wavelet transform. In this paper, we show how the wavelet-based image fusion technique can be improved and easily extended to multi-channel data. First, we pr

This tutorial covers biomedical image reconstruction, from the foundational concepts of system modeling and direct reconstruction to modern sparsity and learning-based approaches. Imaging is a critical tool in biological research and medicine, and most ima ...

Motivation: Rotated template matching is an efficient and versatile algorithm to analyze microscopy images, as it automates the detection of stereotypical structures, such as organelles that can appear at any orientation. Its performance however quickly de ...

We present a new digital two-step reconstruction method for off-axis holograms recorded on a CCD camera. First, we retrieve the complex object wave in the acquisition plane from the hologram's samples. In a second step, if required, we propagate the wave front by using a digital Fresnel transform to achieve proper focus. This algorithm is sufficiently general to be applied to sophisticated optical setups that include a microscope objective. We characterize and evaluate the algorithm by using simulated data

Probably, the most important property of wavelets for signal processing is their multiscale derivative-like behavior when applied to functions. In order to extend the class of problems that can profit of wavelet-based techniques, we propose to build new families of wavelets that behave like an arbitrary scale-covariant operator. Our extension is general and includes many known wavelet bases. At the same time, the method takes advantage a fast filterbank decomposition-reconstruction algorithm. We give necess

Splines come in a variety of flavors that can be characterized in terms of some differential operator L. The simplest piecewise-constant model corresponds to the derivative operator. Likewise, one can extend the traditional notion of total variation by con ...

Because more output data must be created than is available from the input, magnification is an III-posed problem. Traditional magnification relies on resampling an interpolation model at the appropriate rate; unfortunately, this simple solution is blind to the presence of the analog fitter that was implicity present when the samples of the function to be magnified were acquired. Consistent resampling has been introduced to take this into account, but it turns out that this solution is still under-constraine

Localization microscopy enables imaging with resolutions that surpass the conventional optical diffraction limit. Notably, the Maximally INFormative LUminescence eXcitation (MINFLUX) method achieves super-resolution by shaping the excitation point spread f ...

Recently, we have introduced an integrated framework that combines wavelet-based processing with statistical testing in the spatial domain. In this paper, we propose two important enhancements of the framework. First, we revisit the underlying paradigm; i. ...

Many computer vision pipelines involve dynamic programming primitives such as finding a shortest path or the minimum energy solution in a tree-shaped probabilistic graphical model. In such cases, extracting not merely the best, but the set of M-best soluti ...

We propose a new algorithm to find the corpus callosum automatically from midsagittal brain MR (magnetic resonance) images using the statistical characteristics and shape information of the corpus callosum. We first extract regions satisfying the statistical characteristics (gray level distributions) of the corpus callosum that have relatively high intensity values. Then we try to find a region matching the shape information of the corpus callosum. In order to match the shape information, we propose a new d

Hermite splines are commonly used for interpolating data when samples of the derivative are available, in a scheme called Hermite interpolation. Assuming a suitable statistical model, we demonstrate that this method is actually optimal for reconstructing r ...

We introduce a novel generic energy functional that we employ to solve inverse imaging problems within a variational framework. The proposed regularization family, termed as structure tensor total variation (STV), penalizes the eigenvalues of the structure ...

In this work, we exploit the fact that wavelets can represent magnetic resonance images well, with relatively few coefficients. We use this property to improve magnetic resonance imaging (MRI) reconstructions from undersampled data with arbitrary k-space t ...

Michaël Unser

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Design of Steerable Filters for Feature Detection Using Canny-Like Criteria

Normal-Based Interpolating Subdivision For The Geometric Representation Of Deformable Models

Complete Parameterization of Piecewise-Polynomial Interpolation Kernels

Principled Design and Implementation of Steerable Detectors

Spline based iterative phase retrieval algorithm for X-ray differential phase contrast radiography

Extended Depth-of-Focus for Multi-Channel Microscopy Images: A Complex Wavelet Approach

Biomedical Image Reconstruction: From the Foundations to Deep Neural Networks

Steer'n'Detect: fast 2D template detection with accurate orientation estimation

Complex-Wave Retrieval from a Single Off-Axis Hologram

Construction of wavelet bases that mimic the behaviour of some given operator

Splines Are Universal Solutions of Linear Inverse Problems with Generalized TV Regularization

Consistent And Regularized Magnification Of Images

Point-spread-function engineering in MINFLUX: optimality of donut and half-moon excitation patterns

WSPM: Wavelet-Based Statistical Parametric Mapping

Diverse M-Best Solutions by Dynamic Programming

Automated Segmentation of the Corpus Callosum in Midsagittal Brain Magnetic Resonance Images

Statistical Optimality of Hermite Splines

Measuring Complexity of Learning Schemes Using Hessian-Schatten Total Variation

Structure Tensor Total Variation

A Fast Wavelet-Based Reconstruction Method for Magnetic Resonance Imaging