Publications by Michaël Unser

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Our interest is to characterize the spline-like integer-shift-invariant bases capable of reproducing exponential polynomial curves. We prove that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the ...

We present a unifying framework for point-spread function (PSF) models in high-numerical-aperture optical microscopy. Starting from the Richards-Wolf integral, we demonstrate the mathematical equivalence between Fourier-based and Bessel-based approaches as alternative parameterizations of the same propagation integral. This framework enables us to generalize correction factors such as Gibson-Lanni aberrations, apodisation, and arbitrary phase masks to both scalar and vectorial models. We provide an open-sou

We present a generic method to construct orthogonal projectors for two-dimensional landmark-based parametric spline curves. We construct vector spaces that define a geometric transformation (e.g., affine, similarity, and scaling) that is applied to a refer ...

Image processing (IP) can be taught very effectively by complementing the basic lectures with computer laboratories where the participants can actively manipulate and process images. This offering can be made even more attractive by allowing the students to develop their own IP code within a reasonable time frame. After a brief review of existing software packages that can be used for teaching IP, we present a system that we have designed to be as “student-friendly” as possible. The software is built around

To assist neurobiologists investigating the molecular mechanisms involved in neurite formation and differentiation, we have developed an interactive technique for the tracing and quantification of elongated image structures. The technique is based on an improved steerable filter for computing local ridge strength and orientation. It also uses a graph-searching algorithm with a novel cost function exploiting these image features to obtain globally optimal tracings between user-defined control points. To comp

A snakuscule (a minuscule snake) is the simplest active contour that we were able to design while keeping the quintessence of traditional snakes: an energy term governed by the data, and a regularization term. Our construction is an area-based snake, as op ...

In this work, we investigate the relationship between continuous-time autoregressive (AR) models and their sampled version. We consider uniform sampling and derive criteria for uniquely determining the continuous-time parameters from sampled data; the mode ...

The statements on the BIBO stability of continuoustime convolution systems found in engineering textbooks are often either too vague (because of lack of hypotheses) or mathematically incorrect. What is more troubling is that they usually exclude the identi ...

We extend Schoenberg's B-splines to all fractional degrees α > -1/2. These splines are constructed using linear combinations of the integer shifts of the power functions

x _{ + } ^{ \alpha }

(one-sided) or

|x| _{ * } ^{ \alpha }

(symmetric); in each case, they are α-Hölder continuous for α > 0. They satisfy most of the properties of the traditional B-splines; in particular, the Riesz basis condition and the two-scale relation, which makes them suitable for the construction of new families of wavelet

Practical image-acquisition systems are often modeled as a continuous-domain prefilter followed by an ideal sampler, where generalized samples are obtained after convolution with the impulse response of the device. In this paper, our goal is to interpolate ...

Active contours constitute a computationally attractive framework for image segmentation. In this paper, we describe a fully parametric design that relies on B-spline bases and is specified by control points on the image. Our technique yields successful se ...

The detection of landmarks or patterns is of interest for extracting features in biological images. Hence, algorithms for finding these keypoints have been extensively investigated in the literature, and their localization and detection properties are well ...

Many feedforward neural networks (NNs) generate continuous and piecewise-linear (CPWL) mappings. Specifically, they partition the input domain into regions on which the mapping is affine. The number of these so-called linear regions offers a natural metric ...

Wavelet-based statistical analysis methods for fMRI are able to detect brain activity without smoothing the data. Typically, the statistical inference is performed in the wavelet domain by testing the t-values of each wavelet coefficient; subsequently, an activity map is reconstructed from the significant coefficients. The limitation of this approach is that there is no direct statistical interpretation of the reconstructed map. In this paper, we propose a new methodology that takes advantage of wavelet pro

The goal of derivative sampling is to reconstruct a signal from the samples of the function and of its first-order derivative. In this paper, we consider this problem over a shift-invariant reconstruction subspace generated by two compact-support functions ...

We propose to design the reduction operator of an image pyramid so as to minimize the approximation error in the

l _{ p }

sense (not restricted to the usual p = 2), where p can take non-integer values. The underlying image model is specified using arbitrary shift-invariant basis functions such as splines. The solution is determined by an iterative optimization algorithm, based on digital filtering. Its convergence is accelerated by the use of first and second derivatives. For p = 1, our modified pyramid

We present an elastic registration algorithm for the alignment of biological images. Our method combines and extends some of the best techniques available in the context of medical imaging. We express the deformation field as a B-spline model, which allows ...

Motivation: SpotCaliper is a novel wavelet-based image-analysis software providing a fast automatic detection scheme for circular patterns (spots), combined with the precise estimation of their size. It is implemented as an ImageJ plugin with a friendly us ...

We introduce a novel variational framework for the regularized reconstruction of time-resolved volumetric flow fields. Our objective functional takes the physical characteristics of the underlying flow into account in both the spatial and the temporal doma ...

Background: For the investigation of the molecular mechanisms involved in neurite outgrowth and differentiation, accurate and reproducible segmentation and quantification of neuronal processes are a prerequisite. To facilitate this task, we developed a semiautomatic neurite tracing technique. This article describes the design and validation of the technique. Methods: The technique was compared to fully manual delineation. Four observers repeatedly traced selected neurites in 20 fluorescence microscopy image

Michaël Unser

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Exponential splines and minimal-support bases for curve representation

Revisiting PSF models: theory and implementation

Shape Projectors for Landmark-Based Spline Curves

Teaching Image-Processing Programming in Java

Neurite Tracing in Fluorescence Microscopy Images Using Ridge Filtering and Graph Searching: Principles and Validation

Snakuscules

On the Unique Identification of Continuous-Time Autoregressive Models From Sampled Data

A Note on BIBO Stability

Construction of Fractional Spline Wavelet Bases

Anisotropic Interpolation of Sparse Generalized Image Samples

Spline-based framework for interactive segmentation in biomedical imaging

Angular Accuracy of Steerable Feature Detectors

On the number of regions of piecewise linear neural networks

Wavelet-Based fMRI Statistical Analysis and Spatial Interpretation: A Unifying Approach

Optimal Spline Generators for Derivative Sampling

Non-Euclidean Pyramids

Elastic Registration of Biological Images Using Vector-Spline Regularization

SpotCaliper: Fast Wavelet-Based Spot Detection with Accurate Size Estimation

Spatio-Temporal Regularization Of Flow-Fields

Design and Validation of a Tool for Neurite Tracing and Analysis in Fluorescence Microscopy Images