Publications by Philippe Thévenaz

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Interpolation is the means by which a continuously defined model is fit to discrete data samples. When the data samples are exempt of noise, it seems desirable to build the model by fitting them exactly. In medical imaging, where quality is of paramount im ...

This paper presents an algorithm based on a continuous framework for a posteriori angular and translational assignment in three-dimensional electron microscopy (3DEM) of single particles. Our algorithm can be used advantageously to refine the assignment of ...

We propose a new method for the intermodal registration of images using a criterion known as mutual information. Our main contribution is an optimizer that we specifically designed for this criterion. We show that this new optimizer is well adapted to a multiresolution approach because it typically converges in fewer criterion evaluations than other optimizers. We have built a multiresolution image pyramid, along with an interpolation process, an optimizer, and the criterion itself, around the unifying conc

Based on the theory of approximation, this paper presents a unified analysis of interpolation and resampling techniques. An important issue is the choice of adequate basis functions. We show that, contrary to the common belief, those that perform best are not interpolating. By opposition to traditional interpolation, we call their use generalized interpolation; they involve a prefiltering step when correctly applied. We explain why the approximation order inherent in any basis function is important to limit

The most essential ingredient of interpolation is its basis function. We have shown in previous papers that this basis need not be necessarily interpolating to achieve good results. On the contrary, several recent studies have confirmed that non-interpolating bases, such as B-splines and O-moms, perform best. This opens up a much wider choice of basis functions. In this paper, we give to the designer the tools that will allow him to characterize this enlarged space of functions. In particular, he will be ab

This work aims at the precise and efficient computation of the x-ray projection of an image represented by a linear combination of general shifted basis functions that typically overlap. We achieve this with a suitable adaptation of ray tracing, which is one of the most efficient methods to compute line integrals. In our work, the cases in which the image is expressed as a spline are of particular relevance. The proposed implementation is applicable to any projection geometry as it computes the forward and

Three-dimensional (3D) electron microscopy (3DEM) aims at the determination of the spatial distribution of the Coulomb potential of macromolecular complexes. The 3D reconstruction of a macromolecule using single-particle techniques involves thousands of 2D projections. One of the key parameters required to perform such a 3D reconstruction is the orientation of each projection image as well as its in-plane orientation. This information is unknown experimentally and must be determined using image-processing t

We propose a system to characterize the 3-D diffusion properties of the probing bead trapped by a photonic-force microscope. We follow a model-based approach, where the model of the dynamics of the bead is given by the Langevin equation. Our procedure comb ...

We construct parametric active contours (snakes) for outlining cells in histology images. These snakes are defined in terms of cubic B-spline basis functions. We use a steerable ridge detector for obtaining a reliable map of the cell boundaries. Using the ...

We present an automatic sub-pixel registration algorithm that minimizes the mean square difference of intensities between a reference and a test data set, which can be either tri-dimensional (3-D) volumes or bi-dimensional (2-D) images. It uses spline processing, is based on a coarse-to-fine strategy (pyramid approach), and performs minimization according to a new variation of the iterative Marquardt-Levenberg algorithm for non-linear least-square optimization (MLA). The geometric deformation model is a glo

In the field of image segmentation, most of level-set-based active contour approaches are based on a discrete representation of the associated implicit function. We present in this paper a different formulation where the level-set is modelled as a continuo ...

We address the task of rendering by ray tracing the isosurface of a high-quality continuous spline model of volumetric discrete and regular data. By expressing the spline model as a sum of nonnegative B-splines, we are able to confine the potential location of the isosurface within a thin binary shell. We then show how to use the space-embedding property of splines to further shrink this shell to essentially a single-voxel width. We also propose a new illumination model that highlights the outline of the re

One of the main factors that affect the accuracy of intensity-based registration of two-dimensional (2D) X-ray fluoroscopy to three-dimensional (3D) CT data is the similarity measure, which is a criterion function that is used in the registration procedure ...

We address the task of rendering by ray tracing the isosurface of a high-quality continuous model of volumetric discrete and regular data. Based on first principles, we identify the quadratic B-spline as the best model for our purpose. The nonnegativity of this basis function allows us to confine the potential location of the isosurface within a binary shell. We then show how to use the space-embedding property of splines to further shrink this shell to essentially a single voxel width. Not all rays traced

The aim of this study is to obtain voxel-by-voxel images of binding parameters between [11C]-Flumazenil and benzodiazepine receptors using positron emission tomography (PET). We estimate five local parameters (k1, k2, B'max, kon/VR, koff) by fitting a three-compartment ligand-receptor model for each voxel of a PET time series. It proves difficult to fit the ligand-receptor model to the data. We trade noise and spatial resolution to get better results. Our strategy is based on the use of a multiresolution py

Objective—To develop software for automated registration and intensity calibration of serial dental radiographs for the analysis of longitudinal changes in bone density. Methods—Serial dental radiographs were acquired using a positioning device designed to minimize projection divergence. Each radiograph included an image of a standardized aluminium wedge. The radiographs were scanned on a flatbed scanner (AGFA Duo Scan) with a spatial resolution of 300 dpi, and pixel intensity coded in 16-bit grey scale. Th

Purpose: To improve the quantification of myocardial perfusion by registering the time series of magnetic resonance (MR) images with injection of gadolinium. Materials and Methods: Eight patients underwent MR scans to perform myocardial perfusion exam. Two short axis views of the left ventricle (LV) were acquired in free breathing. Two masks for performing the spatial registration of the images were evaluated. The registration was based on pixel intensity in a multi-resolution scheme. The efficiency of this

This chapter presents a survey of interpolation and resampling techniques in the context of exact, separable interpolation of regularly sampled data. In this context, the traditional view of interpolation is to represent an arbitrary continuous function as a discrete sum of weighted and shifted synthesis functions—in other words, a mixed convolution equation. An important issue is the choice of adequate synthesis functions that satisfy interpolation properties. Examples of finite-support ones are the square

We present a novel algorithm for the registration of 2D image sequences that combines the principles of multiresolution B-spline-based elastic registration and those of bidirectional consistent registration. In our method, consecutive triples of images are ...

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 ...

Philippe Thévenaz

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Regularized Interpolation for Noisy Images

Spline-Based Image-to-Volume Registration for Three-Dimensional Electron Microscopy

Optimization of Mutual Information for Multiresolution Image Registration

Interpolation Revisited

Complete Parametrization of Piecewise-Polynomial Interpolators According to Degree, Support, Regularity, and Order

Generalized Ray Tracing with Basis Functions for Tomographic Projections

A Multiresolution Approach to Orientation Assignment in 3D Electron Microscopy of Single Particles

Model-Based Estimation of Three-Dimensional Stiffness Parameters in Photonic-Force Microscopy

Parametric B-Spline Snakes on Distance Maps—Application to Segmentation of Histology Images

A Pyramid Approach to Subpixel Registration Based on Intensity

Variational B-Spline Level-Set Method for Fast Image Segmentation

High-Quality Isosurface Rendering with Exact Gradient

Point Similarity Measures Based on MRF Modeling of Difference Images for Spline-Based 2D-3D Rigid Registration of x-Ray Fluoroscopy to CT Images

Precision Isosurface Rendering of 3-D Image Data

Multiresolution Imaging of In Vivo Ligand-Receptor Interactions

Geometric Alignment and Chromatic Calibration of Serial Radiographic Images

Improvement in the Quantification of Myocardial Perfusion Using an Automatic Spline-Based Registration Algorithm

Image Interpolation and Resampling

Non-Rigid Consistent Registration of 2D Image Sequences

Snakuscules