Digital Surface Regularization With Guarantees.

Voxel based modeling is a very attractive way to represent complex multi-material objects. Beside artistic choices of pixel/voxel arts, representing objects as voxels allows efficient and dynamic interactions with the scene. For geometry processing purposes, many applications in material sciences, medical imaging or numerical simulation rely on a regular partitioning of the space with labeled voxels. In this article, we consider a variational approach to reconstruct interfaces in multi-labeled digital images. This approach efficiently produces piecewise smooth quadrangulated surfaces with some theoretical stability guarantee. Non-manifold parts at intersecting interfaces are handled naturally by our model. We illustrate the strength of our tool for digital surface regularization, as well as voxel art regularization by transferring colorimetric information to regularized quads and computing isotropic geodesic on digital surfaces.

PET-based dose delivery verification in proton therapy: a GATE based simulation study of five PET system designs in clinical conditions.

PET is a promising technique for in vivo treatment verification in hadrontherapy. Three main PET geometries dedicated to in-beam treatment monitoring have been proposed in the literature: the dual-head PET geometry, the OpenPET geometry and the slanted-closed ring geometry. The aim of this work is to characterize the performance of two of these dedicated PET detectors in realistic clinical conditions. Several configurations of the dual-head PET and OpenPET systems were simulated using GATE v6.2. For the dual-head configuration, two aperture angles (15° and 45°) were studied. For the OpenPET system, two gaps between rings were investigated (110 and 160 mm). A full-ring PET system was also simulated as a reference. After preliminary evaluation of the sensitivity and spatial resolution using a Derenzo phantom, a real small-field head and neck treatment plan was simulated, with and without introducing patient displacements. No wash-out was taken into account. 3D maps of the annihilation photon locations were deduced from the PET data acquired right after the treatment session (5 min acquisition) using a dedicated OS-EM reconstruction algorithm. Detection sensitivity at the center of the field-of-view (FOV) varied from 5.2% (45° dual-head system) to 7.0% (full-ring PET). The dual-head systems had a more uniform efficiency within the FOV than the OpenPET systems. The spatial resolution strongly depended on the location within the FOV for the ϕ = 45° dual-head system and for the two OpenPET systems. All investigated architectures identified the magnitude of mispositioning introduced in the simulations within a 1.5 mm accuracy. The variability on the estimated mispositionings was less than 2 mm for all PET systems.

Phase-based block matching applied to motion estimation with unconventional beamforming strategies.

A phase-based block matching method adapted to motion estimation with unconventional beamforming strategies is presented. The unconventional beamforming technique used allows us to obtain 2-D RF images with axial and lateral modulations. Based on these images, we propose a method that uses phase images instead of amplitude images. This way of proceeding allows us to provide an analytical solution to the local displacement estimation so that no minimization of a classical cost function is used for the local estimation. For this reason, the local estimator is directly applied to signals, without the need to process a complex cross-correlation function, as is done with most of the phase shift estimators. In this paper, the method is applied to elastography. Results with simulated data show that a downsampling of axial and lateral modulated signals leads to very little change in the accuracy and in the spatial resolution of the proposed method. For example, for decimation factors of 2 in the axial direction and of 4 in the lateral direction, the mean axial absolute error is 3 mum. The same estimation with original images provides a mean axial error of 0.7 microm. The accuracy of the lateral motion is unchanged in this case. The accuracy of our method with downsampled signals is an important issue in the purpose of a real-time implementation. With experimental data, for the same level of estimation error, classical block matching using the maximum of cross correlation as a local estimator requires images that are 36 times larger (in number of pixels) and consequently a computational time roughly 10 times longer. Our phase block matching is also shown to provide 10 percent less error than a motion estimation method based on seeking the zero of the complex correlation function phase. Finally, it is shown that given the separability of the local estimator that we propose, our method can be applied on both n-D signals and classical RF ultrasound images. The phase block matching method presented was implemented in real time on an ultrasound research scanner.

Lateral RF image synthesis using a synthetic aperture imaging technique.

The oscillating profile naturally present in ultrasound images has been shown to be extremely valuable in different applications, particularly in motion estimation. Recent studies have shown that it is possible to produce images with transverse oscillations (TOs) based on a specific type of beamforming. However, there is still a great difference between the nature of the lateral oscillations produced with current methods and the axial profile of ultrasound images. In this study, we propose to combine synthetic aperture imaging (synthetic transmit aperture, STA) using a specific beamformer in both transmit mode and receive mode combined with a heterodyning demodulation method to produce lateral radiofrequency signals (LRFs). The aim was to produce lateral signals as close as possible to conventional axial signals, which would make it possible to estimate lateral displacements with the same accuracy as in the axial direction. The feasibility of this approach was validated in simulation and experimentally on an ultrasound research platform, the Ultrasonix RP system. We show that the combination of STA and the heterodyning demodulation can divide the wavelength of the LRF signals by 4 and divide the width of the lateral envelope of the point spread function (PSF) by 2 compared with the previous approaches using beamforming in receive mode only. Finally, we also illustrate the potential of our beamforming for motion estimation compared with previous TO methods.

Two-dimensional least-squares estimation for motion tracking in ultrasound elastography.

This paper proposes a method of 2-D translations estimation using an a priori signal model. Two analytical signals defined with multidimensional Hilbert transform are considered and shown to have linear phases with respect to the translations to estimate. A least squares estimator (LSE) is then developed to adjust the measured phases of the complex signals to their theoretical forms. Moreover, the LSE provides an analytical solution to the 2-D translation estimation problem. The estimator is then included in a block matching method for motion tracking with ultrasound images. We compared our results with those obtained with a classical sum of absolute differences (SAD) cost function. We show that with our method there is no need of interpolating the images. Thus, for images at the original resolution level, the results obtained with the proposed estimator are largely more accurate than with SAD. Moreover, we show that using SAD on images with resolution five times higher provide roughly the same results as with our method, but the processing time is ten times higher in this case.