Rémy Prost

An Oblivious Watermarking for 3-D Polygonal Meshes Using Distribution of Vertex Norms

Although it has been known that oblivious (or blind) watermarking schemes are less robust than nonoblivious ones, they are more useful for various applications where a host signal is not available in the watermark detection procedure. From a viewpoint of oblivious watermarking for a three-dimensional (3-D) polygonal mesh model, distortionless attacks, such as similarity transforms and vertex reordering, might be more serious than distortion attacks including adding noise, smoothing, simplification, remeshing, clipping, and so on. Clearly, it is required to develop an oblivious watermarking that is robust against distortionless as well as distortion attacks. In this paper, we propose two oblivious watermarking methods for 3-D polygonal mesh models, which modify the distribution of vertex norms according to the watermark bit to be embedded. One method is to shift the mean value of the distribution and another is to change its variance. Histogram mapping functions are introduced to modify the distribution. These mapping functions are devised to reduce the visibility of watermark as much as possible. Since the statistical features of vertex norms are invariant to the distortionless attacks, the proposed methods are robust against such attacks. In addition, our methods employ an oblivious watermark detection scheme, which can extract the watermark without referring to the cover mesh model. Through simulations, we demonstrate that the proposed approaches are remarkably robust against distortionless attacks. In addition, they are fairly robust against various distortion attacks

Generic Remeshing of 3D Triangular Meshes with Metric-Dependent Discrete Voronoi Diagrams

In this paper, we propose a generic framework for 3D surface remeshing. Based on a metric-driven Discrete Voronoi Diagram construction, our output is an optimized 3D triangular mesh with a user-defined vertex budget. Our approach can deal with a wide range of applications, from high-quality mesh generation to shape approximation. By using appropriate metric constraints, the method generates isotropic or anisotropic elements. Based on point sampling, our algorithm combines the robustness and theoretical strength of Delaunay criteria with the efficiency of an entirely discrete geometry processing. Besides the general described framework, we show the experimental results using isotropic, quadric-enhanced isotropic, and anisotropic metrics, which prove the efficiency of our method on large meshes at a low computational cost.

Fractal geometry of arterial coronary bifurcations: a quantitative coronary angiography and intravascular ultrasound analysis.

AIMS Coronary artery bifurcations present a harmonious asymmetric geometry that is fractal in nature. Interventional treatment of bifurcation lesions is a major technical issue. The present study is aimed at a precise quantification of this geometry in the hope of deriving a formulation that would be simple to calculate. METHODS AND RESULTS Forty seven patients with strictly normal coronarographic results obtained ahead of valve replacement were enrolled, and 27 of these underwent IVUS examination to confirm that their arteries were indeed normal. Three reference diameters were measured: those of the mother vessel (Dm) and of either daughter vessel (Dd1, Dd2). One hundred and seventy-three bifurcations were thus subjected to quantitative analysis. The mean diameter of the mother vessels was 3.33+/-0.94 mm, of the major daughter vessels 2.70+/-0.77 mm, and of the minor daughter vessels 2.23+/-0.68 mm. The ratio R=Dm/(Dd1+Dd2) of mother-vessel diameter to the sum of the two daughter-vessel diameters was 3.39/(2.708+2.236)=0.678. This ratio held at all levels of bifurcation: i.e., whatever diameter the mother vessel. CONCLUSION The study confirmed the fractal nature of the geometry of the epicardial coronary artery tree, and gave a simple and accurate fractal ratio between the diameters of the mother and two daughter vessels such that Dm=0.678 (Dd1+Dd2). This makes it easy to calculate the precise diameter of any of the three vessels when those of the other two are known.

Wavelet-based progressive compression scheme for triangle meshes: wavemesh

We propose a new lossy to lossless progressive compression scheme for triangular meshes, based on a wavelet multiresolution theory for irregular 3D meshes. Although remeshing techniques obtain better compression ratios for geometric compression, this approach can be very effective when one wants to keep the connectivity and geometry of the processed mesh completely unchanged. The simplification is based on the solving of an inverse problem. Optimization of both the connectivity and geometry of the processed mesh improves the approximation quality and the compression ratio of the scheme at each resolution level. We show why this algorithm provides an efficient means of compression for both connectivity and geometry of 3D meshes and it is illustrated by experimental results on various sets of reference meshes, where our algorithm performs better than previously published approaches for both lossless and progressive compression.

A unified definition for the discrete-time, discrete-frequency, and discrete-time/Frequency Wigner distributions

Various discrete definitions of the Wigner distribution (WD) for discrete-time signals have been proposed in previous works. The formulation developed in this paper leads to natural and unified definitions of discrete versions of the WD. They are directly related to the continuous and preserve most of its properties. The discretization is first considered in the time domain (DTWD), in the frequency domain (DFWD), and then in both domains simultaneously (DTFWD). In each case, the aliasing problem is studied and generalized interpolation formulas allowing the reconstruction of the continuous WD are derived. The DTFWD is particulary relevant for computer implementation of the WD.

Discrete constrained iterative deconvolution algorithms with optimized rate of convergence

Abstract In this paper, some new constrained discrete deconvolution algorithms based on an iterative equation are presented. The constraints are—the signal extent (signal support)—the positivity—the level bounds. The algorithms minimize either the error energy or a positive functional. The connections with previous works are studied. An experimental comparison of the algorithms convergence speed is studied with a synthetic sequence to be recovered. The restoration error and both the deconvoluted signal and its spectrum show clearly the performances of the algorithms and their ability to achieve a spectral extrapolation. The deconvolution from noisy data is investigated.

Compactly Supported Radial Basis Functions Based Collocation Method for Level-Set Evolution in Image Segmentation

The partial differential equation driving level-set evolution in segmentation is usually solved using finite differences schemes. In this paper, we propose an alternative scheme based on radial basis functions (RBFs) collocation. This approach provides a continuous representation of both the implicit function and its zero level set. We show that compactly supported RBFs (CSRBFs) are particularly well suited to collocation in the framework of segmentation. In addition, CSRBFs allow us to reduce the computation cost using a kd-tree-based strategy for neighborhood representation. Moreover, we show that the usual reinitialization step of the level set may be avoided by simply constraining the l1-norm of the CSRBF parameters. As a consequence, the final solution is topologically more flexible, and may develop new contours (i.e., new zero-level components), which are difficult to obtain using reinitialization. The behavior of this approach is evaluated from numerical simulations and from medical data of various kinds, such as 3-D CT bone images and echocardiographic ultrasound images.

A Tracking Compton-Scattering Imaging System for Hadron Therapy Monitoring

Hadron therapy for, e.g., cancer treatment requires an accurate dose deposition (total amount and location). As a consequence, monitoring is crucial for the success of the treatment. Currently employed PET imaging systems are not able to provide information about the deposed dose fast enough to allow stopping the therapy in case of a discordance with the treatment plan. We are currently investigating an imaging system based on a combined Compton scattering and pair creation camera capable of imaging gamma rays up to 50 MeV. The camera would be able to measure the complete spectrum of emitted gamma rays during the therapy session. We have performed Monte Carlo simulations for three different proton beam energies in a typical hadron therapy scenario. They show that the location of the gamma-ray distribution decay and the falloff region of the deposed dose are related. The reconstructed images prove that the proposed system could provide the required imaging and dose location capabilities.

Pre-beamformed RF signal reconstruction in medical ultrasound using compressive sensing.

Compressive sensing (CS) theory makes it possible - under certain assumptions - to recover a signal or an image sampled below the Nyquist sampling limit. In medical ultrasound imaging, CS could allow lowering the amount of acquired data needed to reconstruct the echographic image. CS thus offers the perspective of speeding up echographic acquisitions and could have many applications, e.g. triplex acquisitions for CFM/B-mode/Doppler imaging, high-frame-rate echocardiography, 3D imaging using matrix probes, etc. The objective of this paper is to study the feasibility of CS for the reconstruction of channel RF data, i.e. the 2D set of raw RF lines gathered at the receive elements. Successful application of CS implies selecting a representation basis where the data to be reconstructed have a sparse expansion. Because they consist mainly in warped oscillatory patterns, channel RF data do not easily lend themselves to a sparse representation and thus represent a specific challenge. Within this perspective, we propose to perform and assess CS reconstruction of channel RF data using the recently introduced wave atoms [1] representation, which exhibit advantageous properties for sparsely representing such oscillatory patterns. Reconstructions obtained using wave atoms are compared with the reconstruction performed with two conventional representation bases, namely Fourier and Daubechies wavelets. The first experiment was conducted on simulated channel RF data acquired from a numerical cyst phantom. The quality of the reconstructions was quantified through the mean absolute error at varying subsampling rates by removing 50-90% of the original samples. The results obtained for channel RF data reconstruction yield error ranges of [0.6-3.0]×10(-2), [0.2-2.6]×10(-2), [0.1-1.5]×10(-2), for wavelets, Fourier and wave atoms respectively. The error ranges observed for the associated beamformed log-envelope images are [2.4-20.6]dB, [1.1-12.2]dB, and [0.5-8.8dB] using wavelets, Fourier, and wave atoms, respectively. These results thus show the superiority of the wave atom representation and the feasibility of CS for the reconstruction of US RF data. The second experiment aimed at showing the experimental feasibility of the method proposed using a data set acquired by imaging a general-purpose phantom (CIRS Model 054GS) using an Ultrasonix MDP scanner. The reconstruction was performed by removing 80% of the initial samples and using wave atoms. The reconstructed image was found to reliably preserve the speckle structure and was associated with an error of 5.5dB.

Progressive lossless mesh compression via incremental parametric refinement

In this paper, we propose a novel progressive lossless mesh compression algorithm based on Incremental Parametric Refinement, where the connectivity is uncontrolled in a first step, yielding visually pleasing meshes at each resolution level while saving connectivity information compared to previous approaches. The algorithm starts with a coarse version of the original mesh, which is further refined by means of a novel refinement scheme. The mesh refinement is driven by a geometric criterion, in spirit with surface reconstruction algorithms, aiming at generating uniform meshes. The vertices coordinates are also quantized and transmitted in a progressive way, following a geometric criterion, efficiently allocating the bit budget. With this assumption, the generated intermediate meshes tend to exhibit a uniform sampling. The potential discrepancy between the resulting connectivity and the original one is corrected at the end of the algorithm. We provide a proof‐of‐concept implementation, yielding very competitive results compared to previous works in terms of rate/distortion trade‐off.