Magnetic resonance spectroscopic imaging (MRSI) has multiple interests in clinical practice, and especially for brain disease diagnosis. However, it faces quite long acquisition time in practice which limits their use in a clinical environment. Fast MRI acquisitions can help to reduce this acquisition time and intensify their clinical use. In this work, a new fast Magnetic Resonance Spectroscopic image acquisition method is introduced and evaluated based on a k-t space spiral sampling. The time-domain subsampling, below the Shannon-Nyquist rate, is allowed on the hypothesis of a sparse spectrum with an a priori known support. Then the nonzero components of the spectrum of each voxel are recovered using an over-determined least square problem. When data are noise-free the recovered spectrum is exact. In the real-world noisy scenario the error in the recovered spectrum highly depends on the acquired samples. We reduce this error to an acceptable level by selecting irregularly the samples using the Sequential Backward Selection algorithm. A realistic simulated irregular spiral acquisition proves the feasibility of the proposed approach.

We propose a system for automatic positioning of identified landmarks on anatomical structures generated from medical images. We obtain a rigid registration of 3-D shapes using the Iterative Closest Point (ICP) algorithm where a curvature constraint is added as a supplementary dimension in order to improve robustness. A dichotomic scale search and a local rigid registration allow fast local adjustment. We show the effectiveness of the proposed approach by comparing the automatic positioning of anatomical landmarks against the manual positioning by a trained operator.

We derive shortest-path constraints from graph models of structure adjacency relations and introduce them in a joint centroidal Voronoi image clustering and Graph Cut multiobject semiautomatic segmentation framework. The vicinity prior model thus defined is a piecewise-constant model incurring multiple levels of penalization capturing the spatial configuration of structures in multiobject segmentation. Qualitative and quantitative analyses and comparison with a Potts prior-based approach and our previous contribution on synthetic, simulated, and real medical images show that the vicinity prior allows for the correct segmentation of distinct structures having identical intensity profiles and improves the precision of segmentation boundary placement while being fairly robust to clustering resolution. The clustering approach we take to simplify images prior to segmentation strikes a good balance between boundary adaptivity and cluster compactness criteria furthermore allowing to control the trade-off. Compared with a direct application of segmentation on voxels, the clustering step improves the overall runtime and memory footprint of the segmentation process up to an order of magnitude without compromising the quality of the result.

We propose an application of multi-label “Graph Cut” optimization algorithms to the simultaneous segmentation of multiple anatomical structures, initialized via an over-segmentation of the image computed by a fast centroidal Voronoi diagram (CVD) clustering algorithm. With respect to comparable segmentations computed directly on the voxels of image volumes, we demonstrate performance improvements on both execution speed and memory footprint by, at least, an order of magnitude, making it possible to process large volumes on commodity hardware which could not be processed pixel-wise.

In the compressed sensing framework, different algorithms have been proposed for sparse signal recovery from an incomplete set of linear measurements. The most known can be classified into two categories: l(1) norm minimization-based algorithms and l(0) pseudo-norm minimization with greedy matching pursuit algorithms. In this paper, we propose a modified matching pursuit algorithm based on the orthogonal matching pursuit (OMP). The idea is to replace the correlation step of the OMP, with a neural network. Simulation results show that in the case of random sparse signal reconstruction, the proposed method performs as well as the OMP. Complexity overhead, for training and then integrating the network in the sparse signal recovery is thus not justified in this case. However, if the signal has an added structure, it is learned and incorporated in the proposed new OMP. We consider three structures: first, the sparse signal is positive, second the positions of the non zero coefficients of the sparse signal follow a certain spatial probability density function, the third case is a combination of both. Simulation results show that, for these signals of interest, the probability of exact recovery with our modified OMP increases significantly. Comparisons with l(1) based reconstructions are also performed. We thus present a framework to reconstruct sparse signals with added structure by embedding, through neural network training, additional knowledge to the decoding process in order to have better performance in the recovery of sparse signals of interest.

Trabecular bone is made of a complex network of plate and rod structures, the proportion of which evolves with age or disease. Thus the identification of trabecular plates and rods is important in understanding bone fragility. We propose a novel approach based on 3D multi-scale adjacency graph analysis of high resolution 3D tomographic images of bone structures. The purpose of this new method is to classify each voxel of the 3D images in two classes: plate and rod voxels. We show that the use of a multi-scale framework is very efficient at detecting rods with different sizes. We present applications of our method to both synthetic images and experimental bone synchrotron radiation micro-CT images.

In this paper, we present a novel method for medial axis approximation based on Constrained Centroidal Voronoi Diagram of discrete data (image, volume). The proposed approach is based on the shape boundary subsampling controled by a clustering approach which generates a Voronoi Diagram well suited for Medial Axis extraction. The resulting Voronoi Diagram is further filtered in order to capture the correct topology of the medial axis. The main contribution of this paper is the integration of both a curvature maps and a distance map for controlling the local variability of Voronoi cells densities. Examples of complex shape processing prove the effectiveness of the proposed approach.

Abstract 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.

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 entirely discrete geometry processing . Besides the general described framework, we show experimental results using isotropic, quadric-enhanced isotropic and anisotropic metrics which prove the efficiency of our method on large meshes, for a low computational cost.

This work presents an algorithm for the segmentation of myocardial regions in echocardiography imaging based on the statistics of the radiofrequency image. We formulate the problem of segmentation in a maximum likelihood framework using the Generalized Gaussian as an a priori distribution. We minimize the resulting functional using a radial basis functions-based multiphase level set model. Numerical results obtained on both simulation and in vivo data demonstrate the capacity of our approach to segment myocardial regions in echocardiography imaging.

We consider a recent parametric level-set segmentation approach where the implicit interface is the zero level of a continuous function expanded onto compactly supported radial basis functions, defined by their centers, coefficients and supports. We propose to introduce prior knowledge of the shape to be recovered by placing the centers quasi-uniformly over an uncertainty area.

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.

This paper presents a new method for 3-D tomographic reconstruction of stent in X-ray cardiac rotational angiography. The method relies on 2-D motion correction from two radiopaque markerballs located on each side of the stent. The two markerballs are on a guidewire and linked to the balloon, which is introduced into the artery. Once the balloon has been inflated, deflated, and the stent deployed, a rotational sequence around the patient is acquired. Under the assumption that the guidewire and the stent have the same 3-D motion during rotational acquisition, we developed an algorithm to correct cardiac stent motion on the 2-D X-ray projection images. The 3-D image of the deployed stent is then reconstructed with the Feldkamp algorithm using all the available projections. Although the correction is an approximation, we show that the intrinsic geometrical error of our method has no visual impact on the reconstruction when the 2-D markerball centers are exactly detected and the markerballs have the same 3-D motion as the stent. Qualitative and quantitative results on simulated sequences under different realistic conditions demonstrate the robustness of the method. Finally, results from animal data acquired on a rotational angiography device are presented.

We propose a novel method for reconstructing d dimensional signals with irregular samples, without any restriction on their positions. We develop a multi-resolution approximation scheme using compactly supported radial basis functions (CSRBFs). Samples are first clustered using principal component analysis and their centroids define CSRBF centers. The mean square error is minimized by selecting centers where the largest local error at the previous level is. We shall prove the effectiveness of our algorithm in one-and two-dimensional cases with Gaussian noise

We propose a new method for watermarking of 3D surface mesh. After irregular wavelet analysis, the watermark is embedded in the scale coefficients. We modify the mean of the distribution of the vertex norm of the approximation mesh in order to obtain blind scheme which does not require the original mesh for detection. Experimental results show the effectiveness of the proposed algorithm both in terms of invisibility and robustness against simplification and progressive lossy compression

In this paper, we present a wavelet-based progressive compression method for 3-D dynamic meshes. Our method exploits the spatial and temporal redundancy. We encode the geometry of base mesh, the wavelet coefficients and the connectivity of each resolution level in order to reduce the spatial redundancy of intra meshes. For inter mesh coding, we encode the differences of geometry of base meshes and of their wavelet coefficients between adjacent frames to reduce the temporal redundancy. Our proposal is based on the wavelet-based multiresolution analysis which uses a perfect reconstruction filter bank and therefore it enables not only progressive representation but also lossless compression. The simulation results demonstrate that the proposed method is applicable to lossy and lossless compression of 3-D dynamic meshes.

We propose a new approach for surface reconstruction from any unorganized point set, with a fixed amount of parameters. First, we consider some local approximations by compactly supported radial basis functions (CSRBFs), then blend them by a partition of unity method (PU). In our scheme, we start by selecting CSRBFs centers, then construct partitions, finally parameters are calculated in order to minimize, on each sub-domain, the mean square error with a regularization constraint. We demonstrate the effectiveness of our approach on several models with different points distributions.

Most of the meshes coming from a variety of source are over sampled and exhibit highly irregular connectivity that prevent efficient wavelet analysis. Remeshing comes as a solution to sampling and connectivity optimization with respect to the geometry. The main drawback of existing subdivision remeshing approaches is the lack of control either on the number of triangles or on the geometrical error. We propose a new remeshing scheme that directly produces wavelet-based multiresolution meshes which does not suffer from the previous limitations. We provide a finer control on the resulting number of triangles by using an adaptive subdivision scheme. We also show a lowering of the local resulting geometrical error by using a new curvature-based subdivision criterion.

In this paper we revisit the triangulated cubes of the marching cubes algorithm in order to regularize the connectivity of the iso-surface mesh i. e. to maximize the valence six vertices. This leads to both an enhancement of the mesh topology and a significant reduction of the connectivity coding cost. We prove the effectiveness of the approach by processing medical examples with various geometry and topology.

This paper extends Lounsbery's multiresolution analysis wavelet-based theory for triangular 3D meshes, which can only be applied to regularly subdivided meshes and thus involves a remeshing of the existing 3D data. Based on a new irregular subdivision scheme, the proposed algorithm can be applied directly to irregular meshes, which can be very interesting when one wants to keep the connectivity and geometry of the processed mesh completely unchanged. This is very convenient in CAD (Computer-Assisted Design), when the mesh has attributes such as texture and color information, or when the 3D mesh is used for simulations, and where a different connectivity could lead to simulation errors. The algorithm faces an inverse problem for which a solution is proposed. For each level of resolution, the simplification is processed in order to keep the mesh as regular as possible. In addition, a geometric criterion is used to keep the geometry of the approximations as close as possible to the original mesh. Several examples on various reference meshes are shown to prove the efficiency of our proposal.

This paper proposes 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.

Wavemesh is a powerful scheme for 3D triangular mesh processing. In sharp contrast with other approaches using wavelets for mesh compression which apply only to meshes having subdivision connectivity, wavemesh can simplify, approximate, and compress meshes even if they do not respect this constraint. Results clearly indicate that wavemesh outperforms the other approaches in terms of progressive lossless compression. We propose in this paper an improvement for our scheme : higher efficiency for meshes with large subdivision connectivity sets, as shown by experimental results. Also, in some cases, the enhanced wavemesh can even perform better than monoresolution approaches in terms of connectivity compression.

In this paper, we propose a new wavelet-based reconstruction method suited to three-dimensional (3-D) cone-beam (CB) tomography. It is derived from the Feldkamp algorithm and is valid for the same geometrical conditions. The demonstration is done in the framework of nonseparable wavelets and requires ideally radial wavelets. The proposed inversion formula yields to a filtered backprojection algorithm but the filtering step is implemented using quincunx wavelet filters. The proposed algorithm reconstructs slice by slice both the wavelet and approximation coefficients of the 3-D image directly from the CB projection data. The validity of this multiresolution approach is demonstrated on simulations from both mathematical phantoms and 3-D rotational angiography clinical data. The same quality is achieved compared with the standard Feldkamp algorithm, but in addition, the multiresolution decomposition allows to apply directly image processing techniques in the wavelet domain during the inversion process. As an example, a fast low-resolution reconstruction of the 3-D arterial vessels with the progressive addition of details in a region of interest is demonstrated. Other promising applications are the improvement of image quality by denoising techniques and also the reduction of computing time using the space localization of wavelets.

In this paper, a new multiresolution reconstruction approach for fan-beam tomography is established. The theoretical development assumes radial wavelets. An approximate reconstruction formula based on a near-radial quincunx multiresolution scheme is proposed. This multiresolution algorithm allows to compute both the quincunx approximation and detail coefficients of an image from its fan-beam projections. Simulations on mathematical phantoms show that wavelet decomposition is acceptable for small beam angles but deteriorates at high angles. The main applications of the method are denoising and wavelet-based image analysis.

We propose an adaptive wavelets based multiresolution scheme by using harmonic maps for 3D irregular meshes. This approach extends the previous works by M. Eck et al. (see SIGGRAPH '95, p.173-82, 1995) and M. Lounsbery (see "Multiresolution Analysis for Surfaces of Arbitrary Topological Type", PhD thesis, Department of Computer Science and Engineering, University of Washington, p.129, 1994) which have been developed for regular triangular mesh subdivision. First, we construct parameterizations of the original mesh that results in a remesh having a subdivision connectivity for the wavelets decomposition. Next, the local subdivision based multiresolution scheme is presented. Our algorithm represents effectively a region of interest or a region having complex and high curvature geometry by using bi-orthogonal wavelets. Through the computer simulation tested on some example meshes, we show that the proposed method is more effective than the previous regular subdivision methods.

The new MPEG-4 standard will provide superior services for the user, as it introduces the video objects concept. However, there is no generic segmentation technique able to provide the segmentation maps for such a coding system. We propose a novel mesh-based video segmentation and objects tracking algorithm with both robust motion estimation and modeling of motion discontinuities. In addition, occlusions and uncovered regions are well managed. This allows the mesh deformation without the need to process remeshing in motion occlusion regions. The spatial properties of each frame are considered to make the mesh edges fit the image contents and a temporal smoothness constraint is also implemented. The proposed algorithm is able to segment multiple objects at the same time. Some experimental results are shown.

In this paper, the use of nonseparable wavelets for tomographic reconstruction is investigated. Local tomography is also presented. The algorithm computes both the quincunx approximation and detail coefficients of a function from its projections. Simulation results showed that nonseparable wavelets provide a reconstruction improvement versus separable wavelets.

In this paper, we consider the texture coding of quadrangular cells which compose active meshes. Active mesh algorithms which have been developed for region based video coding mainly use interpolation techniques to quantize the cell texture. We propose a new quantization scheme which associates image warping and an adaptive JPEG scheme. Our approach leads to an interesting trade-off between mesh complexity and image quality.

We propose a wavelet based local subdivision of 3-D surfaces, which can be effectively applied to a mesh with complex and high curvature faces. The proposed approach is an extension of M. Lounsbery's works (1994), which has been developed only for regular triangular mesh subdivision. For such a purpose, a bi-orthogonal wavelet basis is constructed by defining a local inner product and using the lifting scheme. As only one filter bank is used for the global and local analysis of the surface and also one filter bank for synthesis, this method is very effective. Through the computer simulation tested on some example mesh, we show that the proposed local subdivision is very effective.

We propose a new subdivision scheme derived from the regular 1:4 face split, allowing analysis of irregularly subdivided triangular meshes by the wavelet transforms. Some experimental results on real medical meshes prove the efficiency of this approach in multiresolution schemes. In addition we show the effectiveness of the proposed algorithm for lossless compression.

Two enhanced subband coding schemes using a regularized image restoration technique are proposed: the first controls the global regularity of the decompressed image; the second extends the first approach at each decomposition level. The quantization scheme incorporates scalar quantization (SQ) and pyramidal lattice vector quantization (VQ) with both optimal bit and quantizer allocation. Experimental results show that both the block effect due to VQ and the quantization noise are significantly reduced.

A new transform, called the rounding transform (RT), is introduced in this paper. This transform maps an integer vector onto another integer vector by using weighted average and difference filters followed by a rounding operation. The RT can be applied to lossless pyramid structured coding with various elementary block sizes and filters. In addition, it generalizes other mean based lossless pyramid structured coding schemes.

We propose a new image compression scheme based on fractal coding of wavelet transform coefficients using a fast non-iterative algorithm for the codebook generation. The original image is first decomposed into subbands containing information in different spatial directions and different scales, using an orthogonal wavelet filter bank. Subbands are encoded using local iterated function systems (LIFS) with range and domain blocks presenting horizontal or vertical directionalities. Their sizes are estimated according to the correlation lengths and resolution of each subband. The computational complexity is greatly decreased by using subband decomposition. In addition a fast non-iterative algorithm is implemented for block classification. This algorithm progressively creates the codebook during only one scanning of the training set. We prove the efficiency of the proposed approach both in terms of PSNR/bit rate and computation time.

We propose a new Miller-Tikhonov restoration method where an a priori model of the solution is included. In sharp contrast with the classical method, this approach incorporates local informations. We show that the optimal model can be directly calculated from the data or a priori given and adjusted by minimizing the reconstruction error.

In this study, we consider the DCT based subband decomposition and show the efficiency of this approach for low contrast images in comparison to 9-7 bi-orthogonal FIR filters generally used in such a scheme. First, we consider the theoretical coding gain for the two approaches. Afterwards, the distortion versus rate performances are analyzed and the perceptual qualities of the reconstructed images are discussed. Finally, an edge detection operator is applied on the reconstructed images in order to show the robustness of DCT based subband decomposition to post-processing.

In this paper, a new approach is proposed, the rounding transform (RT) based lossless subband coding. For the such purpose, an extended version of RT, namely overlapping RT (ORT), is defined in the Z-transform domain and used to develop the lossless subband coding system. The main idea is that the polyphase matrix of the analysis filter bank is decomposed into several ORT matrices of size 2 by 2. Compared to the previous scheme (the lifting), the proposed scheme gives not only simpler mathematical representation, but also allows various possibilities when a given filter bank is implemented. As examples, five filter banks are applied to lossless image compression by the proposed ORT and their performances are compared in terms of the total lossless first order entropy.

An error-free image decomposition/reconstruction method for subband coding is introduced. This method is used for blockwise subband coding. A partitioning algorithm is presented. The image is partitioned into blocks of identical size and then adjacent blocks of similar variances are merged. For each block, an adaptation of the subband number and bit allocation is made. The bit allocation algorithm uniformly distributes the quantization error into subbands and blocks. Examples clearly show that the peak-to-peak signal-to-noise ratio of the reconstructed images is better using the block-adaptive partitioning method than for subband coding of the entire image.>

It has been shown, in the kernel splitting method for support constrained deconvolution recently presented, that the restored signal can be obtained from an infinite series of time-functions. In the present work it is proved that the series is finite when the convolution kernel is left-time-limited. Each function of the series is itself a series built from delayed replicas of the convolved signal multiplied by weighted and delayed rectangular windows. The non-overlapping time-regions of the windows are first located and then by zero trivial multiplication are not computed. Then an in-time non-iterative fast algorithm is deduced. Finally the input recovery of a linear system whose transfer function vanishes at several points is investigated both with a noise-free or a noisy output signal. In these conditions where inverse filtering fails, the present algorithm works well.

The principle of the method is to split the kernel into two secondary kernels : r(t)=k(t)+d(t), where d(t) must be invertible and satisfy a convergence condition. Then the deconvolution problem is to solve the following equation :i(t) = i_{o}(t)-\int_{T} i(\tau)g(t-\tau)d\tauwhere T is the signal support,i_{o}(t)=d^{*-1}(t) * o(t)andg(t)=d^{*-1}(t)*k(t). This equation is solved by using successive substitutions. The deconvolution algorithm may be two steps or iterative and gives a super-resolution. Only the iterative form has been experimented. A noise free restoration of two pulses shows the validity of the method and the convergence speed with different splitting modes. Finally deconvolution from noisy data is studied.