In this work, we propose a stochastic level-set method to reconstruct binary tomography cross-sections from few projections. A first reconstruction image is obtained with a level-set regularization method. The reconstruction is then refined with a stochastic partial differential equation based on a Stratanovitch formulation. The reconstruction results are compared with the ones obtained with the classical simulated annealing method. The methods are tested on a complex bone μ- CT cross-section for different noise levels and number of projections. The best reconstruction results are obtained with the stochastic level set-method.

In this work, we propose a stochastic level-set method to reconstruct binary tomography cross-sections from a small number of projections. A first reconstruction image is obtained with a deterministic level-set regularization method. The reconstruction is then refined with a stochastic partial differential equation based on a Stratanovitch formulation. The methods are tested on a slice of bone microstructure having a complex geometry for different noise levels and number of projections.

With hard X-rays synchrotron beams, phase contrast can be obtained with the measurement of the Fresnel diffraction intensity patterns associated to a phase shift induced by the object. We have studied the resolution of this inverse problem with an iterative thresholding algorithm in wavelet coordinates combined with an iterative nonlinear method with a Tikhonov regularization and projection operators. The phase retrieval algorithm was tested for a 3D Shepp-Logan phantom in the presence of noise. The results show that the combined approach outperforms the Mixed, the CTF and the nonlinear methods.

Biological microscopic imaging is receiving increasing interest with the development of new modalities. In this context Synchrotron Radiation (SR) Nano-CT demonstrates a high potential in opening new horizons. We recall the principle of SR micro-CT and its advantages over standard X-ray micro-CT in terms of accuracy and signal to noise ratio. We briefly present data acquisition and reconstruction in absorption and phase CT. While in the first case image reconstruction is based simply on the standard filtered back projection algorithm, in the later case it involves a preliminary step of phase retrieval. Applications of this technique in bone research in conjunction with specific image analysis developments are shown. At the micrometer scale, trabecular and cortical bone have been analyzed in human samples and mice. At the nanometer scale, we present recent data on the osteocyte network which has never before been investigated in 3D. Open problems for the segmentation and quantification of the complex canalicular network are highlighted.

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.

We consider the phase retrieval problem in 3-D holotomography for strongly absorbing objects. Holotomography combines phase retrieval from Fresnel diffraction patterns with tomographic reconstruction to reconstruct the 3-D refractive index distribution. The main interest is the increase in sensitivity of up to three orders of magnitude compared to standard, absorption based tomography. Most existing algorithms are based upon linearization of the forward problem. This is motivated by the large problem size, since it yields computationally efficient solutions. Here, the mixed approach is used, which allows for both strong absorption and long propagation distances. Previous implementations have shown promising results, but in practice often suffer from strong low frequency artifacts. To address this problem, we introduce a homogeneous object assumption through a regularizing term based upon the absorption image. This allows the homogeneous object assumption to be introduced only in the low frequency range. The proportionality constant between absorption and refractive index is assumed to be known. The regularizing parameter is found using the standard L-curve technique. The benefits of our approach are illustrated using data measured at the European Synchrotron Radiation Facility. Low frequency noise in the reconstruction is alleviated, but the result is only quantitative in the areas of the sample where the homogeneous object assumption is fulfilled.

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.

The goal of this work was to find a new parametric model suited to the representation of three-dimensional (3D) bone microarchitecture that can be used as a prior model in tomographic reconstruction or image segmentation. For this purpose, Markov random fields (MRFs) are well adapted. Bone microarchitecture is typically organized as a pseudoperiodic arrangement of parallel plates with a given thickness (/spl sim/ 100 /spl mu/m), and spacing (/spl sim/ 700 /spl mu/m). As standard Ising MRFs could not represent the complexity of bone, we investigated energy functions based on the design of a neighborhood system including local and distant interactions. The parameters of this MRF model were related to the standard morphometric parameters of bone microarchitecture.

3D reconstruction from 2D cone beam projections obtained along a single circular x-ray source trajectory is commonly performed using an algorithm proposed by Feldkamp, Davis and Kress (FDK) in 1983. This reconstruction algorithm involves the rotation of a source and detector in the same plane which is centered with respect to the volume of interest. Both in industrial and in medical applications, the positioning of the object to be scanned can be bound to strong constraints. A stand, an instrument or the shape of the object, for instance, can prevent the conventional acquisition geometry and introduce an off-centred geometry of the computer tomography (CT) acquisition system. Direct application of FDK algorithm is therefore not adapted. This problem led us to propose a generalization of Feldkamp formula to fit any off-centered geometry. This new formula called /spl alpha/-FDK reduces to original FDK when applied to standard geometry. Reconstructions of simulated phantoms give good results with a limited angle of excentration. We analyse artefacts observed in the Radon space.

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, we propose a new approach based on three-dimensional (3-D) medial axis transformation for describing geometrical shapes in three-dimensional images. For 3-D-images, the medial axis, which is composed of both curves and medial surfaces, provides a simplified and reversible representation of structures. The purpose of this new method is to classify each voxel of the three-dimensional images in four classes: boundary, branching, regular and arc points. The classification is first performed on the voxels of the medial axis. It relies on the topological properties of a local region of interest around each voxel. The size of this region of interest is chosen as a function of the local thickness of the structure. Then, the reversibility of the medial axis is used to deduce a labeling of the whole object. The proposed method is evaluated on simulated images. Finally, we present an application of the method to the identification of bone structures from 3-D very high-resolution tomographic images.

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.

The quantification of cancellous bone network from computed tomography (CT) images requires a segmentation step which is crucial and difficult because of the partial volume effect in CT images. In this paper, we present and evaluate a new approach for segmenting cancellous bone network from high-resolution CT (HRCT) slices. The idea is first to detect a skeleton from the crest lines of the structure and then to thicken it to extract the whole bone structure by satisfying local neighborhood constraints. The segmentation requires the adjustment of relative and not absolute parameters like most methods. We quantified the influence of these parameters on architectural measurements. Results were first validated by using a physical phantom and then examined on a series of 12 HRCT images of human lumbar vertebra of different ages. We demonstrated that the choice of segmentation parameters yielded important variability on architectural measurements (up to 20%), but less variability than a more commonly used approach. This stresses the importance of settle on the segmentation parameters for once, which is possible with the proposed method.

3D-shape description requires the partition of objects in different parts. We propose a new approach based on the analysis of a 3D skeleton. The skeleton is a representation of objects by their axis of symmetry. In 3D, it is composed of surfaces associated with plate-like parts of the object and curves associated with cylindrical parts. Our method is two parts. First, four types of skeleton points are identified: boundary, branching, regular and arc points. A skeleton point is labeled according to the intersection of its maximal ball with the object. In order to add tolerance to the process, the radius of maximal balls is slightly increased. Second, the reversibility of the skeleton is used to deduce a labeling of the whole object. Finally, we present an application of the method to the identification of bone structures from 3D high-resolution tomographic images.

A new region growing algorithm is proposed for the automated segmentation of three-dimensional images. No initial parameters such as the homogeneity threshold or the seeds location have to be adjusted. The principle of the authors' method is to build a region growing sequence in increasing the maximal homogeneity threshold from a very small value to large one. On each segmented region, a 3D parameter which has been validated on a test image, evaluates the segmentation quality. This set of values called evaluation function is used to the determination of the best segmentation. The authors' algorithm was tested on 3D MR images for the segmentation of trabecular bone samples in order to quantify osteoporosis. A comparison to automated and manual thresholding showed that the authors' algorithm performs better. Its main advantages are to eliminate isolated points due to the noise and to preserve connectivity of the bone structure.

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.

This paper presents an application of 2D continuous wavelet transform (WT) to texture analysis. A complete set of wavelets is defined from an isotropic mother wavelet called the Mexican hat, allowing the decomposition of an image on different scales. Simple orientation texture features are computed on an analyzing window moving through the resulting images, in order to characterize each region of the image by a feature vector. A multiresolution clustering method, based on Kohonen's (1982) self-organizing map, is then used to group regions into homogeneous areas, according to the similarity of their feature vectors. We show on two examples that the best image segmentation is achieved with a variable size window, depending on the scale of analysis.>

Conventional triangulation algorithms from planar contours suffer from some limitations. For instance, incorrect results can be obtained when the contours are not convex, or when the contours in two successive slices are very different. In the same way, the presence of multiple contours in a slice leads to ambiguities in defining the appropriate links. The purpose of this paper is to define a general triangulation procedure that provides a solution to these problems. We first describe a simple heuristic triangulation algorithm which is extended to nonconvex contours. It uses an original decomposition of an arbitrary contour into elementary convex subcontours. Then the problem of linking one contour in a slice to several contours in an adjacent slice is examined. To this end, a new and unique interpolated contour is generated between the two slices, and the link is created using the previously defined procedure. Next, a solution to the general case of linking multiple contours in each slice is proposed. Finally, the algorithm is applied to the reconstitution of the external surface of a complex shaped object: a human vertebra.

Several possibilities of reducing the troublesome interference terms in the Wigner distributions (WD) of 2D real signals by using different 2D analytic signals are investigated. The results show that interferences between positive and negative spatial frequencies can always be largely reduced by using a 2D analytic signal, without any loss of information, but that the use of any 2D analytic signal does not eliminate all types of interference. It is demonstrated that various kinds of interference exist and that their efficient reduction depends on the appropriate choice of different 2D analytic signals. The appropriate choice of a 2D analytic signal depends on the concrete 2D real signals spectral characteristics.>

Many applications require the acquisition of 3D CT images made of a stack of 2D X- ray slices. The different slices are obtained by the displacement of the patient table, which sets the resolution in the z direction perpendicularly to the slice plane. This resolution is physically limited by the detector width, on which the X-ray radiation is integrated. Those detectors inherently carry out a low pass filtering process and aliasing effects. As a consequence the reconstruction of a slice in any direction can present artefacts. Then we propose to apply a superresolution technique based on a deconvolution method associated to oversampling using subpixel motion in order to improve the resolution in the z-direction. This method requires the acquisition of overlapping slices which are later processed directly in the spatial domain, what is particularly interesting for computer time. Its application provides thinner and accurate new slices. After the presentation of the method, the results obtained on experimental images coming from a conventional CT scanner are presented.