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International audience; For every patient, nowadays, dentists use a software to generate the dental scheme. The dental scheme is basically a diagram representing the whole dentition of the patient. On this diagram, each tooth is represented along with the various operations the patient underwent. The dental scheme for instance shows whether some teeth are missing, or if any treatment was ever performed on the dental roots, it also represents the dental fillings, removable prosthesis, dental crowns or tooth bridges. Filling up the dental scheme may be tedious for dentists, as for every new patient, they would have to carefully make an inventory of every dental care the patient underwent. In this work, we intend to study the feasibility of automatically generating the dental scheme from radiographs. Indeed, we aim to propose an image processing method that would automatically detect missing teeth, as well as any dental care in the dentition, this may save a significant amount of time during the dental consultation. In a first step, our method extracts the relevant portion of the scanner image, i.e. we automatically crop the dentition and thus remove the jaws and chin. The bending of the jaw (dentition curvature) is also estimated, and allows to distinguish the upper and lower jaws. A local minimum/maximum computation coupled with the Hough transform, and a fit with Gaussian Mixture Models helps us to segment the teeth despite strong luminance irregularities due to the imaged spine.

International audience; The Mojette Transform (MT) is an exact discrete form of the Radon transform. It has been originally defined on the lattice Z n (where n is the dimension). We propose to study this transform when using the densest lattices for the dimensions 2 and 3, namely the lattice A 2 and the face-centered cubic lattice A 3. In order to compare the legacy MT using Z n , versus the new MT using A n , we define a fair comparison methodology between the two MT schemes. In particular we detail how to generate the projection angles by exploiting the lattice symmetries and by reordering the Haros-Farey series. Statistic criteria have been also defined to analyse the information distribution on the projections. The experimental results study shows the specific nature of the information distribution on the MT projections due to the high compacity of the A n lattices.

International audience; The Mojette transform is a discrete and exact Radon transform, based on the discrete geometry of the projection and reconstruction lattice. The specific sampling scheme of the Mojette transform results in theoretical exact image reconstruction. In this paper, we compare the reconstructions obtained with the Mojette transform to the ones obtained with several usual projection/backprojection digitized Radon transform. These experiments validate and demonstrate the performance of the Mojette transform sampling over classical implementations based on continuous space.

The Discrete Fourier Transform (DFT) underpins the solution to many inverse problems commonly possessing missing or un-measured frequency information. This incomplete coverage of Fourier space always produces systematic artefacts called Ghosts. In this paper, a fast and exact method for de-convolving cyclic artefacts caused by missing slices of the DFT is presented. The slices discussed here originate from the exact partitioning of DFT space, under the projective Discrete Radon Transform, called the Discrete Fourier Slice Theorem. The method has a computational complexity of O(n log2 n) (where n = N^2) and is constructed from a new Finite Ghost theory. This theory is also shown to unify several aspects of work done on Ghosts over the past three decades. The paper concludes with a significant application to fast, exact, non-iterative image reconstruction from sets of discrete slices obtained for a limited range of projection angles., 10 pages, 18 figures (submitted to IEEE Image Proc.)

Carotid surgery is a frequent act corresponding to 15 to 20 thousands operations per year in France. Cerebral perfusion has to be tracked before and after carotid surgery. In this paper, a diagnosis support using quality metrics is proposed to detect vascular lesions on MR images. Our key stake is to provide a detection tool mimicking the human visual system behavior during the visual inspection. Relevant Human Visual System (HVS) properties should be integrated in our lesion detection method, which must be robust to common distortions in medical images. Our goal is twofold: to help the neuroradiologist to perform its task better and faster but also to provide a way to reduce the risk of bias in image analysis. Objective quality metrics (OQM) are methods whose goal is to predict the perceived quality. In this work, we use Objective Quality Metrics to detect perceivable differences between pairs of images.

Trabecular bone and its microarchitecture are of prime importance for health. This paper focuses onto the relationship between bone microarchitecture and the texture found on micro CT projections. From a small animal study, 5 mice legs were studied by microCT at a resolution of 6μm. The 3D reconstructions are only used as ground truth for their microarchitecture parameters. The study uses 2 different sets of tomographic data : 3 volumes acquired at ANU in Canberra and 2 volumes acquired in Nantes. For each projection set, we determine the texture orientation onto a ROI region of both medial epiphysis and diaphisys using a local variance computed onto Mojette projections from the ROI.

International audience

Trabecular bone and its micro-architecture are of prime importance for health. Changes of bone micro-architecture are linked to different pathological situations like osteoporosis and begin now to be understood. In a previous paper, we started to investigate the relationships between bone and vessels and we also proposed to build a Bone Atlas. This study describes how to proceed for the elaboration and use of such an atlas. Here, we restricted the Atlas to legs (tibia, femur) of rats in order to work with well known geometry of the bone micro-architecture. From only 6 acquired bone, 132 trabecular bone volumes were generated using simple mathematical morphology tools. The variety and veracity of the created micro-architecture volumes is presented in this paper. Medical application and final goal would be to determinate bone micro-architecture with some angulated radiographs (3 or 4) and to easily diagnose the bone status (healthy, pathological or healing bone...).

Trabecular bone and its micro-architecture are of prime importance for health. Changes of bone micro-architecture are linked to different pathological situations like osteoporosis and begin now to be understood. In a previous paper [12], we started to investigate the relationships between bone and vessels and proposed some indices of characterization for the vessels issued from those used for the bone. Our main objective in this paper is to qualify the classical values used for bone as well as those we proposed for vessels according to different acquisition parameters and for several thresholding methods used to separate bone vessels and background. This study is also based on vessels perfusion by a contrast agent (barium sulfate mixed with gelatin) before euthanasia on rats. Femurs and tibias as well as mandibles were removed after rat’s death and were imaged by microCT (Skyscan 1272, Bruker, Belgium) with a resolution ranging from 18 to 3μm. The so obtained images were analyzed with various softwares (NRecon Reconstruction, CtAn, and CtVox from Bruker) in order to calculate bone and vessels micro-architecture parameters (density of bone/blood within the volume), and to know if the results both for bone and vascular micro-architecture are constant along the chosen pixel resolution. The result is clearly negative. We found a very different characterization both for bone and vessels with the 3μm acquisition. Tibia and mandibles bones were also used to show results that can be visually assessed. The largest portions of the vascular tree are orthogonal to the obtained slices of the bone. Therefore, the contrast agent appears as cylinders of various sizes.

In this paper the forward error correction (FEC) codes useful for multimedia wireless transmissions are discussed. The class of usable codes are produced by multiple description (packet equivalence during transmission) after an initial hierarchical representation stage (joint source channel coding). The Mojette transform is used to perform the implementation. A fair comparison with other optimal codes (systematic or not) is provided.JPEG2000 images transmission under a wireless link shows possible strategies.

International audience; The discrete Fourier slice theorem is an important tool for signal processing, especially in the context of the exact reconstruction of an image from its projected views. This paper presents a digital reconstruction algorithm to recover a two dimensional (2-D) image from sets of discrete one dimensional (1-D) projected views. The proposed algorithm has the same computational complexity as the 2-D fast Fourier transform and remains robust to the addition of significant levels of noise. A mapping of discrete projections is constructed to allow aperiodic projections to be converted to projections that assume periodic image boundary conditions. Each remapped projection forms a 1-D slice of the 2-D Discrete Fourier Transform (DFT) that requires no interpolation. The discrete projection angles are selected so that the set of remapped 1-D slices exactly tile the 2-D DFT space. This permits direct and mathematically exact reconstruction of the image via the inverse DFT. The reconstructions are artefact free, except for projection inconsistencies that arise from any additive and remapped noise. We also present methods to generate compact sets of rational projection angles that exactly tile the 2-D DFT space. The improvement in noise suppression that comes with the reconstruction of larger sized images needs to be balanced against the corresponding increase in computation time.

Resume Nous definissons une transformee d'image qui fournit un ensemble redondant d'information. Cette transformee et sa transformee inverse sont construites a partir d'elements structurants a deux pixels. Les ordres de complexite associes sont comparables a ceux de la transformee de Fourier rapide.

Trabecular bone and its microarchitecture are of prime importance for health. Studying vascularization helps to better know the relationship between bone and vascular microarchitecture. This research is an animal study (nine Lewis rats), based on the perfusion of vascularization by a contrast agent (a mixture of 50% barium sulfate with 1.5% of gelatin) before euthanasia. The samples were studied by micro CT at a resolution of 9μm. Softwares were used to show 3D volumes of bone and vessels, to calculate bone and vessels microarchitecture parameters. This study aims to understand simultaneously the bone microarchitecture and its vascular microarchitecture.

International audience; We present algorithms to reconstruct images from minimal sets of discrete Mojette projections using direct back-projection (DBP) with various forms of correction. This paper extends previous work on discrete projection inversion by Servières et al [1, 2, 3]. The number of Mojette projections needed for exact inversion by DBP (EI-DBP) scales as O(N²). A new form of discrete interpolation is developed to expand the point spread function (PSF) of a minimal (Katz-sufficient) set of discrete projections to encompass new directions and thus augment the size of the reconstruction region to which EI-DBP applies. Additionally, we propose a Fourier domain filter for Mojette back-projection that is built from the discrete PSF of the given Mojette angle set and the autocorrelation function of the image domain. These discrete reconstruction methods are targeted for use with noisy sets of real projection data.

International audience; In this paper, we develop an exact, reversible and scale change rotation in the Mojette projection space. The whole process is performed using 1D fast operators and has the advantage to be consistent with standard tomographic geometry.

International audience; Two new methods to perform interpolation mapping from Radon sinogram to Mojette domain are presented. Reconstructions are made from both spaces using FBP and SART algorithms. Assessment of the methods is made both from Shepp-Logan phantom and actual data and demonstrate the efficiency of the proposed algorithms.

International audience; The squamous cell carcinomas of the upper aero-digestive tract represent about ten percent of cancers. External radiation therapy leads to esthetic and functional consequences, and to a decrease of the bone mechanical abilities. For these patients, the oral prosthetic rehabilitation, including possibilities of dental implant placement, is difficult. The effects of radiotherapy on bone microarchitecture parameters are not well known. Thus, the purpose of this study is to assess the effects of external radiation on bone micro architecture in an experimental model of 25 rats using micro CT. 15 rats were irradiated on the hind limbs by a single dose of 20 Grays, and 10 rats were non irradiated. Images of irradiated and healthy bone were compared. Bone microarchitecture parameters (including trabecular thickness, trabecular number, trabecular separation, connectivity density and tissue and bone volume) between irradiated and non-irradiated bones were calculated and compared using a Mann and Whitney test. After 7 and 12 weeks, images of irradiated and healthy bone are different. Differences on the irradiated and the healthy bone populations exhibit a statistical significance. Trabecular number, connectivity density and closed porosity are less important on irradiated bone. Trabecular thickness and separation increase for irradiated bone. These parameters indicate a decrease of irradiated bone properties. Finally, the external irradiation induces changes on the bone micro architecture. This knowledge is of prime importance for better oral prosthetic rehabilitation, including implant placement.

International audience; Bone microarchitecture is the predictor of bone quality or bone disease. It can only be measured on a bone biopsy, which is invasive and not available for all clinical situations. Texture analysis on radiographs is a common way to investigate bone microarchitecture. But relationships between three-dimension histomorphometric parameters and two-dimension texture parameters are not always well known, with poor results. The aim of this paper is twofold : to study one classical parameter namely the fractal dimension which is easily computed on the 2D binary texture and to explore its relationships with the microarchitecture. We performed several experiments in order to check from ground truth the different possible values and their possible explanations. The results show great variations of the fractal dimension according to the size of the window and its location. These variations can be explained by the number of trabecular and their characteristics inside the window where the fractal dimension is computed. This study also shows a specific interest to work with dual fractal dimension of the bone-spongious tissues. This dual information associated with several radiographic images can give a global idea of the number of trabecular segments and their thickness and constitutes a new histomorphometric parameter.

International audience; The precision of a medical LINear ACcelerator (LINAC) gantry rotation angle is crucial for the radiation therapy process, especially in stereotactic radio surgery, given the expected precision of the treatment and in Image Guided Radiation Therapy (IGRT) where the mechanical stability is disturbed due to the additional weight of the kV x-ray tube and detector. We present in this paper an extension of the Winston and Lutz test initially dedicated to control the size and the position of the isocenter of the LINAC and here adapted to test the gantry rotation angle with no additional portal images. This new method uses a test-object patented by QualiFormeD5 and is integrated in the QUALIMAGIQ software platform developed to automatically analyze images acquired for quality control of medical devices.

Last year, we demonstrated the feasibility of a new method to perform dosimetric quality control of Treatment Planning Systems in radiotherapy, this method is based on Monte-Carlo simulations and uses anatomical Digital Test Objects (DTOs). The pelvic DTO was used in order to assess this new method on an ECLIPSE VARIAN Treatment Planning System. Large dose variations were observed particularly in air and bone equivalent material. In this current work, we discuss the results of the previous paper and provide an explanation for observed dose differences, the VARIAN Eclipse (Anisotropic Analytical) algorithm was investigated. Monte Carlo simulations (MC) were performed with a PENELOPE code version 2003. To increase efficiency of MC simulations, we have used our parallelized version based on the standard MPI (Message Passing Interface). The parallel code has been run on a 32- processor SGI cluster. The study was carried out using pelvic DTOs and was performed for low- and high-energy photon beams (6 and 18MV) on 2100CD VARIAN linear accelerator. A square field (10x10 cm2) was used. Assuming the MC data as reference, χ index analyze was carried out. For this study, a distance to agreement (DTA) was set to 7mm while the dose difference was set to 5% as recommended in the TRS-430 and TG-53 (on the beam axis in 3-D inhomogeneities). When using Monte Carlo PENELOPE, the absorbed dose is computed to the medium, however the TPS computes dose to water. We have used the method described by Siebers et al. based on Bragg-Gray cavity theory to convert MC simulated dose to medium to dose to water. Results show a strong consistency between ECLIPSE and MC calculations on the beam axis.© (2011) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

International audience; Bone microarchitecture is the predictor of bone quality or bone disease. It can only be measured on a bone biopsy, which is invasive and not available for all clinical situations. Texture analysis on radiographs is a common way to investigate bone microarchitecture. But relationship between three-dimension histomorphometric parameters and two-dimension texture parameters is not always well known, with poor results. The aim of this study is to performed angulated radiographs of the same region of interest and see if a better relationship between texture analysis on several radiographs and histomorphometric parameters can be developed. Computed radiography images of dog (Beagle) mandible section in molar regions were compared with high-resolution micro-CT (Computed-Tomograph) volumes. Four radiographs with 27° angle (up, down, left, right, using Rinn ring and customized arm positioning system) were performed from initial radiograph position. Bone texture parameters were calculated on all images. Texture parameters were also computed from new images obtained by difference between angulated images. Results of fractal values in different trabecular areas give some caracterisation of bone microarchitecture.

Discrete tomography generally focus on binary image reconstruction from two projections. The Mojette transform allows for a more general framework with any kind of values and any number of projections. Here we use the Mojette transform to address the problem of the 3 materials reconstruction. A new Mojette algorithm is derived and presented in the case of sparse data (reduce number of projections). This algorithm is also generalized for different other uses as for a binary scene reconstruction.

International audience; Shape description is an important step in image analysis. The skeleton is used as a simple, compact representation of a shape. A skeleton represents the line centered in the shape and must be homotopic and one point wide. Current skeletonization algorithms compute the skeleton over several image scans, using either thinning algorithms or distance transforms. The principle of thinning is to delete points as one goes along, preserving the topology of the shape. On the other hand, the maxima of the local distance transform identifies the skeleton and is an equivalent way to calculate the medial axis. However, with this method, the skeleton obtained is disconnected so it is required to connect all the points of the medial axis to produce the skeleton. In this study we introduce a translated distance transform and adapt an existing distance driven homotopic algorithm to perform skeletonization with a single scan and thus allow the processing of unbounded images. This method is applied, in our study, on micro scanner images of trabecular bones. We wish to characterize the bone micro architecture in order to quantify bone integrity.

International audience; For some authors trabecular bone is highly visible in intraoral radiographs. For other authors, the observed intrabony trabecular pattern is a representation of only the endosteal surface of cortical bone, not of intermedullary striae. The purpose of this preliminary study was to investigate the true anatomical structures that are visible in routine dental radiographs and classically denoted trabecular bone. This is a major point for bone texture analysis on radiographs. Computed radiography (CR) images of dog mandible section in molar region were compared with simulations calculated from high-resolution micro-CT volumes. Calculated simulations were obtained using the Mojette Transform. By digitally editing the CT volume, the simulations were separated into trabecular and cortical components into a region of interest. Different images were compared and correlated, some bone micro-architecture parameters calculated. A high correlation was found between computed radiographs and calculated simulations from micro-CT. The Mojette transform was successful to obtain high quality images. Cortical bone did not contribute to change in a major way simulated images. These first results imply that intrabony trabecular pattern observed on radiographs can not only be a representation of the cortical bone endosteal surface and that trabecular bone is highly visible in intraoral radiographs.

In this paper, we deepen the R&D program named DTO-DC (Digital Object Test and Dosimetric Console), which goal is to develop an efficient, accurate and full method to achieve dosimetric quality control (QC) of radiotherapy treatment planning system (TPS). This method is mainly based on Digital Test Objects (DTOs) and on Monte Carlo (MC) simulation using the PENELOPE code [1]. These benchmark simulations can advantageously replace experimental measures typically used as reference for comparison with TPS calculated dose. Indeed, the MC simulations rather than dosimetric measurements allow contemplating QC without tying treatment devices and offer in many situations (i.p. heterogeneous medium, lack of scattering volume...) better accuracy compared to dose measurements with classical dosimetry equipment of a radiation therapy department. Furthermore using MC simulations and DTOs, i.e. a totally numerical QC tools, will also simplify QC implementation, and enable process automation; this allows radiotherapy centers to have a more complete and thorough QC. The program DTO-DC was established primarily on ELEKTA accelerator (photons mode) using non-anatomical DTOs [2]. Today our aim is to complete and apply this program on VARIAN accelerator (photons and electrons mode) using anatomical DTOs. First, we developed, modeled and created three anatomical DTOs in DICOM format: 'Head and Neck', Thorax and Pelvis. We parallelized the PENELOPE code using MPI libraries to accelerate their calculation, we have modeled in PENELOPE geometry Clinac head of Varian Clinac 2100CD (photons mode). Then, to implement this method, we calculated the dose distributions in Pelvis DTO using PENELOPE and ECLIPSE TPS. Finally we compared simulated and calculated dose distributions employing the relative difference proposed by Venselaar [3]. The results of this work demonstrate the feasibility of this method that provides a more accurate and easily achievable QC. Nonetheless, this method, implemented on ECLIPSE TPS version 8.6.15, has revealed large discrepancies (11%) between Monte Carlo simulations and the AAA algorithm calculations especially in equivalent air and equivalent bone areas. Our work will be completed by dose measurement (with film) in the presence of heterogeneous environment to validate MC simulations.

Mechanical stability of a medical LINear ACcelerator (LINAC), particularly the quality of the gantry, collimator and table rotations and the accuracy of the isocenter position, are crucial for the radiation therapy process, especially in stereotactic radio surgery and in Image Guided Radiation Therapy (IGRT) where this mechanical stability is perturbed due to the additional weight the kV x-ray tube and detector. In this paper, we present a new method to evaluate a software which is used to perform an automatic measurement of the "size" (flex map) and the location of the kV and the MV isocenters of the linear accelerator. The method consists of developing a complete numerical 3D simulation of a LINAC and physical phantoms in order to produce Electronic Portal Imaging Device (EPID) images including calibrated distortions of the mechanical movement of the gantry and isocenter misalignments.

A new automated approach for vanishing point detection in images of urban scenes is described. This method is based on the theorem of Thales. The main contribution of this paper is the automatic and simultaneous detection of all vanishing points of the image, achieved by converting this problem into the detection of circles in a complex cloud of points, in which each point corresponds to a segment and is associated with an uncertainty. This extraction of circles uses a RANSAC method, modified to improve its speed by using accumulation techniques (Hough transform or otherwise). This robust estimation is then refined by least squares error propagation using the individual variances of each segment. The algorithm is robust, its accuracy is optimised and it is entirely automatic. Its successful operation has been tested on a large number of images of varied urban scenes. Resume Un algorithme entierement automatique de detection de points de fuite dans des images de scenes urbaines est presente. Cette approche s’appuie sur un theoreme classique (theoreme de Thales), qui permet de transformer le probleme de detection des points de fuite a partir de segments et leur incertitude en un probleme de detection de cercles dans un nuage de points (chaque point correspond a un segment, et a chaque point on associe une incertitude). L’extraction de cercles utilise une methode robuste de type RANSAC, modifiee pour etre tres rapide par rapport a des techniques accumulatives (de type Hough ou autres). Cette estimation robuste est ensuite raffinee par une propagation d’incertitude par moindres carres exploitant les variances individuelles de chaque segment. L’algorithme developpe est robuste, sa precision est la meilleure au sens des moindres carres compte tenu des incertitudes associees aux segments detectes, et en outre il est entierement automatique. Son bon fonctionnement a ete teste sur un grand nombre d’images representant des paysages urbains varies. Zusammenfassung Es wird ein neuer, automatisierter Ansatz zur Bestimmung von Fluchtpunkten in Bildern urbaner Szenen vorgestellt. Die Methode basiert auf dem Satz des Thales. Der wesentliche Beitrag ist die automatische und simultane Detektion aller Fluchtpunkte eines Bildes durch Invertierung dieses Problems in die Aufgabe der Bestimmung von Kreisen in komplexen Punktwolken, in denen jeder Punkt zu einem Segment gehort und mit einer Unsicherheit behaftet ist. Die Extraktion von Kreisen nutzt die RANSAC Methode, die zur Geschwindigkeitssteigerung modifiziert wurde, und sich auf Akkumulationstechniken, wie z.B. die Hough Transformation stutzt. Diese robuste Schatzung wird abschliesend durch Fehlerfortpflanzung nach der Methode der Kleinsten Quadrate unter Ausnutzung der individuellen Varianzen jedes Segments verfeinert. Der Algorithmus arbeitet vollautomatisch, ist robust und die Genauigkeit ist optimiert. Die erfolgreiche Anwendung wurde an einer grosen Anzahl Bildern verschiedenster Stadtszenen getestet. Resumen Este articulo describe un procedimiento completamente automatico para la deteccion de puntos de fuga en imagenes de escenas urbanas. El principio se apoya en un teorema clasico (el teorema de Tales) que permite transformar el problema de la deteccion de los puntos de fuga a partir de segmentos y de su incertidumbre, en un problema de deteccion de circulos dentro de una nube de puntos en la que cada punto corresponde a un segmento y a cada punto se le asocia una incertidumbre. La extraccion de circulos utiliza un metodo robusto tipo RANSAC modificado para mejorar su velocidad comparado con tecnicas de acumulacion del tipo transformada de Hough u otras. Esta estimacion robusta se refina posteriormente mediante propagacion del error por minimos cuadrados utilizando las varianzas individuales de cada segmento. El algoritmo desarrollado es robusto, su precision es la mejor en el sentido de minimos cuadrados teniendo en cuenta las incertidumbres asociadas a los segmentos detectados y, ademas, es completamente automatico. Su buen funcionamiento se ha evaluado procesando muchas imagenes de escenas urbanas variadas.

International audience; This paper presents a new method to solve the relative pose between two images, using three pairs of homologous points and the knowledge of the vertical direction. The vertical direction can be determined in two ways: The first requires direct physical measurements such as the ones provided by an IMU (inertial measurement unit). The other uses the automatic extraction of the vanishing point corresponding to the vertical direction in an image. This knowledge of the vertical direction solves two unknowns among the three parameters of the relative rotation, so that only three homologous couples of points are requested to position a couple of images. Rewriting the coplanarity equations thus leads to a much simpler solution. The remaining unknowns resolution is performed by "hiding a variable" approach. The elements necessary to build a specific algebraic solver are given in this paper, allowing for a real-time implementation. The results on real and synthetic data show the efficiency of this method.

Article accepté à IEEE Pacific-Rim Symposium on Image and Video Technology (PSIVT), Tokyo, Japan, January 2009.; International audience; The goal of this paper is to estimate directly the rotation and translation between two stereoscopic images with the help of five homologous points. The methodology presented does not mix the rotation and translation parameters, which is comparably an important advantage over the methods using the well-known essential matrix. This results in correct behavior and accuracy for situations otherwise knownas quite unfavorable, such as planar scenes, or panoramic sets of images (with a null base length), while providing quite comparable results for more "standard" cases. The resolution of the algebraic polynomials resulting from the modeling of the coplanarity constraint is made with the help of powerful algebraic solver tools (the GrÄobner bases and the Rational Univariate Representation).

International audience; The joint source-channel coding system proposed in this paper has two aims: lossless compression with a progressive mode and the integrity of medical data, which takes into account the priorities of the image and the properties of a network with no guaranteed quality of service. In this context, the use of scalable coding, Locally Adapted Resolution (LAR) and a discrete and exact Radon transform, known as the Mojette transform, meets this twofold requirement. In this paper, details of this joint coding implementation are provided as well as a performance evaluation with respect to the reference CALIC coding and to unequal error protection using Reed-Solomon codes.

International audience; Mojette projections of discrete pixel arrays form good approximations to experimental parallel-beam x-ray intensity absorption profiles. They are discrete sums taken at angles defined by rational fractions. Mojette-like projections form a “half-way house” between a conventional sinogram and fully digital projection data. A new direct and exact image reconstruction technique is proposed here to invert arbitrary but sufficient sets of Mojette data. This new method does not require iterative, statistical solution methods, nor does it use the efficient but noise-sensitive “corner-based” inversion method. It instead exploits the exact invertibility of the prime-sized array Finite Radon Transform (FRT), and the fact that all Mojette projections can be mapped directly into FRT projections. The algorithm uses redundant or “calibrated” areas of an image to expand any asymmetric Mojette set into the smallest symmetric FRT set that contains all of the Mojette data without any re-binning. FRT data will be missing at all angles where Mojette data is not provided, but can be recovered exactly from the “ghost projections” that are generated by back-projecting all the known data across the calibrated regions of the reconstructed image space. Algorithms are presented to enable efficient image reconstruction from any exact Mojette projection set, with a view to extending this approach to invert real x-ray data.

International audience; Tomographic acquisition uses projection angles evenly distributed around 2π. The Mojette transform and the discrete Finite Radon Transform (FRT) both use discrete geometry to overcome the ill-posedeness of the inverse Radon transform. This paper focuses on the transformation of acquired tomographic projections into suitable discrete projection forms. Discrete Mojette and FRT algorithms can then be used for image reconstruction. The impact of physical acquisition parameters (which produce uncertainties in the detected projection data) is also analysed to determine the possible useful interpolations according to the choice of angle acquisitions and the null space of the transform. The mean square error (MSE) reconstruction results obtained for data from analytical phantoms consistently shows the superiority of these discrete approaches when compared to the classical "continuous space" FBP reconstruction.