Nicolas Normand

Monash University (Australia), Melbourne, Victoria, Australia

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Publications (69)9.49 Total impact

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    ABSTRACT: 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.
    IEEE Signal Processing Letters 01/2014; 21(6):682-686. · 1.67 Impact Factor
  • IEEE International Conference on Image Processing; 09/2013
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    ABSTRACT: This paper presents a path-based distance, where local displacement costs vary both according to the displacement vector and with the travelled distance. The corresponding distance transform algorithm is similar in its form to classical propagation-based algorithms, but the more variable distance increments are either stored in look-up-tables or computed on-the-fly. These distances and distance transform extend neighborhood-sequence distances, chamfer distances and generalized distances based on Minkowski sums. We introduce algorithms to compute a translated version of a neighborhood sequence distance map both for periodic and aperiodic sequences and a method to derive the centered distance map. A decomposition of the grid neighbors, in Z2Z2 and Z3Z3, allows to significantly decrease the number of displacement vectors needed for the distance transform. Overall, the distance transform can be computed with minimal delay, without the need to wait for the whole input image before beginning to provide the result image.
    Computer Vision and Image Understanding 04/2013; 117(4):409–417. · 1.23 Impact Factor
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    ABSTRACT: The discrete Fourier transform (DFT) underpins the solution to many inverse problems commonly possessing missing or unmeasured frequency information. This incomplete coverage of the Fourier space always produces systematic artifacts called Ghosts. In this paper, a fast and exact method for deconvolving cyclic artifacts caused by missing slices of the DFT using redundant image regions is presented. The slices discussed here originate from the exact partitioning of the Discrete Fourier Transform (DFT) space, under the projective Discrete Radon Transform, called the discrete Fourier slice theorem. The method has a computational complexity of O(nlog(2)n) (for an n=N×N image) and is constructed from a new cyclic theory of Ghosts. This theory is also shown to unify several aspects of work done on Ghosts over the past three decades. This paper concludes with an application to fast, exact, non-iterative image reconstruction from a highly asymmetric set of rational angle projections that give rise to sets of sparse slices within the DFT.
    IEEE Transactions on Image Processing 06/2012; 21(10):4431-41. · 3.20 Impact Factor
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    ABSTRACT: 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.
    Proc SPIE 02/2012;
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    ABSTRACT: In this paper we propose a new hybrid architecture between client/server and P2P network architectures in order to provide better service quality to the end-user. To distribute and protect the content, we use a discrete geometry tool as the Finite Radon Transform (FRT) in a Maximum Distance Separable (MDS) fashion. The presented results clarify the interest of the proposed architecture in terms of QoS.
    01/2012;
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    ABSTRACT: 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.
    Proc SPIE 03/2011;
  • Conference Proceeding: Properties of Minimal Ghosts.
    Imants D. Svalbe, Nicolas Normand
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    ABSTRACT: A ghost image is an array of signed pixel values so positioned as to create zero-sums in all discrete projections taken across that image for a pre-defined set of angles. The discrete projection scheme used here is the finite Radon transform. Minimal ghosts employ just 2N pixels to generate zero-sum projections at N projection angles. We describe efficient methods to construct N\textthN^\text{th} order minimal ghost images on prime-sized 2D arrays. Ghost images or switching components are important in discrete image reconstruction. Ghosts usually grow larger as they are constrained by more projection angles. When ghosts become too large to be added to an image, image reconstruction from projections becomes unique and exact. Ghosts can be used to synthesize image/anti-image data that will also exhibit zero-sum projections at N pre-defined angles. We examine the remarkable symmetry, cross- and auto-correlation properties of minimal ghosts. The geometric properties of minimal ghost images may make them suitable to embed in data as watermarks.
    Discrete Geometry for Computer Imagery - 16th IAPR International Conference, DGCI 2011, Nancy, France, April 6-8, 2011. Proceedings; 01/2011
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    ABSTRACT: This paper presents a path-based distance where local displacement costs vary both according to the displacement vector and with the travelled distance. The corresponding distance transform algorithm is similar in its form to classical propagation-based algorithms, but the more variable distance increments are either stored in look-up-tables or computed on-the-fly. These distances and distance transform extend neighborhood-sequence distances, chamfer distances and generalized distances based on Minkowski sums. We introduce algorithms to compute, in Z2, a translated version of a neighborhood sequence distance map with a limited number of neighbors, both for periodic and aperiodic sequences. A method to recover the centered distance map from the translated one is also introduced. Overall, the distance transform can be computed with minimal delay, without the need to wait for the whole input image before beginning to provide the result image.
    Discrete Geometry for Computer Imagery. 01/2011;
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    ABSTRACT: A new algorithm for reconstructing a two dimensional object from a set of one dimensional projected views is presented that is both computationally exact and experimentally practical. The algorithm has a computational complexity of O(n log2 n) with n = N^2 for an NxN image, is robust in the presence of noise and produces no artefacts in the reconstruction process, as is the case with conventional tomographic methods. The reconstruction process is approximation free because the object is assumed to be discrete and utilizes fully discrete Radon transforms. Noise in the projection data can be suppressed further by introducing redundancy in the reconstruction. The number of projections required for exact reconstruction and the response to noise can be controlled without comprising the digital nature of the algorithm. The digital projections are those of the Mojette Transform, a form of discrete linogram. A simple analytical mapping is developed that compacts these projections exactly into symmetric periodic slices within the Discrete Fourier Transform. A new digital angle set is constructed that allows the periodic slices to completely fill all of the objects Discrete Fourier space. Techniques are proposed to acquire these digital projections experimentally to enable fast and robust two dimensional reconstructions. Comment: 22 pages, 13 figures, Submitted to Elsevier Signal Processing
    06/2010;
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    ABSTRACT: 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.
    Proc SPIE 03/2010;
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    ABSTRACT: 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.
    Proc SPIE 03/2010;
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    Olivier Déforges, Nicolas Normand, Marie Babel
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    ABSTRACT: This paper presents a new algorithm for an efficient computation of morphological operations for gray images and its specific hardware. The method is based on a new recursive morphological decomposition method of 8-convex structuring elements by only causal two-pixel structuring elements (2PSE). Whatever the element size, erosion or/and dilation can then be performed during a unique raster-like image scan involving a fixed reduced analysis neighborhood. The resulting process offers low computation complexity combined with easy description of the element form. The dedicated hardware is generic and fully regular, built from elementary interconnected stages. It has been synthesized into an FPGA and achieves high frequency performances for any shape and size of structuring element.
    Journal of Real-Time Image Processing 01/2010; · 1.16 Impact Factor
  • Conference Proceeding: On Constructing Minimal Ghosts.
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    ABSTRACT: Ghosts are digital images that contain highly constrained patterns of signed pixel values. The pixels are located so as to create zero-sums when discrete projections are taken across the image at a pre-determined set of angles. Ghosts can be applied to create image/anti-image pairs. An image that is entangled with its anti-image can be used to achieve forward error-correction in redundant data transmission schemes. Ghosts can also be used to help reconstruct images from asymmetric sets of real, noisy tomographic projection data. Minimal ghosts do these tasks most efficiently. We present here new methods to construct minimal ghost images that employ just 2N pixels to obtain zero-sum projections for N angles. Construction of an Nth order ghost had previously required O(2N) pixels.
    International Conference on Digital Image Computing: Techniques and Applications, DICTA 2010, Sydney, Australia, 1-3 December, 2010; 01/2010
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    ABSTRACT: The Mojette transform and the finite Radon transform (FRT) are discrete data projection methods that are exactly invertible and are computed using simple addition operations. Incorporation of a known level of redundancy into data and projection spaces enables the use of the FRT to recover the exact, original data when network packets are lost during data transmission. The FRT can also be shown to be Maximum Distance Separable (MDS). By writing the FRT transform in Vandermonde form, explicit expressions for discrete projection and inversion as matrix operations have been obtained. A cyclic, prime-sized Vandermonde form for the FRT approach is shown here to yield explicit polynomial expressions for the recovery of image rows from projected data and vice-versa. These polynomial solutions are consistent with the heuristic algorithms for "row-solving" that have been published previously. This formalism also opens the way to link "ghost" projections in FRT space and "anti-images" in data space that may provide a key to an efficient method of encoding and decoding general data sets in a systematic form.
    2010 IEEE Wireless Communications and Networking Conference, WCNC 2010, Proceedings, Sydney, Australia, 18-21 April 2010; 01/2010
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    02/2009: pages 135-164; , ISBN: 9781848210806
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    Nicolas Normand, Pierre Evenou
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    ABSTRACT: Chamfer distances are discrete distances based on the propagation of local distances, or weights, defined in a mask. The medial axis, i.e. the centers of maximal balls (balls which are not contained in any other ball), is a powerful tool for shape representation and analysis. The extraction of maximal disks is performed in the general case by testing the inclusion of a ball in a local neighborhood with covering relations usually represented by lookup tables.The proposed method determines if a mask induces a norm and in this case, computes the lookup tables and the test neighborhood based on geometric properties of the balls of chamfer norms, represented as H-polytopes. The method does not need to repeatedly scan the image space, and improves the computation time of both the test neighborhood detection and the lookup table computation.
    Pattern Recognition. 01/2009;
  • 01/2009: pages 29pages;
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    ABSTRACT: 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.
    Computerized Medical Imaging and Graphics 07/2008; 32(4):258-69. · 1.66 Impact Factor
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    ABSTRACT: Quality control of external conformal radiotherapy treatment planning systems softwares is a crucial issue. The treatment quality depends directly on the quality of treatment planning systems (TPS). Radiotherapists need to be sure that softwares compute accurately each parameter of the treatment. This paper focuses on the quality control of geometrical tools of the treatment planning systems, i.e. the virtual simulation software. These TPS compute the geometrical part of the treatment. They define the targets and shapes of the irradiation beams. Four operations done by these TPS are examined in this work. The quality control of the auto-contouring, auto-margin, isocenter computation and collimator conformation tools is treated with a new method based on Digital Test Objects (DTO). Standard methods for this quality control have been set up from the development of some Physical Test Objects (PTO). These methods are time-consuming, incomplete and inaccurate. Results are biased by the CT-scanner acquisition of PTOs and error evaluation is done with the graphic tools of the TPS. Our method uses DTOs and allows for an automated qualitative error evaluation. DTOs present many advantages for TPS quality control. They lead to a fast, accurate, complete and automatic quality assessment. Special DTOs have been developed to control the TPS tools mentioned previously as well as their automatic result analysis methods. A TPS has been controlled with these test objects. The quality assessment shows some errors and highlights some particularities in the TPS tools functioning. This quality control was then compared with the standard quality control.
    Proc SPIE 04/2008;

Publication Stats

138 Citations
374 Downloads
2k Views
9.49 Total Impact Points

Institutions

  • 2011
    • Monash University (Australia)
      Melbourne, Victoria, Australia
  • 2010
    • Unité Inserm U1077
      Caen, Lower Normandy, France
  • 2005
    • University of Nantes
      Naoned, Pays de la Loire, France
  • 2003
    • French National Centre for Scientific Research
      Lutetia Parisorum, Île-de-France, France
  • 2001
    • Ecole Centrale de Nantes
      Naoned, Pays de la Loire, France
    • Institut de Recherche en Communications et Cybernétique de Nantes
      Naoned, Pays de la Loire, France
  • 1997–2000
    • Institut National des Sciences Appliquées de Rennes
      Roazhon, Brittany, France