O uso de Thin-Plate Splines na transformação de coordenadas com modelagem de distorções entre realizações de referenciais geodésicos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Comparison of different methods for thin section EM analysis of Mycobacterium smegmatis

Bacteria are generally difficult specimens to prepare for conventional resin section electron microscopy and mycobacteria, with their thick and complex cell envelope layers being especially prone to artefacts. Here we made a systematic comparison of different methods for preparing Mycobacterium smegmatis for thin section electron microscopy analysis. These methods were: (1) conventional preparation by fixatives and epoxy resins at ambient temperature. (2) Tokuyasu cryo-section of chemically fixed bacteria. (3) rapid freezing followed by freeze substitution and embedding in epoxy resin at room temperature or (4) combined with Lowicryl HM20 embedding and ultraviolet (UV) polymerization at low temperature and (5) CEMOVIS, or cryo electron microscopy of vitreous sections. The best preservation of bacteria was obtained with the cryo electron microscopy of vitreous sections method, as expected, especially with respect to the preservation of the cell envelope and lipid bodies. By comparison with cryo electron microscopy of vitreous sections both the conventional and Tokuyasu methods produced different, undesirable artefacts. The two different types of freeze-substitution protocols showed variable preservation of the cell envelope but gave acceptable preservation of the cytoplasm, but not lipid bodies, and bacterial DNA. In conclusion although cryo electron microscopy of vitreous sections must be considered the 'gold standard' among sectioning methods for electron microscopy, because it avoids solvents and stains, the use of optimally prepared freeze substitution also offers some advantages for ultrastructural analysis of bacteria.

Visualization and prediction of spatial deformation using thin-plate splines in the context of scoliosis

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Visualization and prediction of spatial deformation using thin-plate splines in the context of scoliosis

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Comparison of High Q microresonators operating on a thin plate mode : the Lamé-mode

International audience

A comparison of techniques for the reconstruction of leaf surfaces from scanned data

The foliage of a plant performs vital functions. As such, leaf models are required to be developed for modelling the plant architecture from a set of scattered data captured using a scanning device. The leaf model can be used for purely visual purposes or as part of a further model, such as a fluid movement model or biological process. For these reasons, an accurate mathematical representation of the surface and boundary is required. This paper compares three approaches for fitting a continuously differentiable surface through a set of scanned data points from a leaf surface, with a technique already used for reconstructing leaf surfaces. The techniques which will be considered are discrete smoothing D2-splines [R. Arcangeli, M. C. Lopez de Silanes, and J. J. Torrens, Multidimensional Minimising Splines, Springer, 2004.], the thin plate spline finite element smoother [S. Roberts, M. Hegland, and I. Altas, Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions, SIAM, 1 (2003), pp. 208--234] and the radial basis function Clough-Tocher method [M. Oqielat, I. Turner, and J. Belward, A hybrid Clough-Tocher method for surface fitting with application to leaf data., Appl. Math. Modelling, 33 (2009), pp. 2582-2595]. Numerical results show that discrete smoothing D2-splines produce reconstructed leaf surfaces which better represent the original physical leaf.

Multi-modal deformable medical image registration

Non-rigid image registration is an essential tool required for overcoming the inherent local anatomical variations that exist between images acquired from different individuals or atlases. Furthermore, certain applications require this type of registration to operate across images acquired from different imaging modalities. One popular local approach for estimating this registration is a block matching procedure utilising the mutual information criterion. However, previous block matching procedures generate a sparse deformation field containing displacement estimates at uniformly spaced locations. This neglects to make use of the evidence that block matching results are dependent on the amount of local information content. This paper presents a solution to this drawback by proposing the use of a Reversible Jump Markov Chain Monte Carlo statistical procedure to optimally select grid points of interest. Three different methods are then compared to propagate the estimated sparse deformation field to the entire image including a thin-plate spline warp, Gaussian convolution, and a hybrid fluid technique. Results show that non-rigid registration can be improved by using the proposed algorithm to optimally select grid points of interest.

The development of virtual leaf surface models for interactive agrichemical spray applications

This project constructed virtual plant leaf surfaces from digitised data sets for use in droplet spray models. Digitisation techniques for obtaining data sets for cotton, chenopodium and wheat leaves are discussed and novel algorithms for the reconstruction of the leaves from these three plant species are developed. The reconstructed leaf surfaces are included into agricultural droplet spray models to investigate the effect of the nozzle and spray formulation combination on the proportion of spray retained by the plant. A numerical study of the post-impaction motion of large droplets that have formed on the leaf surface is also considered.

PREDICTING THE SPATIAL-DISTRIBUTION OF CLIMATE - TEMPERATURE IN GREAT-BRITAIN

1. The prediction and mapping of climate in areas between climate stations is of increasing importance in ecology.

2. Four categories of model, simple interpolation, thin plate splines, multiple linear regression and mixed spline-regression, were tested for their ability to predict the spatial distribution of temperature on the British mainland. The models were tested by external cross-verification.

3. The British distribution of mean daily temperature was predicted with the greatest accuracy by using a mixed model: a thin plate spline fitted to the surface of the country, after correction of the data by a selection from 16 independent topographical variables (such as altitude, distance from the sea, slope and topographic roughness), chosen by multiple regression from a digital terrain model (DTM) of the country.

4. The next most accurate method was a pure multiple regression model using the DTM. Both regression and thin plate spline models based on a few variables (latitude, longitude and altitude) only were comparatively unsatisfactory, but some rather simple methods of surface interpolation (such as bilinear interpolation after correction to sea level) gave moderately satisfactory results. Differences between the methods seemed to be dependent largely on their ability to model the effect of the sea on land temperatures.

5. Prediction of temperature by the best methods was greater than 95% accurate in all months of the year, as shown by the correlation between the predicted and actual values. The predicted temperatures were calculated at real altitudes, not subject to sea-level correction.

6. A minimum of just over 30 temperature recording stations would generate a satisfactory surface, provided the stations were well spaced.

7. Maps of mean daily temperature, using the best overall methods are provided; further important variables, such as continentality and length of growing season, were also mapped. Many of these are believed to be the first detailed representations at real altitude.

8. The interpolated monthly temperature surfaces are available on disk.

Patient-specific model of a scoliotic torso for surgical planning

A method for the construction of a patient-specific model of a scoliotic torso for surgical planning via inter- patient registration is presented. Magnetic Resonance Images (MRI) of a generic model are registered to surface topography (TP) and X-ray data of a test patient. A partial model is first obtained via thin-plate spline registration between TP and X-ray data of the test patient. The MRIs from the generic model are then fit into the test patient using articulated model registration between the vertebrae of the generic model’s MRIs in prone position and the test patient’s X-rays in standing position. A non-rigid deformation of the soft tissues is performed using a modified thin-plate spline constrained to maintain bone rigidity and to fit in the space between the vertebrae and the surface of the torso. Results show average Dice values of 0.975 ± 0.012 between the MRIs following inter-patient registration and the surface topography of the test patient, which is comparable to the average value of 0.976 ± 0.009 previously obtained following intra-patient registration. The results also show a significant improvement compared to rigid inter-patient registration. Future work includes validating the method on a larger cohort of patients and incorporating soft tissue stiffness constraints. The method developed can be used to obtain a geometric model of a patient including bone structures, soft tissues and the surface of the torso which can be incorporated in a surgical simulator in order to better predict the outcome of scoliosis surgery, even if MRI data cannot be acquired for the patient.

Multimodal image registration of the scoliotic torso for surgical planning

Background This paper presents a method that registers MRIs acquired in prone position, with surface topography (TP) and X-ray reconstructions acquired in standing position, in order to obtain a 3D representation of a human torso incorporating the external surface, bone structures, and soft tissues. Methods TP and X-ray data are registered using landmarks. Bone structures are used to register each MRI slice using an articulated model, and the soft tissue is confined to the volume delimited by the trunk and bone surfaces using a constrained thin-plate spline. Results The method is tested on 3 pre-surgical patients with scoliosis and shows a significant improvement, qualitatively and using the Dice similarity coefficient, in fitting the MRI into the standing patient model when compared to rigid and articulated model registration. The determinant of the Jacobian of the registration deformation shows higher variations in the deformation in areas closer to the surface of the torso. Conclusions The novel, resulting 3D full torso model can provide a more complete representation of patient geometry to be incorporated in surgical simulators under development that aim at predicting the effect of scoliosis surgery on the external appearance of the patient’s torso.

Functional and historical determinants of shape in the scapula of Xenarthran mammals: Evolution of a complex morphological structure

The mammalian scapula is a complex morphological structure, composed of two ossification plates that fuse into a single structure. Most studies on morphological differentiation in the scapula have considered it to be a simple, spatially integrated structure, primarily influenced by the important locomotor function presented by this element. We used recently developed geometric morphometric techniques to test and quantify functional and phylogenetic influences on scapular shape variation in fossil and extant xenarthran mammals. The order Xenarthra is well represented in the fossil record and presents a stable phylogenetic hypothesis for its genealogical history. In addition, its species present a large variety of locomotor habits. Our results show that approximately half of the shape variation in the scapula is due to phylogenetic heritage. This is contrary to the view that the scapula is influenced only by functional demands. There are large-scale shape transformations that provide biomechanical adaptation for the several habits (arboreality, terrestriality, and digging), and small scale-shape transformations (mostly related to the coracoid process) that are not influenced by function. A nonlinear relationship between morphometric and phylogenetic distances indicates the presence of a complex mixture of evolutionary processes acting on shape differentiation of the scapula. J. Morphol. 241,251-263, 1999. (C) 1999 Wiley-Liss, Inc.

Classificação fuzzy de vertentes por krigagem e TPS com agregação de regiões via diagrama de Voronoi

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Algorithms For Automatic And Robust Registration Of 3D Head Scans

wo methods for registering laser-scans of human heads and transforming them to a new semantically consistent topology defined by a user-provided template mesh are described. Both algorithms are stated within the Iterative Closest Point framework. The first method is based on finding landmark correspondences by iteratively registering the vicinity of a landmark with a re-weighted error function. Thin-plate spline interpolation is then used to deform the template mesh and finally the scan is resampled in the topology of the deformed template. The second algorithm employs a morphable shape model, which can be computed from a database of laser-scans using the first algorithm. It directly optimizes pose and shape of the morphable model. The use of the algorithm with PCA mixture models, where the shape is split up into regions each described by an individual subspace, is addressed. Mixture models require either blending or regularization strategies, both of which are described in detail. For both algorithms, strategies for filling in missing geometry for incomplete laser-scans are described. While an interpolation-based approach can be used to fill in small or smooth regions, the model-driven algorithm is capable of fitting a plausible complete head mesh to arbitrarily small geometry, which is known as "shape completion". The importance of regularization in the case of extreme shape completion is shown.