Length Constrained Multiresolution Deformation for Surface Wrinkling

International audienceWe present a method for deforming piescewise linear 3D curves on surfaces with constant length constraint. We show how this constraint can be integrated into a multiresolution editing tool allowing an intuitive control of the deformation's extent and aspect. The constraint is enforced following two steps. A first step consists in approximating the initial length by modifying the multiresolution decomposition at some specified scale. In a second step the constraint is axactly enforced by constrained minimization of a smoothness criterion. This process then provides the core of an integrated wrinkling tool for soft tissues modelling. A curve on the mesh is deformed, providing a deformation profile which is propagated in a user-defined neighbourhood

Magnetic Helicity Flow in the Sun and Heliosphere

Magnetic helicity, the measure of entanglement within a magnetic field, has the capability to further our knowledge of the magnetic fields which are ubiquitous across the physical universe. Discovered half a century ago by Lodewijk Woltjer in 1958, it was only given physical meaning by Keith Moffatt in 1969. Progress was initially slow due to the constraints on its calculation: it is assumed that the volume within which we wish to measure helicity does not have any magnetic field crossing its boundaries. But, in 1984, Mitchell Berger and George Field provided a resolution to this problem which allowed it to be applied to open astrophysical fields. From there, and particularly in the last two decades, interest in magnetic helicity has grown exponentially within the research community, resulting in this thesis. We will begin by providing a semi--formal introduction to the topic, in particular that of magnetohydrodynamics, which describes how a magnetic field and associated plasma co-interact. We provide a mathematical introduction to magnetic helicity, and demonstrate that unsolved problems remain in our understanding of the Sun's magnetic field that are associated with its magnetic helicity. With this knowledge in hand, we first tackle the topic of predicting the Solar Cycle, which has been an unachieved goal of the solar physics community for longer than we care to remember. We show that magnetic helicity, which is intrinsically linked to the emergence of sunspots, is a statistically stronger candidate for the predictor of activity than that of the polar field strength, which is the current 'best of the worst' of the known predictors. We then, for the first time, measure how much helicity is generated on the solar surface due to shear motions in a surface flux transport model, which is a method of modelling the magnetic field on the surface of the sun. We show that the results are not as obvious as we expect, and indeed that the flux of magnetic helicity within each hemisphere is carefully balanced between latitudes. We also provide an estimate of how much helicity is produced in a solar cycle, and correlate this with the dipole strength of that cycle. This is followed by the main result of the thesis: we demonstrate that helicity can be completely generalised for any physical system in terms of a two--point correlation, and fully described in terms of spatial scales and locality using wavelet analysis. In particular, we show that our generalised measure of helicity offers a physical meaning to this localisation. Our methods are demonstrated to have some notable advantages to that of Fourier analysis, which is shown to sometimes produce spurious results. Finally, we explore the hypothesis that the shape of a magnetic field domain can contribute to the magnetic helicity when using a toroidal--poloidal decomposition. Indeed, in some cases the asymmetry contains the entirety of the magnetic helicity, which we demonstrate numerically

Multiresolution curve editing with linear constraints

The use of multiresolution control toward the editing of freeform curves and surfaces has already been recognized as a valuable modeling too

Multiscale Analysis for Characterization of Remotely Sensed Images.

In this study we addressed fundamental characteristics of image analysis in remote sensing, enumerated unavoidable problems in spectral analysis, and highlighted the spatial structure and features that increase information amount and measurement accuracy. We addressed the relationship between scale and spatial structure and the difficulties in characterizing them in complex remotely sensed images. We suggested that it is necessary to employ multiscale analysis techniques for analyzing and extracting information from remotely sensed images. We developed a multiscale characterization software system based on an existing software called ICAMS (Image Characterization And Modeling System), and applied the system to various test data sets including both simulated and real remote sensing data in order to evaluate the performance of these methods. In particular, we analyzed the fractal and wavelet methods. For the fractal methods, the results from using a set of simulated surfaces suggested that the triangular prism surface area method was the best technique for estimating the fractal dimension of remote sensing images. Through examining Landsat TM images of four different land covers, we found that fractal dimension and energy signatures derived from wavelets can measure some interesting aspects of the spatial content of remote sensing data, such as spatial complexity, spatial frequency, and textural orientation. Forest areas displayed the highest fractal dimension values, followed by coastal, urban, and agriculture respectively. However, fractal dimension by itself is insufficient for accurate classification of TM images. Wavelet analysis is more accurate for characterizing spatial structures. A longer wavelet was shown to be more accurate in the representation and discrimination of land-cover classes than a similar function of shorter length, and the combination of energy signatures from multiple decomposition levels and multispectral bands led to better characterization results than a single resolution and single band decomposition. Significant improvements in classification accuracy were achieved by using fractal dimensions in conjunction with the energy signature. This study has shown that multiscale analysis techniques are very useful to complement spectral classification techniques to extract information from remotely sensed images

Automatic face recognition using stereo images

Face recognition is an important pattern recognition problem, in the study of both natural and artificial learning problems. Compaxed to other biometrics, it is non-intrusive, non- invasive and requires no paxticipation from the subjects. As a result, it has many applications varying from human-computer-interaction to access control and law-enforcement to crowd surveillance. In typical optical image based face recognition systems, the systematic vaxiability arising from representing the three-dimensional (3D) shape of a face by a two-dimensional (21)) illumination intensity matrix is treated as random vaxiability. Multiple examples of the face displaying vaxying pose and expressions axe captured in different imaging conditions. The imaging environment, pose and expressions are strictly controlled and the images undergo rigorous normalisation and pre-processing. This may be implemented in a paxtially or a fully automated system. Although these systems report high classification accuracies (>90%), they lack versatility and tend to fail when deployed outside laboratory conditions. Recently, more sophisticated 3D face recognition systems haxnessing the depth information have emerged. These systems usually employ specialist equipment such as laser scanners and structured light projectors. Although more accurate than 2D optical image based recognition, these systems are equally difficult to implement in a non-co-operative environment. Existing face recognition systems, both 2D and 3D, detract from the main advantages of face recognition and fail to fully exploit its non-intrusive capacity. This is either because they rely too much on subject co-operation, which is not always available, or because they cannot cope with noisy data. The main objective of this work was to investigate the role of depth information in face recognition in a noisy environment. A stereo-based system, inspired by the human binocular vision, was devised using a pair of manually calibrated digital off-the-shelf cameras in a stereo setup to compute depth information. Depth values extracted from 2D intensity images using stereoscopy are extremely noisy, and as a result this approach for face recognition is rare. This was cofirmed by the results of our experimental work. Noise in the set of correspondences, camera calibration and triangulation led to inaccurate depth reconstruction, which in turn led to poor classifier accuracy for both 3D surface matching and 211) 2 depth maps. Recognition experiments axe performed on the Sheffield Dataset, consisting 692 images of 22 individuals with varying pose, illumination and expressions