Two-dimensional images and three-dimensional volumes have become a staple ingredient of our artistic, cultural, and scientific appetite. Images capture and immortalize an instance such as natural scenes, through a photograph camera. Moreover, they can capture details inside biological subjects through the use of CT (computer tomography) scans, X-Rays, ultrasound, etc. Three-dimensional volumes of objects are also of high interest in medical imaging, engineering, and analyzing cultural heritage. They are produced using tomographic reconstruction, a technique that combine a large series of 2D scans captured from multiple views. Typically, penetrative radiation is used to obtain each 2D scan: X-Rays for CT scans, radio-frequency waves for MRI (magnetic resonance imaging), electron-positron annihilation for PET scans, etc. Unfortunately, their acquisition is influenced by noise caused by different factors. Noise in two-dimensional images could be caused by low-light illumination, electronic defects, low-dose of radiation, and a mispositioning tool or object. Noise in three-dimensional volumes also come from a variety of sources: the limited number of views, lack of captor sensitivity, high contrasts, the reconstruction algorithms, etc. The constraint that data acquisition be noiseless is unrealistic. It is desirable to reduce, or eliminate, noise at the earliest stage in the application. However, removing noise while preserving the sharp features of an image or volume object remains a challenging task. We propose a multi-scale method to smooth 2D images and 3D tomographic data while preserving features at a specified scale. Our algorithm is controlled using a single user parameter - the minimum scale of features to be preserved. Any variation that is smaller than the specified scale is treated as noise and smoothed, while discontinuities such as corners, edges and detail at a larger scale are preserved. We demonstrate that our smoothed data produces clean images and clean contour surfaces of volumes using standard surface-extraction algorithms. In addition to, we compare our results with results of previous approaches. Our method is inspired by anisotropic diffusion. We compute our diffusion tensors from the local continuous histograms of gradients around each pixel in image

Les images et données volumiques sont devenues importantes dans notre vie quotidienne que ce soit sur le plan artistique, culturel, ou scientifique. Les données volumiques ont un intérêt important dans l'imagerie médicale, l'ingénierie, et l'analyse du patrimoine culturel. Ils sont créées en utilisant la reconstruction tomographique, une technique qui combine une large série de scans 2D capturés de plusieur points de vue. Chaque scan 2D est obtenu par des methodes de rayonnement : Rayons X pour les scanners CT, ondes radiofréquences pour les IRM, annihilation électron-positron pour les PET scans, etc. L'acquisition des images et données volumique est influencée par le bruit provoqué par différents facteurs. Le bruit dans les images peut être causée par un manque d'éclairage, des défauts électroniques, faible dose de rayonnement, et un mauvais positionnement de l'outil ou de l'objet. Le bruit dans les données volumique peut aussi provenir d'une variété de sources : le nombre limité de points de vue, le manque de sensibilité dans les capteurs, des contrastes élevé, les algorithmes de reconstruction employés, etc. L'acquisition de données non bruitée est iréalisable. Alors, il est souhaitable de réduire ou d'éliminer le bruit le plus tôt possible dans le pipeline. La suppression du bruit tout en préservant les caractéristiques fortes d'une image ou d'un objet volumique reste une tâche difficile. Nous proposons une méthode multi-échelle pour lisser des images 2D et des données tomographiques 3D tout en préservant les caractéristiques à l'échelle spécifiée. Notre algorithme est contrôlé par un seul paramètre – la taille des caractéristiques qui doivent être préservées. Toute variation qui est plus petite que l'échelle spécifiée est traitée comme bruit et lissée, tandis que les discontinuités telles que des coins, des bords et des détails à plus grande échelle sont conservés. Nous démontrons les données lissées produites par notre algorithme permettent d'obtenir des images nettes et des iso-surfaces plus propres. Nous comparons nos résultats avec ceux des methodes précédentes. Notre méthode est inspirée par la diffusion anisotrope. Nous calculons nos tenseurs de diffusion à partir des histogrammes continues locaux de gradients autour de chaque pixel dans les images et autour de chaque voxel dans des volumes. Comme notre méthode de lissage fonctionne entièrement sur GPU, il est extrêmement rapide. / Two-dimensional images and three-dimensional volumes have become a staple ingredient of our artistic, cultural, and scientific appetite. Images capture and immortalize an instance such as natural scenes, through a photograph camera. Moreover, they can capture details inside biological subjects through the use of CT (computer tomography) scans, X-Rays, ultrasound, etc. Three-dimensional volumes of objects are also of high interest in medical imaging, engineering, and analyzing cultural heritage. They are produced using tomographic reconstruction, a technique that combine a large series of 2D scans captured from multiple views. Typically, penetrative radiation is used to obtain each 2D scan: X-Rays for CT scans, radio-frequency waves for MRI (magnetic resonance imaging), electron-positron annihilation for PET scans, etc. Unfortunately, their acquisition is influenced by noise caused by different factors. Noise in two-dimensional images could be caused by low-light illumination, electronic defects, low-dose of radiation, and a mispositioning tool or object. Noise in three-dimensional volumes also come from a variety of sources: the limited number of views, lack of captor sensitivity, high contrasts, the reconstruction algorithms, etc. The constraint that data acquisition be noiseless is unrealistic. It is desirable to reduce, or eliminate, noise at the earliest stage in the application. However, removing noise while preserving the sharp features of an image or volume object remains a challenging task. We propose a multi-scale method to smooth 2D images and 3D tomographic data while preserving features at a specified scale. Our algorithm is controlled using a single user parameter – the minimum scale of features to be preserved. Any variation that is smaller than the specified scale is treated as noise and smoothed, while discontinuities such as corners, edges and detail at a larger scale are preserved. We demonstrate that our smoothed data produces clean images and clean contour surfaces of volumes using standard surface-extraction algorithms. In addition to, we compare our results with results of previous approaches. Our method is inspired by anisotropic diffusion. We compute our diffusion tensors from the local continuous histograms of gradients around each pixel in image

Scientific visualization is an essential and indispensable tool for the systematic study of computational (CFD) datasets. There are numerous methods currently used for the unwieldy task of processing and visualizing the characteristically large datasets. Feature extraction is one such technique and has become a significant means for enabling effective visualization. This thesis proposes different modules to refine the maps which are generated from a feature detection on a dataset. The specific example considered in this work is the vortical flow in a two-dimensional oceanographic dataset. This thesis focuses on performing feature extraction by detecting the features and processing the feature maps in three different modules, namely, denoising, segmenting and ranking. The denoising module exploits a wavelet-based multiresolution analysis (MRA). Although developed for two-dimensional datasets, these techniques are directly extendable to three-dimensional cases. A comparative study of the performance of Optimal Feature-Preserving (OFP) filters and non-OFP filters for denoising is presented. A computationally economical implementation for segmenting the feature maps as well as different algorithms for ranking the regions of interest (ROI's) are also discussed in this work.