A general nonparametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure, the mean shift. We prove for discrete data the convergence of a recursive mean shift procedure to the nearest stationary point of the underlying density function and thus its utility in detecting the modes of the density. The equivalence of the mean shift procedure to the Nadaraya–Watson estimator from kernel regression and the robust M-estimators of location is also established. Algorithms for two low-level vision tasks, discontinuity preserving smoothing and image segmentation are described as applications. In these algorithms the only user set parameter is the resolution of the analysis, and either gray level or color images are accepted as input. Extensive experimental results illustrate their excellent performance.

In this paper, a common framework is outlined for nonlinear diffusion, adaptive smoothing, bilateral filtering and mean shift procedure. Previously, the relationship between bilateral filtering and the nonlinear diffusion equation was explored by using a consistent adaptive smoothing formulation. However, both nonlinear diffusion and adaptive smoothing were treated as local processes applying a window at each iteration. Here, these two approaches are extended to an arbitrary window, showing their equivalence and stressing the importance of using large windows for edge-preserving smoothing. Subsequently, it follows that bilateral filtering is a particular choice of weights in the extended diffusion process that is obtained from geometrical considerations. We then show that kernel density estimation applied in the joint spatial-range domain yields a powerful processing paradigm - the mean shift procedure, related to bilateral filtering but having additional flexibility. This establishes an attractive relationship between the theory of statistics and that of diffusion and energy minimization. We experimentally compare the discussed methods and give insights on their performance. Keywords: Nonlinear Diffusion, Adaptive Smoothing, Bilateral filtering, Mean Shift Procedure. 1

To be able to enlarge a digital image from a single frame preserving the perceptive cues is a relevant research issue. The best algorithms take into account the presence of edges due to the variation of luminance, to interpolate correctly the original samples/pixels of the original image. This produces pictures where the interpolated artifacts (aliasing blurring effect, ...) are limited. The zooming algorithm proposed in this paper reduces the noise and enhance the contrast to the borders/edges of the enlarged picture using classical anisotropic diffusion improved by a smart heuristics strategy. The method requires limited computational resources and it works on graylevel images, RGB color pictures and Bayer data. Our experiments show that this algorithm outperforms in quality and efficiency the classical interpolation methods (replication, bilinear, bicubic).

Reconstruction techniques exploit a first building process using Low-resolution (LR) images to obtain a "draft " High Resolution (HR) image and then update the estimated HR by back-projection error reduction. This paper presents different HR draft image construction techniques and shows methods providing the best solution in terms of final perceived/measured quality. The following algorithms have been analysed: a proprietary Resolution Enhancement method (RE-ST); a Locally Adaptive Zooming Algorithm (LAZA); a Smart Interpolation by Anisotropic Diffusion (SIAD); a Directional Adaptive Edge-Interpolation (DAEI); a classical Bicubic interpolation and a Nearest Neighbour algorithm. The resulting HR images are obtained by merging the zoomed LR-pictures using two different strategies: average or median. To improve the corresponding HR images two adaptive error reduction techniques are applied in the last step: auto-iterative and uncertainty-reduction. 1.

Reconstruction techniques exploit a first building process using Low-resolution (LR) images to obtain a "draft " High Resolution (HR) image and then update the estimated HR by back-projection error reduction. This paper presents different HR draft image construction techniques and shows methods providing the best solution in terms of final perceived/measured quality. The following algorithms have been analysed: a proprietary Resolution Enhancement method (RE-ST); a Locally Adaptive Zooming Algorithm (LAZA); a Smart Interpolation by Anisotropic Diffusion (SIAD); a Directional Adaptive Edge-Interpolation (DAEI); a classical Bicubic interpolation and a Nearest Neighbour algorithm. The resulting HR images are obtained by merging the zoomed LR-pictures using two different strategies: average or median. To improve the corresponding HR images two adaptive error reduction techniques are applied in the last step: auto-iterative and uncertainty-reduction. 1.

First and foremost, I would like to thank my Mother, Dorothy Mountainland, for all of her love and support throughout this dissertation and throughout my life. Without all of your help, none of this would have been possible and I dedicate this dissertation to you. My Dad, Edward Mountainland, has provided endless amounts of support and a sympathetic ear. I appreciate your willingness to discuss all of the various situations and problems that I have had. Your advice and input is very valuable and always welcome. Thank you, Ed, for everything. I would also like to thank my Grandparents, Mary and Alvin Wilke, for all of their love, help, and support. Nikita Wood NAC AD has provided me with more support than humanly possible. His ability to make me laugh and to see that there is more to life than science and mathematics has been especially important to me. Nikita has also ensured that I never forget to stop and sniff, I mean smell, the roses among other things. Thank you, Bubber, for putting up with me and waiting patiently for me to come home. I would like to thank Eric Schwartz for providing me with an opportunity to work with