Binary morphological shape-based interpolation applied to 3-D tooth reconstruction

In this paper we propose an interpolation algorithm using a mathematical morphology morphing approach. The aim of this algorithm is to reconstruct the $n$-dimensional object from a group of (n-1)-dimensional sets representing sections of that object. The morphing transformation modifies pairs of consecutive sets such that they approach in shape and size. The interpolated set is achieved when the two consecutive sets are made idempotent by the morphing transformation. We prove the convergence of the morphological morphing. The entire object is modeled by successively interpolating a certain number of intermediary sets between each two consecutive given sets. We apply the interpolation algorithm for 3-D tooth reconstruction

Optimising Spatial and Tonal Data for PDE-based Inpainting

Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the biharmonic operator, and edge-enhancing anisotropic diffusion (EED). The quality of such approaches depends substantially on the selection of the data that is kept. Optimising this data in the domain and codomain gives rise to challenging mathematical problems that shall be addressed in our work. In the 1D case, we prove results that provide insights into the difficulty of this problem, and we give evidence that a splitting into spatial and tonal (i.e. function value) optimisation does hardly deteriorate the results. In the 2D setting, we present generic algorithms that achieve a high reconstruction quality even if the specified data is very sparse. To optimise the spatial data, we use a probabilistic sparsification, followed by a nonlocal pixel exchange that avoids getting trapped in bad local optima. After this spatial optimisation we perform a tonal optimisation that modifies the function values in order to reduce the global reconstruction error. For homogeneous diffusion inpainting, this comes down to a least squares problem for which we prove that it has a unique solution. We demonstrate that it can be found efficiently with a gradient descent approach that is accelerated with fast explicit diffusion (FED) cycles. Our framework allows to specify the desired density of the inpainting mask a priori. Moreover, is more generic than other data optimisation approaches for the sparse inpainting problem, since it can also be extended to nonlinear inpainting operators such as EED. This is exploited to achieve reconstructions with state-of-the-art quality. We also give an extensive literature survey on PDE-based image compression methods

Detection of dirt impairments from archived film sequences : survey and evaluations

Film dirt is the most commonly encountered artifact in archive restoration applications. Since dirt usually appears as a temporally impulsive event, motion-compensated interframe processing is widely applied for its detection. However, motion-compensated prediction requires a high degree of complexity and can be unreliable when motion estimation fails. Consequently, many techniques using spatial or spatiotemporal filtering without motion were also been proposed as alternatives. A comprehensive survey and evaluation of existing methods is presented, in which both qualitative and quantitative performances are compared in terms of accuracy, robustness, and complexity. After analyzing these algorithms and identifying their limitations, we conclude with guidance in choosing from these algorithms and promising directions for future research

Evaluation of registration, compression and classification algorithms. Volume 1: Results

The registration, compression, and classification algorithms were selected on the basis that such a group would include most of the different and commonly used approaches. The results of the investigation indicate clearcut, cost effective choices for registering, compressing, and classifying multispectral imagery

Example Based Image Analysis and Synthesis

Image analysis and graphics synthesis can be achieved with learning techniques using directly image examples without physically-based, 3D models. In our technique: -- the mapping from novel images to a vector of "pose" and "expression" parameters can be learned from a small set of example images using a function approximation technique that we call an analysis network; -- the inverse mapping from input "pose" and "expression" parameters to output images can be synthesized from a small set of example images and used to produce new images using a similar synthesis network. The techniques described here have several applications in computer graphics, special effects, interactive multimedia and very low bandwidth teleconferencing

A fast empirical method for galaxy shape measurements in weak lensing surveys

We describe a simple and fast method to correct ellipticity measurements of galaxies from the distortion by the instrumental and atmospheric point spread function (PSF), in view of weak lensing shear measurements. The method performs a classification of galaxies and associated PSFs according to measured shape parameters, and corrects the measured galaxy ellipticites by querying a large lookup table (LUT), built by supervised learning. We have applied this new method to the GREAT10 image analysis challenge, and present in this paper a refined solution that obtains the competitive quality factor of Q = 104, without any shear power spectrum denoising or training. Of particular interest is the efficiency of the method, with a processing time below 3 ms per galaxy on an ordinary CPU.Comment: 8 pages, 6 figures. Metric values updated according to the final GREAT10 analysis software (Kitching et al. 2012, MNRAS 423, 3163-3208), no qualitative changes. Associated code available at http://lastro.epfl.ch/megalu