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

Bézier Method For Image Processing

This project concerns about Bézier method in Computer Aided GeometricDesign (CAGD) involving Bézier Curve and Bézier Surface which widely related to the other theorem and method. The aim of this project is to introduce the basic of Bézier method and then generate the Bézier curves, Bézier surfaces, theory and properties and develop Bézier method in image processing application specifically image compression by using MATLAB

Joint segmentation of color and depth data based on splitting and merging driven by surface fitting

This paper proposes a segmentation scheme based on the joint usage of color and depth data together with a 3D surface estimation scheme. Firstly a set of multi-dimensional vectors is built from color, geometry and surface orientation information. Normalized cuts spectral clustering is then applied in order to recursively segment the scene in two parts thus obtaining an over-segmentation. This procedure is followed by a recursive merging stage where close segments belonging to the same object are joined together. At each step of both procedures a NURBS model is fitted on the computed segments and the accuracy of the fitting is used as a measure of the plausibility that a segment represents a single surface or object. By comparing the accuracy to the one at the previous step, it is possible to determine if each splitting or merging operation leads to a better scene representation and consequently whether to perform it or not. Experimental results show how the proposed method provides an accurate and reliable segmentation

Representation and coding of 3D video data

Livrable D4.1 du projet ANR PERSEECe rapport a été réalisé dans le cadre du projet ANR PERSEE (n° ANR-09-BLAN-0170). Exactement il correspond au livrable D4.1 du projet

Compression domain volume rendering for distributed environments

This paper describes a method for volume data compression and rendering which bases on wavelet splats. The underlying concept is especially designed for distributed and networked applications, where we assume a remote server to maintain large scale volume data sets, being inspected, browsed through and rendered interactively by a local client. Therefore, we encode the server‘s volume data using a newly designed wavelet based volume compression method. A local client can render the volumes immediately from the compression domain by using wavelet footprints, a method proposed earlier. In addition, our setup features full progression, where the rendered image is refined progressively as data comes in. Furthermore, framerate constraints are considered by controlling the quality of the image both locally and globally depending on the current network bandwidth or computational capabilities of the client. As a very important aspect of our setup, the client does not need to provide storage for the volume data and can be implemented in terms of a network application. The underlying framework enables to exploit all advantageous properties of the wavelet transform and forms a basis for both sophisticated lossy compression and rendering. Although coming along with simple illumination and constant exponential decay, the rendering method is especially suited for fast interactive inspection of large data sets and can be supported easily by graphics hardware