Optimising Different Feature Types for Inpainting-based Image Representations

Inpainting-based image compression is a promising alternative to classical transform-based lossy codecs. Typically it stores a carefully selected subset of all pixel locations and their colour values. In the decoding phase the missing information is reconstructed by an inpainting process such as homogeneous diffusion inpainting. Optimising the stored data is the key for achieving good performance. A few heuristic approaches also advocate alternative feature types such as derivative data and construct dedicated inpainting concepts. However, one still lacks a general approach that allows to optimise and inpaint the data simultaneously w.r.t. a collection of different feature types, their locations, and their values. Our paper closes this gap. We introduce a generalised inpainting process that can handle arbitrary features which can be expressed as linear equality constraints. This includes e.g. colour values and derivatives of any order. We propose a fully automatic algorithm that aims at finding the optimal features from a given collection as well as their locations and their function values within a specified total feature density. Its performance is demonstrated with a novel set of features that also includes local averages. Our experiments show that it clearly outperforms the popular inpainting with optimised colour data with the same density

Perceptual error optimization for Monte Carlo rendering

Realistic image synthesis involves computing high-dimensional light transport integrals which in practice are numerically estimated using Monte Carlo integration. The error of this estimation manifests itself in the image as visually displeasing aliasing or noise. To ameliorate this, we develop a theoretical framework for optimizing screen-space error distribution. Our model is flexible and works for arbitrary target error power spectra. We focus on perceptual error optimization by leveraging models of the human visual system's (HVS) point spread function (PSF) from halftoning literature. This results in a specific optimization problem whose solution distributes the error as visually pleasing blue noise in image space. We develop a set of algorithms that provide a trade-off between quality and speed, showing substantial improvements over prior state of the art. We perform evaluations using both quantitative and perceptual error metrics to support our analysis, and provide extensive supplemental material to help evaluate the perceptual improvements achieved by our methods

Gaining Insights into Denoising by Inpainting

The filling-in effect of diffusion processes is a powerful tool for various image analysis tasks such as inpainting-based compression and dense optic flow computation. For noisy data, an interesting side effect occurs: The interpolated data have higher confidence, since they average information from many noisy sources. This observation forms the basis of our denoising by inpainting (DbI) framework. It averages multiple inpainting results from different noisy subsets. Our goal is to obtain fundamental insights into key properties of DbI and its connections to existing methods. Like in inpainting-based image compression, we choose homogeneous diffusion as a very simple inpainting operator that performs well for highly optimized data. We propose several strategies to choose the location of the selected pixels. Moreover, to improve the global approximation quality further, we also allow to change the function values of the noisy pixels. In contrast to traditional denoising methods that adapt the operator to the data, our approach adapts the data to the operator. Experimentally we show that replacing homogeneous diffusion inpainting by biharmonic inpainting does not improve the reconstruction quality. This again emphasizes the importance of data adaptivity over operator adaptivity. On the foundational side, we establish deterministic and probabilistic theories with convergence estimates. In the non-adaptive 1-D case, we derive equivalence results between DbI on shifted regular grids and classical homogeneous diffusion filtering via an explicit relation between the density and the diffusion time