arXiv subjects

Vassillen Chizhov

Publications and source records attributed to Vassillen Chizhov.

8 recordsLinked to original sources

arXiv2026

Optimizing Multiple Feature Types for Image Inpainting in the Linear and Nonlinear Setting

Inpainting-based compression stores a carefully optimized subset of the full image data and reconstructs the missing data by inpainting. The quality of these lossy codecs depends decisively on the stored data. So far, these data consist almost exclusively of pixel locations along with their grayscale or color values. In the present paper, we present a general theory and a practical framework that allows to incorporate arbitrary features which can be described by linear or nonlinear equations. This includes e.g. derivatives of arbitrary order or local integrals. Our features can be combined with linear or nonlinear inpainting operators. Moreover, we present an algorithm that automatically optimizes the location and the type of the selected feature. The approach of allowing different types of optimized features turns inpainting-based compression into a more general, versatile and powerful paradigm. Our experiments report a consistent quality gain when increasing the number of feature types from 1 to 5. With the same amount of stored data, the average peak signal-to-noise improvement is 2.76 dB for harmonic (homogeneous diffusion) inpainting, and 1.82 dB for edge-enhancing diffusion inpainting.

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arXiv2026

Optimising Inpainting Data with Delaunay Averages

Inpainting-based image compression usually stores an optimised subset of all pixel locations and their colour values. In the decoding phase, the missing data are approximated via inpainting. Since the reconstruction quality depends critically on the selection of the stored data, we introduce a novel feature type: We store the vertex locations of a Delaunay triangulation together with the average colour values inside all triangles. We show that combining this feature type with homogeneous diffusion inpainting creates an elegant mathematical formulation with a positive definite linear system of equations. Even a simple solver such as the conjugate gradient method allows the handling of large images. To make our Delaunay averages maximally adaptive to the image, we develop an efficient data optimisation strategy specifically tailored to them. It incorporates ideas successfully used in the stippling literature. Experiments show that our approach outperforms the popular inpainting with optimised colour values by a large margin. Last but not least, we discover a favourable scaling behaviour: Doubling the image resolution allows us to halve the percentage of stored data while maintaining the quality level. This is attractive for compressing modern high-resolution images, where even data densities below 1 % yield appealing reconstructions.

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arXiv2024

Connecting Image Inpainting with Denoising in the Homogeneous Diffusion Setting

While local methods for image denoising and inpainting may use similar concepts, their connections have hardly been investigated so far. The goal of this work is to establish links between the two by focusing on the most foundational scenario on both sides: the homogeneous diffusion setting. To this end, we study a denoising by inpainting (DbI) framework: It averages multiple inpainting results from different noisy subsets. We derive equivalence results between DbI on shifted regular grids and homogeneous diffusion filtering in 1D via an explicit relation between the density and the diffusion time. We also provide an empirical extension to the 2-D case. We present experiments that confirm our theory and suggest that it can also be generalized to diffusions with non-homogeneous data or non-homogeneous diffusivities. More generally, our work demonstrates that the hardly explored idea of data adaptivity deserves more attention: It can be as powerful as some popular models with operator adaptivity.

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arXiv2024

Efficient Parallel Data Optimization for Homogeneous Diffusion Inpainting of 4K Images

Homogeneous diffusion inpainting can reconstruct missing image areas with high quality from a sparse subset of known pixels, provided that their location as well as their gray or color values are well optimized. This property is exploited in inpainting-based image compression, which is a promising alternative to classical transform-based codecs such as JPEG and JPEG2000. However, optimizing the inpainting data is a challenging task. Current approaches are either fairly slow or do not produce high quality results. As a remedy we propose fast spatial and tonal optimization algorithms for homogeneous diffusion inpainting that efficiently utilize GPU parallelism, with a careful adaptation of some of the most successful numerical concepts. We propose a densification strategy using ideas from error-map dithering combined with a Delaunay triangulation for the spatial optimization. For the tonal optimization we design a domain decomposition solver that solves the corresponding normal equations in a matrix-free fashion and supplement it with a Voronoi-based initialization strategy. With our proposed methods we are able to generate high quality inpainting masks for homogeneous diffusion and optimized tonal values in a runtime that outperforms prior state-of-the-art by a wide margin.

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arXiv2024

Efficient Parallel Algorithms for Inpainting-Based Representations of 4K Images -- Part I: Homogeneous Diffusion Inpainting

In recent years inpainting-based compression methods have been shown to be a viable alternative to classical codecs such as JPEG and JPEG2000. Unlike transform-based codecs, which store coefficients in the transform domain, inpainting-based approaches store a small subset of the original image pixels and reconstruct the image from those by using a suitable inpainting operator. A good candidate for such an inpainting operator is homogeneous diffusion inpainting, as it is simple, theoretically well-motivated, and can achieve good reconstruction quality for optimized data. However, a major challenge has been to design fast solvers for homogeneous diffusion inpainting that scale to 4K image resolution ($3840 \times 2160$ pixels) and are real-time capable. We overcome this with a careful adaptation and fusion of two of the most efficient concept from numerical analysis: multigrid and domain decomposition. Our domain decomposition algorithm efficiently utilizes GPU parallelism by solving inpainting problems on small overlapping blocks. Unlike simple block decomposition strategies such as the ones in JPEG, our approach yields block artifact-free reconstructions. Furthermore, embedding domain decomposition in a full multigrid scheme provides global interactions and allows us to achieve optimal convergence by reducing both low- and high-frequency errors at the same rate. We are able to achieve 4K color image reconstruction at more than $60$ frames per second even from very sparse data - something which has been previously unfeasible.

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arXiv2023

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.

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arXiv2022

Perceptual error optimization for Monte Carlo rendering

Synthesizing realistic images involves computing high-dimensional light-transport integrals. In practice, these integrals are numerically estimated via Monte Carlo integration. The error of this estimation manifests itself as conspicuous aliasing or noise. To ameliorate such artifacts and improve image fidelity, we propose a perception-oriented framework to optimize the error of Monte Carlo rendering. We leverage models based on human perception from the halftoning literature. The result is an optimization problem whose solution distributes the error as visually pleasing blue noise in image space. To find solutions, we present a set of algorithms that provide varying trade-offs between quality and speed, showing substantial improvements over prior state of the art. We perform evaluations using quantitative and error metrics, and provide extensive supplemental material to demonstrate the perceptual improvements achieved by our methods.

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arXiv2021

Efficient Data Optimisation for Harmonic Inpainting with Finite Elements

Harmonic inpainting with optimised data is very popular for inpainting-based image compression. We improve this approach in three important aspects. Firstly, we replace the standard finite differences discretisation by a finite element method with triangle elements. This does not only speed up inpainting and data selection, but even improves the reconstruction quality. Secondly, we propose highly efficient algorithms for spatial and tonal data optimisation that are several orders of magnitude faster than state-of-the-art methods. Last but not least, we show that our algorithms also allow working with very large images. This has previously been impractical due to the memory and runtime requirements of prior algorithms.

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