arXiv subjects

Pascal Peter

Publications and source records attributed to Pascal Peter.

25 records · Page 2Linked to original sources

arXiv2021

Quantisation Scale-Spaces

Recently, sparsification scale-spaces have been obtained as a sequence of inpainted images by gradually removing known image data. Thus, these scale-spaces rely on spatial sparsity. In the present paper, we show that sparsification of the co-domain, the set of admissible grey values, also constitutes scale-spaces with induced hierarchical quantisation techniques. These quantisation scale-spaces are closely tied to information theoretical measures for coding cost, and therefore particularly interesting for inpainting-based compression. Based on this observation, we propose a sparsification algorithm for the grey-value domain that outperforms uniform quantisation as well as classical clustering approaches.

eess.IV↗

arXiv2020

Compressing Colour Images with Joint Inpainting and Prediction

Inpainting-based codecs store sparse, quantised pixel data directly and decode by interpolating the discarded image parts. This interpolation can be used simultaneously for efficient coding by predicting pixel data to be stored. Such joint inpainting and prediction approaches yield good results with simple components such as regular grids and Shepard interpolation on grey value images, but they lack a dedicated mode for colour images. Therefore, we evaluate different approaches for inpainting-based colour compression. Inpainting operators are able to reconstruct a large range of colours from a small colour palette of the known pixels. We exploit this with a luma preference mode which uses higher sparsity in YCbCr colour channels than in the brightness channel. Furthermore, we propose the first full vector quantisation mode for an inpainting-based codec that stores only a small codebook of colours. Our experiments reveal that both colour extensions yield significant improvements.

eess.IV↗

arXiv2020

Compressing Piecewise Smooth Images with the Mumford-Shah Cartoon Model

Compressing piecewise smooth images is important for many data types such as depth maps in 3D videos or optic flow fields for motion compensation. Specialised codecs that rely on explicitly stored segmentations excel in this task since they preserve discontinuities between smooth regions. However, current approaches rely on ad hoc segmentations that lack a clean interpretation in terms of energy minimisation. As a remedy, we derive a generic region merging algorithm from the Mumford-Shah cartoon model. It adapts the segmentation to arbitrary reconstruction operators for the segment content. In spite of its conceptual simplicity, our framework can outperform previous segment-based compression methods as well as BPG by up to 3 dB.

eess.IV↗

arXiv2020

Translating Diffusion, Wavelets, and Regularisation into Residual Networks

Convolutional neural networks (CNNs) often perform well, but their stability is poorly understood. To address this problem, we consider the simple prototypical problem of signal denoising, where classical approaches such as nonlinear diffusion, wavelet-based methods and regularisation offer provable stability guarantees. To transfer such guarantees to CNNs, we interpret numerical approximations of these classical methods as a specific residual network (ResNet) architecture. This leads to a dictionary which allows to translate diffusivities, shrinkage functions, and regularisers into activation functions, and enables a direct communication between the four research communities. On the CNN side, it does not only inspire new families of nonmonotone activation functions, but also introduces intrinsically stable architectures for an arbitrary number of layers.

cs.LG↗

arXiv2020

Compressing Flow Fields with Edge-aware Homogeneous Diffusion Inpainting

In spite of the fact that efficient compression methods for dense two-dimensional flow fields would be very useful for modern video codecs, hardly any research has been performed in this area so far. Our paper addresses this problem by proposing the first lossy diffusion-based codec for this purpose. It keeps only a few flow vectors on a coarse grid. Additionally stored edge locations ensure the accurate representation of discontinuities. In the decoding step, the missing information is recovered by homogeneous diffusion inpainting that incorporates the stored edges as reflecting boundary conditions. In spite of the simple nature of this codec, our experiments show that it achieves remarkable quality for compression ratios up to 800 : 1.

eess.IV↗

arXiv2020

Space-Filling Curve Indices as Acceleration Structure for Exemplar-Based Inpainting

Exemplar-based inpainting is the process of reconstructing missing parts of an image by searching the remaining data for patches that fit seamlessly. The image is completed to a plausible-looking solution by repeatedly inserting the patch that is the best match according to some cost function. We present an acceleration structure that uses a multi-index scheme to accelerate this search procedure drastically, particularly in the case of very large datasets. The index scheme uses ideas such as dimensionality reduction and k-nearest neighbor search on space-filling curves that are well known in the field of multimedia databases. Our method has a theoretic runtime of O(log2 n) per iteration and reaches a speedup factor of up to 660 over the original method. The approach has the advantage of being agnostic to most modelbased parts of exemplar-based inpainting such as the order in which patches are processed and the cost function used to determine patch similarity. Thus, the acceleration structure can be used in conjunction with most exemplar-based inpainting algorithms.

cs.CV↗

arXiv2017

Clustering-Based Quantisation for PDE-Based Image Compression

Finding optimal data for inpainting is a key problem in the context of partial differential equation based image compression. The data that yields the most accurate reconstruction is real-valued. Thus, quantisation models are mandatory to allow an efficient encoding. These can also be understood as challenging data clustering problems. Although clustering approaches are well suited for this kind of compression codecs, very few works actually consider them. Each pixel has a global impact on the reconstruction and optimal data locations are strongly correlated with their corresponding colour values. These facts make it hard to predict which feature works best. In this paper we discuss quantisation strategies based on popular methods such as k-means. We are lead to the central question which kind of feature vectors are best suited for image compression. To this end we consider choices such as the pixel values, the histogram or the colour map. Our findings show that the number of colours can be reduced significantly without impacting the reconstruction quality. Surprisingly, these benefits do not directly translate to a good image compression performance. The gains in the compression ratio are lost due to increased storage costs. This suggests that it is integral to evaluate the clustering on both, the reconstruction error and the final file size.

cs.CV↗