Pascal Peter
The Hamilton-Jacobi skeleton, also known as the medial axis, is a powerful shape descriptor that represents binary objects in terms of the centres of maximal inscribed discs. Despite its broad applicability, the medial axis suffers from…
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…
The medial axis transform is a well-known tool for shape recognition. Instead of the object contour, it equivalently describes a binary object in terms of a skeleton containing all centres of maximal inscribed discs. While this shape…
Inpainting-based codecs store sparse selected pixel data and decode by reconstructing the discarded image parts by inpainting. Successful codecs (coders and decoders) traditionally use inpainting operators that solve partial differential…
Diffusion probabilistic models excel at sampling new images from learned distributions. Originally motivated by drift-diffusion concepts from physics, they apply image perturbations such as noise and blur in a forward process that results…
Deep learning has revolutionized the field of computer vision by introducing large scale neural networks with millions of parameters. Training these networks requires massive datasets and leads to intransparent models that can fail to…
Probabilistic diffusion models enjoy increasing popularity in the deep learning community. They generate convincing samples from a learned distribution of input images with a wide field of practical applications. Originally, these…
With well-selected data, homogeneous diffusion inpainting can reconstruct images from sparse data with high quality. While 4K colour images of size 3840 x 2160 can already be inpainted in real time, optimising the known data for…
Image blending is an integral part of many multi-image applications such as panorama stitching or remote image acquisition processes. In such scenarios, multiple images are connected at predefined boundaries to form a larger image. A…
Diffusion-based inpainting can reconstruct missing image areas with high quality from sparse data, provided that their location and their values are well optimised. This is particularly useful for applications such as image compression,…
Image inpainting is a restoration method that reconstructs missing image parts. However, a carefully selected mask of known pixels that yield a high quality inpainting can also act as a sparse image representation. This challenging spatial…
Diffusion-based inpainting is a powerful tool for the reconstruction of images from sparse data. Its quality strongly depends on the choice of known data. Optimising their spatial location -- the inpainting mask -- is challenging. A…
We investigate numerous structural connections between numerical algorithms for partial differential equations (PDEs) and neural architectures. Our goal is to transfer the rich set of mathematical foundations from the world of PDEs to…
Partial differential equation (PDE) models and their associated variational energy formulations are often rotationally invariant by design. This ensures that a rotation of the input results in a corresponding rotation of the output, which…
Inpainting-based compression represents images in terms of a sparse subset of its pixel data. Storing the carefully optimised positions of known data creates a lossless compression problem on sparse and often scattered binary images. This…
We investigate what can be learned from translating numerical algorithms into neural networks. On the numerical side, we consider explicit, accelerated explicit, and implicit schemes for a general higher order nonlinear diffusion equation…
Inpainting-based image compression is emerging as a promising competitor to transform-based compression techniques. Its key idea is to reconstruct image information from only few known regions through inpainting. Specific partial…
Compression methods based on inpainting are an evolving alternative to classical transform-based codecs for still images. Attempts to apply these ideas to video compression are rare, since reaching real-time performance is very challenging.…
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…
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…