Digital image processing of the Ghent altarpiece : supporting the painting's study and conservation treatment

In this article, we show progress in certain image processing techniques that can support the physical restoration of the painting, its art-historical analysis, or both. We show how analysis of the crack patterns could indicate possible areas of overpaint, which may be of great value for the physical restoration campaign, after further validation. Next, we explore how digital image inpainting can serve as a simulation for the restoration of paint losses. Finally, we explore how the statistical analysis of the relatively simple and frequently recurring objects (such as pearls in this masterpiece) may characterize the consistency of the painter’s style and thereby aid both art-historical interpretation and physical restoration campaign

ShearLab 3D: Faithful Digital Shearlet Transforms based on Compactly Supported Shearlets

Wavelets and their associated transforms are highly efficient when approximating and analyzing one-dimensional signals. However, multivariate signals such as images or videos typically exhibit curvilinear singularities, which wavelets are provably deficient of sparsely approximating and also of analyzing in the sense of, for instance, detecting their direction. Shearlets are a directional representation system extending the wavelet framework, which overcomes those deficiencies. Similar to wavelets, shearlets allow a faithful implementation and fast associated transforms. In this paper, we will introduce a comprehensive carefully documented software package coined ShearLab 3D (www.ShearLab.org) and discuss its algorithmic details. This package provides MATLAB code for a novel faithful algorithmic realization of the 2D and 3D shearlet transform (and their inverses) associated with compactly supported universal shearlet systems incorporating the option of using CUDA. We will present extensive numerical experiments in 2D and 3D concerning denoising, inpainting, and feature extraction, comparing the performance of ShearLab 3D with similar transform-based algorithms such as curvelets, contourlets, or surfacelets. In the spirit of reproducible reseaerch, all scripts are accessible on www.ShearLab.org.Comment: There is another shearlet software package (http://www.mathematik.uni-kl.de/imagepro/members/haeuser/ffst/) by S. H\"auser and G. Steidl. We will include this in a revisio

Gen-L-Video: Multi-Text to Long Video Generation via Temporal Co-Denoising

Leveraging large-scale image-text datasets and advancements in diffusion models, text-driven generative models have made remarkable strides in the field of image generation and editing. This study explores the potential of extending the text-driven ability to the generation and editing of multi-text conditioned long videos. Current methodologies for video generation and editing, while innovative, are often confined to extremely short videos (typically less than 24 frames) and are limited to a single text condition. These constraints significantly limit their applications given that real-world videos usually consist of multiple segments, each bearing different semantic information. To address this challenge, we introduce a novel paradigm dubbed as Gen-L-Video, capable of extending off-the-shelf short video diffusion models for generating and editing videos comprising hundreds of frames with diverse semantic segments without introducing additional training, all while preserving content consistency. We have implemented three mainstream text-driven video generation and editing methodologies and extended them to accommodate longer videos imbued with a variety of semantic segments with our proposed paradigm. Our experimental outcomes reveal that our approach significantly broadens the generative and editing capabilities of video diffusion models, offering new possibilities for future research and applications. The code is available at https://github.com/G-U-N/Gen-L-Video.Comment: The code is available at https://github.com/G-U-N/Gen-L-Vide

Novel Video Completion Approaches and Their Applications

Video completion refers to automatically restoring damaged or removed objects in a video sequence, with applications ranging from sophisticated video removal of undesired static or dynamic objects to correction of missing or corrupted video frames in old movies and synthesis of new video frames to add, modify, or generate a new visual story. The video completion problem can be solved using texture synthesis and/or data interpolation to fill-in the holes of the sequence inward. This thesis makes a distinction between still image completion and video completion. The latter requires visually pleasing consistency by taking into account the temporal information. Based on their applied concepts, video completion techniques are categorized as inpainting and texture synthesis. We present a bandlet transform-based technique for each of these categories of video completion techniques. The proposed inpainting-based technique is a 3D volume regularization scheme that takes advantage of bandlet bases for exploiting the anisotropic regularities to reconstruct a damaged video. The proposed exemplar-based approach, on the other hand, performs video completion using a precise patch fusion in the bandlet domain instead of patch replacement. The video completion task is extended to two important applications in video restoration. First, we develop an automatic video text detection and removal that benefits from the proposed inpainting scheme and a novel video text detector. Second, we propose a novel video super-resolution technique that employs the inpainting algorithm spatially in conjunction with an effective structure tensor, generated using bandlet geometry. The experimental results show a good performance of the proposed video inpainting method and demonstrate the effectiveness of bandlets in video completion tasks. The proposed video text detector and the video super resolution scheme also show a high performance in comparison with existing methods

A dual framework for low-rank tensor completion

One of the popular approaches for low-rank tensor completion is to use the latent trace norm regularization. However, most existing works in this direction learn a sparse combination of tensors. In this work, we fill this gap by proposing a variant of the latent trace norm that helps in learning a non-sparse combination of tensors. We develop a dual framework for solving the low-rank tensor completion problem. We first show a novel characterization of the dual solution space with an interesting factorization of the optimal solution. Overall, the optimal solution is shown to lie on a Cartesian product of Riemannian manifolds. Furthermore, we exploit the versatile Riemannian optimization framework for proposing computationally efficient trust region algorithm. The experiments illustrate the efficacy of the proposed algorithm on several real-world datasets across applications.Comment: Aceepted to appear in Advances of Nueral Information Processing Systems (NIPS), 2018. A shorter version appeared in the NIPS workshop on Synergies in Geometric Data Analysis 201