Tomáš Karella

Reassembling fragmented artwork is essential to recover both the image on the object and its physical shape, which provides stability and prevents further damage. However, it is a labor-intensive and technically demanding task due to the similarity of fragments, deformation, and information loss. Here, we present an automated pipeline (available as open-source software) for the digital reassembly of a fragmented dry-plate photographic negative. The pipeline uses advanced image processing techniques in a jigsaw-puzzle-inspired strategy. Local osculating circle shape descriptors and contour color profiles are used to propose pairwise fragment matches. These candidate matches are then verified and refined using the Iterative Closes Point (ICP) algorithm, and finally a genetic search assembles consistent clusters into a global solution. The proposed pipeline was rigorously tested on synthetic datasets, digitized jigsaw puzzle pieces, and applied to a severely damaged early 20th-century dry plate negative. The automated procedure successfully reassembled 12 of 14 fragments in a fraction of the time required for manual reconstruction, while preserving the alignment accuracy achieved by manual assembly. The results demonstrate the potential of this method as an efficient and reliable tool to support digital restoration workflows in photographic conservation.

Recognition of 3D objects is an important task in many bio-medical and industrial applications. The recognition algorithms should work regardless of a particular orientation of the object in the space. In this paper, we introduce new 3D rotation moment invariants, which are composed of non-separable Appell moments. We show that non-separable moments may outperform the separable ones in terms of recognition power and robustness thanks to a better distribution of their zero surfaces over the image space. We test the numerical properties and discrimination power of the proposed invariants on three real datasets—MRI images of human brain, 3D scans of statues, and confocal microscope images of worms. We show the robustness to resampling errors improved more than twice and the recognition rate increased by 2–10 % comparing to most common descriptors. In the last section, we show how these invariants can be used in state-of-the-art neural networks for image recognition. The proposed H-NeXtA architecture improved the recognition rate by 2–5 % over the current networks.

The widespread popularity of equivariant networks underscores the significance of parameter efficient models and effective use of training data. At a time when robustness to unseen deformations is becoming increasingly important, we present H-NeXt, which bridges the gap between equivariance and invariance. H-NeXt is a parameter-efficient roto-translation invariant network that is trained without a single augmented image in the training set. Our network comprises three components: an equivariant backbone for learning roto-translation independent features, an invariant pooling layer for discarding roto-translation information, and a classification layer. H-NeXt outperforms the state of the art in classification on unaugmented training sets and augmented test sets of MNIST and CIFAR-10.