EMAG: Differentiable 4D Gaussian Mixture Splatting for EEG Spatial Super-Resolution

High-density electroencephalography (HD-EEG) enables fine-grained measurement of cortical activity but requires expensive hardware and lengthy setup times, limiting its clinical and research accessibility. We propose EMAG (EEG Mixture of Anisotropic Gaussians), a differentiable framework that reconstructs HD-EEG signals from a sparse subset of low-density (LD) electrodes by representing brain electrical sources as a mixture of anisotropic 4D space-time Gaussians. EMAG places a mixture of multiple Gaussians at each point of a spherical brain grid, each parameterized by a full 4 x 4 precision matrix, enabling anisotropic spatial spreads and explicit coupling between spatial and temporal dimensions. The forward model renders scalp EEG via differentiable Gaussian field contributions at electrode locations, enabling end-to-end training without explicit source localization supervision. We evaluate EMAG on three public EEG benchmarks (Localize-MI, SEED, and SEED-IV) at super-resolution factors of 2x through 8/16x. EMAG outperforms the current state-of-the-art EEG super-resolution method at most super-resolution factors on three standard benchmarks (Localize-MI, SEED, SEED-IV). The explicit Gaussian parameterization further enables direct visualization and interpretability of learned brain source configurations, potentially opening avenues for clinical and neuroscientific applications, such as source localization or biomarker discovery.

The Missing GAP: From Solving Square Jigsaw Puzzles to Handling Real World Archaeological Fragments

Jigsaw puzzle solving has been an increasingly popular task in the computer vision research community. Recent works have utilized cutting-edge architectures and computational approaches to reassemble groups of pieces into a coherent image, while achieving increasingly good results on well established datasets. However, most of these approaches share a common, restricting setting: operating solely on strictly square puzzle pieces. In this work, we introduce GAP, a set of novel jigsaw puzzles datasets containing synthetic, heavily eroded pieces of unrestricted shapes, generated by a learned distribution of real-world archaeological fragments. We also introduce PuzzleFlow, a novel ViT and Flow-Matching based framework for jigsaw puzzle solving, capable of handling complex puzzle pieces and demonstrating superior performance on GAP when compared to both classic and recent prominent works in this domain.

Seq2Seq Models Reconstruct Visual Jigsaw Puzzles without Seeing Them

Jigsaw puzzles are primarily visual objects, whose algorithmic solutions have traditionally been framed from a visual perspective. In this work, however, we explore a fundamentally different approach: solving square jigsaw puzzles using language models, without access to raw visual input. By introducing a specialized tokenizer that converts each puzzle piece into a discrete sequence of tokens, we reframe puzzle reassembly as a sequence-to-sequence prediction task. Treated as "blind" solvers, encoder-decoder transformers accurately reconstruct the original layout by reasoning over token sequences alone. Despite being deliberately restricted from accessing visual input, our models achieve state-of-the-art results across multiple benchmarks, often outperforming vision-based methods. These findings highlight the surprising capability of language models to solve problems beyond their native domain, and suggest that unconventional approaches can inspire promising directions for puzzle-solving research.

Solving Convex Partition Visual Jigsaw Puzzles

Jigsaw puzzle solving requires the rearrangement of unordered pieces into their original pose in order to reconstruct a coherent whole, often an image, and is known to be an intractable problem. While the possible impact of automatic puzzle solvers can be disruptive in various application domains, most of the literature has focused on developing solvers for square jigsaw puzzles, severely limiting their practical use. In this work, we significantly expand the types of puzzles handled computationally, focusing on what is known as Convex Partitions, a major subset of polygonal puzzles whose pieces are convex. We utilize both geometrical and pictorial compatibilities, introduce a greedy solver, and report several performance measures next to the first benchmark dataset of such puzzles.

Recognizing Artistic Style of Archaeological Image Fragments Using Deep Style Extrapolation

Ancient artworks obtained in archaeological excavations usually suffer from a certain degree of fragmentation and physical degradation. Often, fragments of multiple artifacts from different periods or artistic styles could be found on the same site. With each fragment containing only partial information about its source, and pieces from different objects being mixed, categorizing broken artifacts based on their visual cues could be a challenging task, even for professionals. As classification is a common function of many machine learning models, the power of modern architectures can be harnessed for efficient and accurate fragment classification. In this work, we present a generalized deep-learning framework for predicting the artistic style of image fragments, achieving state-of-the-art results for pieces with varying styles and geometries.

Re-assembling the past: The RePAIR dataset and benchmark for real world 2D and 3D puzzle solving

This paper proposes the RePAIR dataset that represents a challenging benchmark to test modern computational and data driven methods for puzzle-solving and reassembly tasks. Our dataset has unique properties that are uncommon to current benchmarks for 2D and 3D puzzle solving. The fragments and fractures are realistic, caused by a collapse of a fresco during a World War II bombing at the Pompeii archaeological park. The fragments are also eroded and have missing pieces with irregular shapes and different dimensions, challenging further the reassembly algorithms. The dataset is multi-modal providing high resolution images with characteristic pictorial elements, detailed 3D scans of the fragments and meta-data annotated by the archaeologists. Ground truth has been generated through several years of unceasing fieldwork, including the excavation and cleaning of each fragment, followed by manual puzzle solving by archaeologists of a subset of approx. 1000 pieces among the 16000 available. After digitizing all the fragments in 3D, a benchmark was prepared to challenge current reassembly and puzzle-solving methods that often solve more simplistic synthetic scenarios. The tested baselines show that there clearly exists a gap to fill in solving this computationally complex problem.