World-wide detailed 2D maps require enormous collective efforts. OpenStreetMap is the result of 11 million registered users manually annotating the GPS location of over 1.75 billion entries, including distinctive landmarks and common urban objects. At the same time, manual annotations can include errors and are slow to update, limiting the map's accuracy. Mapsfrom Motion (MfM) is a step for-ward to automatize such time-consuming map making procedure by computing 2D maps of semantic objects directly from a collection of uncalibrated multi-view images. From each image, we extract a set of object detections, and estimate their spatial arrangement in a top-down local map centered in the reference frame of the camera that captured the image. Aligning these local maps is not a trivial problem, since they provide incomplete, noisy fragments of the scene, and matching detections across them is unreliable because of the presence of repeated pattern and the limited appearance variability of urban objects. We address this with a novel graph-based framework, that encodes the spatial and semantic distribution of the objects detected in each image, and learns how to combine them to predict the objects' poses in a global reference system, while taking into account all possible detection matches and preserving the topology observed in each image. Despite the complexity of the problem, our best model achieves global2D registration with an average accuracy within 4 meters (i.e. below GPS accuracy) even on sparse sequences with strong view-point change, on which COLMAP has an 80% failure rate. We provide extensive evaluation on synthetic and real-world data, showing how the method obtains a solution even in scenarios where standard optimization techniques fail. Find more information at matteot90.github.io/MapsFromMotion.

The task of reassembly is a significant challenge across multiple domains, including archaeology, genomics, and molecular docking, requiring the precise placement and orientation of elements to reconstruct an original structure. In this work, we address key limitations in state-of-the-art Deep Learning methods for reassembly, namely i) scalability; ii) multimodality; and iii) real-world applicability: beyond square or simple geometric shapes, realistic and complex erosion, or other real-world problems. We propose ReassembleNet, a method that reduces complexity by representing each input piece as a set of contour keypoints and learning to select the most informative ones by Graph Neural Networks pooling inspired techniques. ReassembleNet effectively lowers computational complexity while enabling the integration of features from multiple modalities, including both geometric and texture data. Further enhanced through pretraining on a semi-synthetic dataset. We then apply diffusion-based pose estimation to recover the original structure. We improve on prior methods by 57% and 87% for RMSE Rotation and Translation, respectively.

We introduce QuaterGCN, a spectral Graph Convolutional Network (GCN) with quaternion-valued weights at whose core lies the Quaternionic Laplacian, a quaternion-valued Laplacian matrix by whose proposal we generalize two widely-used Laplacian matrices: the classical Laplacian (defined for undirected graphs) and the complex-valued Sign-Magnetic Laplacian (proposed within the spectral GCN SigMaNet to handle digraphs with weights of arbitrary sign). In addition to its generality, QuaterGCN is the only Laplacian to completely preserve the (di)graph topology that we are aware of, as it can handle graphs and digraphs containing antiparallel pairs of edges (digons) of different weight without reducing them to a single (directed or undirected) edge as done by other Laplacians. Experimental results show the superior performance of QuaterGCN compared to other state-of-the-art GCNs, particularly in scenarios where the information the digons carry is crucial to successfully address the task at hand.

Reassembly tasks play a fundamental role in many fields and multiple approaches exist to solve specific reassembly problems. In this context, we posit that a general unified model can effectively address them all, irrespective of the input data type (images, 3D, etc.). We introduce DiffAssemble, a Graph Neural Network (GNN)-based architecture that learns to solve reassembly tasks using a diffusion model formulation. Our method treats the elements of a set, whether pieces of 2D patch or 3D object fragments, as nodes of a spatial graph. Training is performed by introducing noise into the position and rotation of the elements and iteratively denoising them to reconstruct the coherent initial pose. DiffAssemble achieves state-of-the-art (SOTA) results in most 2D and 3D reassembly tasks and is the first learning-based approach that solves 2D puzzles for both rotation and translation. Furthermore, we highlight its remarkable reduction in run-time, performing 11 times faster than the quickest optimization-based method for puzzle solving. Code available at https://github.com/IIT-PAVIS/DiffAssemble.

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.

Positional reasoning is the process of ordering an unsorted set of parts into a consistent structure. To address this problem, we present Positional Diffusion , a plug-and-play graph formulation with Diffusion Probabilistic Models. Using a diffusion process, we add Gaussian noise to the set elements’ position and map them to a random position in a continuous space. Positional Diffusion learns to reverse the noising process and recover the original positions through an Attention-based Graph Neural Network. To evaluate our method, we conduct extensive experiments on three different tasks and seven datasets, comparing our approach against the state-of-the-art methods for visual puzzle-solving, sentence ordering, and room arrangement, demonstrating that our method outperforms long-lasting research on puzzle solving with up to + 17 % compared to the second-best deep learning method, and performs on par against the state-of-the-art methods on sentence ordering and room rearrangement. Our work highlights the suitability of diffusion models for ordering problems and proposes a novel formulation and method for solving various ordering tasks. We release our code at https://github.com/IIT-PAVIS/Positional_Diffusion . • The article presents a novel method for Ordering Elements of a Set in 1D and 2D space. • We propose a task-agnostic method, Positional Diffusion for different ordering tasks • Our approach combines Graph Neural Networks with Diffusion Probabilistic Models. • Without any task-specific modes, our method can outperform task-specific approaches. • We test our approach on Sentence ordering, Visual Puzzles, and Furniture Arrangement.

This paper introduces SigMaNet, a generalized Graph Convolutional Network (GCN) capable of handling both undirected and directed graphs with weights not restricted in sign nor magnitude. The cornerstone of SigMaNet is the Sign-Magnetic Laplacian (LSM), a new Laplacian matrix that we introduce ex novo in this work. LSM allows us to bridge a gap in the current literature by extending the theory of spectral GCNs to (directed) graphs with both positive and negative weights. LSM exhibits several desirable properties not enjoyed by other Laplacian matrices on which several state-of-the-art architectures are based, among which encoding the edge direction and weight in a clear and natural way that is not negatively affected by the weight magnitude. LSM is also completely parameter-free, which is not the case of other Laplacian operators such as, e.g., the Magnetic Laplacian. The versatility and the performance of our proposed approach is amply demonstrated via computational experiments. Indeed, our results show that, for at least a metric, SigMaNet achieves the best performance in 15 out of 21 cases and either the first- or second-best performance in 21 cases out of 21, even when compared to architectures that are either more complex or that, due to being designed for a narrower class of graphs, should---but do not---achieve a better performance.

Urban computing techniques harnessing digital mobility traces can assume a pivotal role in comprehending travel patterns and behavioral dynamics within an urban context. These methodologies yield invaluable insights for transportation planners, enabling them to make informed decisions and augment the overall efficiency of urban transportation systems. The goal of this research is to analyze the parking phenomenon in urban areas and develop predictive models for parking-related indicators. Specifically, we introduce two quantitative metrics: the Average Parking Time and the Average Number of Simultaneously Parked Vehicles, aimed at characterizing parking activities from temporal and volumetric perspectives. A large collection of raw GPS traces from a sample of private cars in the metropolitan areas of Rome was used to investigate and model the spatiotemporal dynamics of parking demand and saturation on public streets. Our investigation entailed the application of a diverse array of Machine Learning and Deep Learning techniques, encompassing statistical models, Graph Convolutional Networks (GCNs), and Convolutional Neural Networks (CNNs), for the prediction of these indicator values. In our experiments, we found that the 3D-CLoST model excelled in accurately predicting parking indicators compared to other techniques. Interestingly, we also observed that statistical models were able to achieve performance levels that were similar to those of more complex models.

The problem of reliably predicting vehicle flows is paramount for traffic management, risk assessment, and public safety. It is a challenging problem as it is influenced by multiple factors, such as spatio-temporal dependencies with external factors (as events and weather conditions). In recent years, with the exponential data growth and technological advancement, deep learning has been adopted to approach urban mobility problems by addressing spatial dependency with convolutional neural networks and the temporal one with recurrent neural networks. We propose a spatio-temporal flow prediction framework, called 3D-CLoST, that exploits the synergy between 3D convolution and long short-term memory (LSTM) networks to jointly learn the characteristics of the space-time correlation from low to high levels. To the best of our knowledge, no method currently proposes such a structure for this problem. The results achieved on the two real-world datasets show that 3D-CLoST can learn behaviors from the data effectively.

Advisors assist students in developing successful course pathways through the curriculum. The purpose of this project is to augment advisor institutional and tacit knowledge with knowledge from predictive algorithms (i.e., Matrix Factorization and Classifiers) specifically developed to identify risk. We use a participatory action research approach that directly involves key members from both advising and research communities in the assessment and provisioning of information from the predictive analytics. The knowledge gained from predictive algorithms is evaluated using a mixed method approach. We first compare the predictive evaluations with advisors evaluations of student performance in courses and actual outcomes in those courses We next expose and classify advisor knowledge of student risk and identify ways to enhance the value of the prediction model. The results highlight the contribution that this collaborative approach can give to the constructive integration of Learning Analytics in higher education settings.