João Paulo Costeira

Gabriel Moreira, Manuel Marques, João Paulo Costeira et al.

We introduce Spectral Guidance, a framework for controlling diffusion models by leveraging the intrinsic geometry of the generative process. As data is progressively corrupted by noise, only a small number of features remain informative for control. We characterize them as the singular functions of a conditional expectation operator and show that they can be learned via a self-supervised objective. Once recovered, this basis enables the projection of arbitrary guidance signals, such as labels, CLIP embeddings, or masks, directly onto the sampling trajectory. This approach allows for stable, high-fidelity control without retraining or denoiser backpropagation during sampling. Empirically, we improve conditional accuracy on CIFAR-10 by 37 percentage points over the strongest training-free baseline while offering $4\times$ faster sampling. Moreover, the same representations that support label and CLIP guidance also enable spatial control, such as mask-based guidance, without auxiliary models. Finally, our framework reveals a phase transition in the generative process, pinpointing the optimal time window for effective guidance.

José Celestino, Manuel Marques, Jacinto C. Nascimento et al.

Head orientation is a challenging Computer Vision problem that has been extensively researched having a wide variety of applications. However, current state-of-the-art systems still underperform in the presence of occlusions and are unreliable for many task applications in such scenarios. This work proposes a novel deep learning approach for the problem of head pose estimation under occlusions. The strategy is based on latent space regression as a fundamental key to better structure the problem for occluded scenarios. Our model surpasses several state-of-the-art methodologies for occluded HPE, and achieves similar accuracy for non-occluded scenarios. We demonstrate the usefulness of the proposed approach with: (i) two synthetically occluded versions of the BIWI and AFLW2000 datasets, (ii) real-life occlusions of the Pandora dataset, and (iii) a real-life application to human-robot interaction scenarios where face occlusions often occur. Specifically, the autonomous feeding from a robotic arm.

Gabriel Moreira, Manuel Marques, João Paulo Costeira et al.

Recent research in representation learning has shown that hierarchical data lends itself to low-dimensional and highly informative representations in hyperbolic space. However, even if hyperbolic embeddings have gathered attention in image recognition, their optimization is prone to numerical hurdles. Further, it remains unclear which applications stand to benefit the most from the implicit bias imposed by hyperbolicity, when compared to traditional Euclidean features. In this paper, we focus on prototypical hyperbolic neural networks. In particular, the tendency of hyperbolic embeddings to converge to the boundary of the Poincaré ball in high dimensions and the effect this has on few-shot classification. We show that the best few-shot results are attained for hyperbolic embeddings at a common hyperbolic radius. In contrast to prior benchmark results, we demonstrate that better performance can be achieved by a fixed-radius encoder equipped with the Euclidean metric, regardless of the embedding dimension.

Gabriel Moreira, Manuel Marques, João Paulo Costeira et al.

The precise estimation of camera poses within large camera networks is a foundational problem in computer vision and robotics, with broad applications spanning autonomous navigation, surveillance, and augmented reality. In this paper, we introduce a novel methodology that extends state-of-the-art Pose Graph Optimization (PGO) techniques. Departing from the conventional PGO paradigm, which primarily relies on camera-camera edges, our approach centers on the introduction of a dynamic element - any rigid object free to move in the scene - whose pose can be reliably inferred from a single image. Specifically, we consider the bipartite graph encompassing cameras, object poses evolving dynamically, and camera-object relative transformations at each time step. This shift not only offers a solution to the challenges encountered in directly estimating relative poses between cameras, particularly in adverse environments, but also leverages the inclusion of numerous object poses to ameliorate and integrate errors, resulting in accurate camera pose estimates. Though our framework retains compatibility with traditional PGO solvers, its efficacy benefits from a custom-tailored optimization scheme. To this end, we introduce an iterative primal-dual algorithm, capable of handling large graphs. Empirical benchmarks, conducted on a new dataset of simulated indoor environments, substantiate the efficacy and efficiency of our approach.

Gabriel Moreira, Zita Marinho, Manuel Marques et al.

Traditional neural embeddings represent concepts as points, excelling at similarity but struggling with higher-level reasoning and asymmetric relationships. We introduce a novel paradigm: embedding concepts as linear subspaces. This framework inherently models generality via subspace dimensionality and hierarchy through subspace inclusion. It naturally supports set-theoretic operations like intersection (conjunction), linear sum (disjunction) and orthogonal complements (negations), aligning with classical formal semantics. To enable differentiable learning, we propose a smooth relaxation of orthogonal projection operators, allowing for the learning of both subspace orientation and dimension. Our method achieves state-of-the-art results in reconstruction and link prediction on WordNet. Furthermore, on natural language inference benchmarks, our subspace embeddings surpass bi-encoder baselines, offering an interpretable formulation of entailment that is both geometrically grounded and amenable to logical operations.

Gabriel Moreira, Manuel Marques, João Paulo Costeira

A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In spite of being an integral part of bundle adjustment and structure-from-motion, averaging rotations is both a non-convex and high-dimensional optimization problem. In this paper, we address it from a maximum likelihood estimation standpoint and make a twofold contribution. Firstly, we set forth a novel initialization-free primal-dual method which we show empirically to converge to the global optimum. Further, we derive what is to our knowledge, the first optimal closed-form solution for rotation averaging in cycle graphs and contextualize this result within spectral graph theory. Our proposed methods achieve a significant gain both in precision and performance.

Cláudia Soares, João Gomes, Beatriz Ferreira et al.

How to self-localize large teams of underwater nodes using only noisy range measurements? How to do it in a distributed way, and incorporating dynamics into the problem? How to reject outliers and produce trustworthy position estimates? The stringent acoustic communication channel and the accuracy needs of our geophysical survey application demand faster and more accurate localization methods. We approach dynamic localization as a MAP estimation problem where the prior encodes dynamics, and we devise a convex relaxation method that takes advantage of previous estimates at each measurement acquisition step; The algorithm converges at an optimal rate for first order methods. LocDyn is distributed: there is no fusion center responsible for processing acquired data and the same simple computations are performed for each node. LocDyn is accurate: experiments attest to a smaller positioning error than a comparable Kalman filter. LocDyn is robust: it rejects outlier noise, while the comparing methods succumb in terms of positioning error.