Learning image representations that capture rich semantic relationships remains a significant challenge. Existing approaches are either contrastive, lacking robust theoretical guarantees, or struggle to effectively represent the partial orders inherent to structured visual-semantic data. In this paper, we introduce a nuclear norm-based loss function, grounded in the same information theoretic principles that have proved effective in self-supervised learning. We present a theoretical characterization of this loss, demonstrating that, in addition to promoting class orthogonality, it encodes the spectral geometry of the data within a subspace lattice. This geometric representation allows us to associate logical propositions with subspaces, ensuring that our learned representations adhere to a predefined symbolic structure.

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.

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.

Every year, the VISion Understanding and Machine intelligence (VISUM) summer school runs a competition where participants can learn and share knowledge about Computer Vision and Machine Learning in a vibrant environment. 2021 VISUM's focused on applying those methodologies in fashion. Recently, there has been an increase of interest within the scientific community in applying computer vision methodologies to the fashion domain. That is highly motivated by fashion being one of the world's largest industries presenting a rapid development in e-commerce mainly since the COVID-19 pandemic. Computer Vision for Fashion enables a wide range of innovations, from personalized recommendations to outfit matching. The competition enabled students to apply the knowledge acquired in the summer school to a real-world problem. The ambition was to foster research and development in fashion outfit complementary product retrieval by leveraging vast visual and textual data with domain knowledge. For this, a new fashion outfit dataset (acquired and curated by FARFETCH) for research and benchmark purposes is introduced. Additionally, a competitive baseline with an original negative sampling process for triplet mining was implemented and served as a starting point for participants. The top 3 performing methods are described in this paper since they constitute the reference state-of-the-art for this particular problem. To our knowledge, this is the first challenge in fashion outfit complementary product retrieval. Moreover, this joint project between academia and industry brings several relevant contributions to disseminating science and technology, promoting economic and social development, and helping to connect early-career researchers to real-world industry challenges.

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.

Pose Graph Optimization (PGO) is an important problem in Computer Vision, particularly in motion estimation, whose objective consists of finding the rigid transformations that achieve the best global alignment of visual data on a common reference frame. The vast majority of PGO approaches rely on iterative techniques which refine an initial estimate until convergence is achieved. On the other hand, recent works have identified a global constraint which has cast this problem into the matrix completion domain. The success which both these formulations have had in computing accurate solutions efficiently has been overshadowed by large-scale industrial applications such as autonomous flight, self-driving cars and smart-cities, where it is necessary to fuse numerous images covering large areas but where each one of them has few pairwise observations. We propose a highly efficient algorithm to solve PGO which leverages the sparsity of the data by combining the Krylov- Schur method for spectral decomposition with Cholesky LDL factorization. Our method allows for high scalability, low computational cost and high precision, simultaneously.