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Davide Buoso

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math.SP math.AP math.OC Artificial Intelligence Robotics Computer Vision math.DS math.FA

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preprint2026arXiv

Fixed External Cameras as Common Prior Maps for Active 3D Scene Graph Generation

Commonly available prior information, such as BIM models, floor plans, and remote sensing images, can provide valuable geometric and semantic context for autonomous robotic systems. In this paper, we treat observations from fixed external RGB cameras as Common Prior Maps (CPMs): wide-field views of the environment that initialize a semantic and geometric scene prior before any robot motion begins. We present an RGB-only framework for active, incremental 3D scene graph (3DSG) generation that seamlessly fuses observations from both onboard robot cameras and fixed external cameras within a single hardware-agnostic pipeline. By relying solely on RGB observations processed by a feed-forward 3D reconstruction model, the system treats all cameras - onboard or external - identically, requiring no hardware modifications. A graph-based active semantic exploration framework then directly leverages the partial scene graph to guide the robot toward regions of high semantic uncertainty, progressively completing and refining the prior. Experiments demonstrate that bootstrapping the scene graph with even a single external camera increases initial object recall by up to +79%, and that the richer context of the prior significantly improves the efficiency of subsequent active exploration.

preprint2026arXiv

GAP: Geometric Anchor Pre-training for Data-Efficient Visuomotor Learning of Manipulation Tasks

Learning visuomotor policies from scarce expert demonstrations remains a core challenge in robotic manipulation. A primary hurdle lies in distilling high-dimensional RGB representations into control-relevant geometry without overfitting. While using frozen pre-trained Vision Foundation Models (VFMs) improves data efficiency, it also shifts most task adaptation onto a small spatial pooling module, which can latch onto task-irrelevant shortcuts and lose geometric grounding when finetuned with few data samples. More broadly, pre-trained visual representations used for policy learning have been observed to struggle under even minor scene perturbations, highlighting the need for robustness-oriented inductive biases. We propose Geometric Anchor Pre-training (GAP), a simple, action-free warm-up stage that regularizes the spatial adapter before downstream imitation learning. GAP pre-trains the pooling layer on a lightweight simulated proxy task where object masks are available at no cost, encouraging the adapter to produce keypoints that lie on the object, cover its spatial extent, and remain sharp and repeatable over time. This yields stable geometric anchors that provide a reliable coordinate interface for few-shot policy learning, while keeping the VFM frozen. We evaluate GAP on RoboMimic and ManiSkill under severe data scarcity (15-50 demonstrations) and domain shift. A simple adapter regularized with GAP consistently outperforms stronger attention-based poolers and end-to-end fine-tuning, achieving 62% success on RoboMimic Can with 15 demonstrations (+16% over AFA), 63% on the long-horizon high-precision Tool Hang task with 50 demonstrations, and 61% on ManiSkill StackCube with 30 demonstrations (+11% over full fine-tuning). The proxy stage is lightweight and fully decoupled from downstream tasks, making it practical to reuse across environments and manipulation skills.

preprint2026arXiv

RGB-only Active 3D Scene Graph Generation for Indoor Mobile Robots

Current approaches to 3D scene graph generation rely on dedicated depth sensors, such as LiDAR or RGB-D cameras, for metric 3D reconstruction. This limits deployment to specialized robotic platforms and excludes settings where only RGB cameras are available, such as fixed external infrastructure. Existing pipelines also typically operate on passively collected observation trajectories, rather than selecting viewpoints based on the partially built scene representation, and therefore fail to effectively exploit the semantic and spatial information encoded within the graph during exploration. This paper presents a fully visual framework for the active, incremental construction of 3D scene graphs from RGB input only, addressing both limitations. The proposed approach unifies perception and planning around a shared structured representation that captures object semantics, 3D geometry, relational context, and information from multiple viewpoints. Because the framework is hardware-agnostic and relies only on RGB observations, it can incorporate inputs from both onboard robot cameras and fixed external cameras within the same representation. Experiments on the Replica dataset show that the RGB-only pipeline achieves F1-score parity with baselines using ground-truth depth. Active exploration experiments on ReplicaCAD further show that semantic-driven viewpoint selection detects more than twice as many objects as a geometric frontier-based baseline under the same exploration budget. Finally, the external-camera setting demonstrates that complementary RGB views can effectively bootstrap the scene graph and improve contextual understanding at no additional exploration cost.

preprint2022arXiv

Bulk-Boundary eigenvalues for Bilaplacian problems

We initiate the study of a bulk-boundary eigenvalue problem for the Bilaplacian with a particular third order boundary condition that arises from the study of dynamical boundary conditions for the Cahn-Hilliard equation. First we consider continuity properties under parameter variation (in which the parameter also affects the domain of definition of the operator). Then we look at the ball and the annulus geometries (together with the punctured ball), obtaining the eigenvalues as solutions of a precise equation involving special functions. An interesting outcome of our analysis in the annulus case is the presence of a bifurcation from the zero eigenvalue depending on the size of the annulus.

preprint2019arXiv

The buckling eigenvalue problem in the annulus

We consider the buckling eigenvalue problem for a clamped plate in the annulus. We identify the first eigenvalue in dependence of the inner radius, and study the number of nodal domains of the corresponding eigenfunctions. Moreover, in order to investigate the asymptotic behavior of eigenvalues and eigenfunctions as the inner radius approaches the outer one, we provide an analytical study of the buckling problem in rectangles with mixed boundary conditions.

preprint2016arXiv

Analyticity and criticality results for the eigenvalues of the biharmonic operator

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.

preprint2016arXiv

On the stability of some isoperimetric inequalities for the fundamental tones of free plates

We provide a quantitative version of the isoperimetric inequality for the fundamental tone of a biharmonic Neumann problem. Such an inequality has been recently established by Chasman adapting Weinberger's argument for the corresponding second order problem. Following a scheme introduced by Brasco and Pratelli for the second order case, we prove that a similar quantitative inequality holds also for the biharmonic operator. We also prove the sharpness of both such an inequality and the corresponding one for the biharmonic Steklov problem.

preprint2016arXiv

On the variation of longitudinal and torsional frequencies in a partially hinged rectangular plate

We consider a partially hinged rectangular plate and its normal modes. There are two families of modes, longitudinal and torsional. We study the variation of the corresponding eigenvalues under domain deformations. We investigate the possibility of finding a shape functional able to quantify the torsional instability of the plate, namely how prone is the plate to transform longitudinal oscillations into torsional ones. This functional should obey several rules coming from both theoretical and practical evidences. We show that a simple functional obeying all the required rules does not exist and that the functionals available in literature are not reliable.

preprint2015arXiv

A few shape optimization results for a biharmonic Steklov problem

We derive the equation of a free vibrating thin plate whose mass is concentrated at the boundary, namely a Steklov problem for the biharmonic operator. We provide Hadamard-type formulas for the shape derivatives of the corresponding eigenvalues and prove that balls are critical domains under volume constraint. Finally, we prove an isoperimetric inequality for the first positive eigenvalue.

preprint2015arXiv

On the eigenvalues of a biharmonic Steklov problem

We consider an eigenvalue problem for the biharmonic operator with Steklov-type boundary conditions. We obtain it as a limiting Neumann problem for the biharmonic operator in a process of mass concentration at the boundary. We study the dependence of the spectrum upon the domain. We show analyticity of the symmetric functions of the eigenvalues under isovolumetric perturbations and prove that balls are critical points for such functions under measure constraint. Moreover, we show that the ball is a maximizer for the first positive eigenvalue among those domains with a prescribed fixed measure.

preprint2014arXiv

On a classical spectral optimization problem in linear elasticity

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space. We survey recent results concerning the analytic dependence of the elementary symmetric functions of the eigenvalues upon domain perturbation and the role of balls as critical points of such functions subject to volume constraint. Our discussion concerns Dirichlet and buckling-type problems for polyharmonic operators, the Neumann and the intermediate problems for the biharmonic operator, the Lamé and the Reissner-Mindlin systems.

preprint2014arXiv

Shape differentiability of the eigenvalues of elliptic systems

We consider second order elliptic systems of partial differential equations subject to Dirichlet and Neumann boundary conditions. We prove analyticity of the elementary symmetric functions of the eigenvalues, and compute Hadamard-type formulas for such functions. Then we provide a characterization of criticality of the domain under volume constraint, and prove that if the system is rotation invariant, then balls are critical domains for all those functions.

preprint2014arXiv

Shape sensitivity analysis of the eigenvalues of the Reissner-Mindlin system

We consider the eigenvalue problem for the Reissner-Mindlin system arising in the study of the free vibration modes of an elastic clamped plate. We provide quantitative estimates for the variation of the eigenvalues upon variation of the shape of the plate. We also prove analyticity results and establish Hadamard-type formulas. Finally, we address the problem of minimization of the eigenvalues in the case of isovolumetric domain perturbations. In the spirit of the Rayleigh conjecture for the biharmonic operator, we prove that balls are critical points with volume constraint for all simple eigenvalues and the elementary symmetric functions of multiple eigenvalues.

preprint2012arXiv

Eigenvalues of poly-harmonic operators on variable domains

We consider a class of eigenvalue problems for poly-harmonic operators, including Dirichlet and buckling-type eigenvalue problems. We prove an analyticity result for the dependence of the symmetric functions of the eigenvalues upon domain perturbations and compute Hadamard-type formulas for the Frechét differentials. We also consider isovolumetric domain perturbations and characterize the corresponding critical domains for the symmetric functions of the eigenvalues. Finally, we prove that balls are critical domains.

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