arXiv subjects

Simone Melzi

Publications and source records attributed to Simone Melzi.

At least 19 recordsLinked to original sources

arXiv2026

Towards Reliable and Reproducible Fetal Brain Biometry: A Deep Learning Approach Using MRI

Fetal brain biometry is essential for quantitative assessment of brain development, supporting gestational age estimation, developmental monitoring, and detection of abnormalities. In clinical practice, measurements are manually performed, making them time-consuming and prone to variability. While automated approaches have been proposed, reproducible methods remain limited, particularly those providing anatomically interpretable landmark localization. We present a fully automated deep learning-based framework for reliable and reproducible brain biometry from 3D super-resolution-reconstructed fetal brain MRI. The proposed four-step pipeline derives biometric parameters by jointly estimating linear measurements and their corresponding anatomical landmarks. A 3D convolutional neural network is trained to regress landmark coordinates from brain segmentation label maps, followed by measurement-specific geometric optimization to refine landmark positions and compute measurements. The pipeline is evaluated on two publicly available fetal MRI datasets comprising 150 volumes (gestational age range: 20-37 weeks) acquired across different scanners and protocols, assessing five key biometric measurements across varying acquisition settings and providing a comprehensive evaluation of both measurement accuracy and landmark localization using quantitative metrics and visual assessment. Compared with the only available automated pipeline, the proposed method achieves comparable or improved accuracy for most measurements. In conclusion, we introduce a straightforward pipeline for reliable biometry estimations, with efficiency, interpretability and scalability that support integration into clinical workflows.

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arXiv2025

FUSE: A Flow-based Mapping Between Shapes

We introduce a novel neural representation for maps between 3D shapes based on flow-matching models, which is computationally efficient and supports cross-representation shape matching without large-scale training or data-driven procedures. 3D shapes are represented as the probability distribution induced by a continuous and invertible flow mapping from a fixed anchor distribution. Given a source and a target shape, the composition of the inverse flow (source to anchor) with the forward flow (anchor to target), we map points between the two surfaces. By encoding the shapes with a pointwise task-tailored embedding, this construction provides an invertible and modality-agnostic representation of maps between shapes across point clouds, meshes, signed distance fields (SDFs), and volumetric data. The resulting representation consistently achieves high coverage and accuracy across diverse benchmarks and challenging settings in shape matching. Beyond shape matching, our framework shows promising results in other tasks, including UV mapping and registration of raw point cloud scans of human bodies.

cs.CV↗

arXiv2025

Blending Concepts with Text-to-Image Diffusion Models

Diffusion models have dramatically advanced text-to-image generation in recent years, translating abstract concepts into high-fidelity images with remarkable ease. In this work, we examine whether they can also blend distinct concepts, ranging from concrete objects to intangible ideas, into coherent new visual entities under a zero-shot framework. Specifically, concept blending merges the key attributes of multiple concepts (expressed as textual prompts) into a single, novel image that captures the essence of each concept. We investigate four blending methods, each exploiting different aspects of the diffusion pipeline (e.g., prompt scheduling, embedding interpolation, or layer-wise conditioning). Through systematic experimentation across diverse concept categories, such as merging concrete concepts, synthesizing compound words, transferring artistic styles, and blending architectural landmarks, we show that modern diffusion models indeed exhibit creative blending capabilities without further training or fine-tuning. Our extensive user study, involving 100 participants, reveals that no single approach dominates in all scenarios: each blending technique excels under certain conditions, with factors like prompt ordering, conceptual distance, and random seed affecting the outcome. These findings highlight the remarkable compositional potential of diffusion models while exposing their sensitivity to seemingly minor input variations.

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arXiv2025

Volumetric Functional Maps

Computing volumetric correspondences between 3D shapes is a prominent tool for medical and industrial applications. In this work, we pave the way for spectral volume mapping, extending for the first time the surface-based functional maps framework. We show that the eigenfunctions of the volumetric Laplace operator define a functional space that is suitable for high-quality signal transfer. We also experiment with various techniques that edit this functional space, porting them to volume domains. We validate our method on novel volumetric datasets and on tetrahedralizations of well established surface datasets, also showcasing practical applications involving both discrete and continuous signal mapping, for segmentation transfer, mesh connectivity transfer and solid texturing. Finally, we show that the volumetric spectrum greatly improves the accuracy for classical shape matching tasks among surfaces, consistently outperforming surface-only spectral methods.

cs.GR↗

arXiv2025

Escaping Plato's Cave: Towards the Alignment of 3D and Text Latent Spaces

Recent works have shown that, when trained at scale, uni-modal 2D vision and text encoders converge to learned features that share remarkable structural properties, despite arising from different representations. However, the role of 3D encoders with respect to other modalities remains unexplored. Furthermore, existing 3D foundation models that leverage large datasets are typically trained with explicit alignment objectives with respect to frozen encoders from other representations. In this work, we investigate the possibility of a posteriori alignment of representations obtained from uni-modal 3D encoders compared to text-based feature spaces. We show that naive post-training feature alignment of uni-modal text and 3D encoders results in limited performance. We then focus on extracting subspaces of the corresponding feature spaces and discover that by projecting learned representations onto well-chosen lower-dimensional subspaces the quality of alignment becomes significantly higher, leading to improved accuracy on matching and retrieval tasks. Our analysis further sheds light on the nature of these shared subspaces, which roughly separate between semantic and geometric data representations. Overall, ours is the first work that helps to establish a baseline for post-training alignment of 3D uni-modal and text feature spaces, and helps to highlight both the shared and unique properties of 3D data compared to other representations. Our code and weights are available at https://github.com/Souhail-01/3d-text-alignment

cs.CV↗

arXiv2024

SShaDe: scalable shape deformation via local representations

With the increase in computational power for the available hardware, the demand for high-resolution data in computer graphics applications increases. Consequently, classical geometry processing techniques based on linear algebra solutions are starting to become obsolete. In this setting, we propose a novel approach for tackling mesh deformation tasks on high-resolution meshes. By reducing the input size with a fast remeshing technique and preserving a consistent representation of the original mesh with local reference frames, we provide a solution that is both scalable and robust in multiple applications, such as as-rigid-as-possible deformations, non-rigid isometric transformations, and pose transfer tasks. We extensively test our technique and compare it against state-of-the-art methods, proving that our approach can handle meshes with hundreds of thousands of vertices in tens of seconds while still achieving results comparable with the other solutions.

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arXiv2024

Deformation Recovery: Localized Learning for Detail-Preserving Deformations

We introduce a novel data-driven approach aimed at designing high-quality shape deformations based on a coarse localized input signal. Unlike previous data-driven methods that require a global shape encoding, we observe that detail-preserving deformations can be estimated reliably without any global context in certain scenarios. Building on this intuition, we leverage Jacobians defined in a one-ring neighborhood as a coarse representation of the deformation. Using this as the input to our neural network, we apply a series of MLPs combined with feature smoothing to learn the Jacobian corresponding to the detail-preserving deformation, from which the embedding is recovered by the standard Poisson solve. Crucially, by removing the dependence on a global encoding, every \textit{point} becomes a training example, making the supervision particularly lightweight. Moreover, when trained on a class of shapes, our approach demonstrates remarkable generalization across different object categories. Equipped with this novel network, we explore three main tasks: refining an approximate shape correspondence, unsupervised deformation and mapping, and shape editing. Our code is made available at https://github.com/sentient07/LJN

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arXiv2024

Localized Gaussians as Self-Attention Weights for Point Clouds Correspondence

Current data-driven methodologies for point cloud matching demand extensive training time and computational resources, presenting significant challenges for model deployment and application. In the point cloud matching task, recent advancements with an encoder-only Transformer architecture have revealed the emergence of semantically meaningful patterns in the attention heads, particularly resembling Gaussian functions centered on each point of the input shape. In this work, we further investigate this phenomenon by integrating these patterns as fixed attention weights within the attention heads of the Transformer architecture. We evaluate two variants: one utilizing predetermined variance values for the Gaussians, and another where the variance values are treated as learnable parameters. Additionally we analyze the performances on noisy data and explore a possible way to improve robustness to noise. Our findings demonstrate that fixing the attention weights not only accelerates the training process but also enhances the stability of the optimization. Furthermore, we conducted an ablation study to identify the specific layers where the infused information is most impactful and to understand the reliance of the network on this information.

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arXiv2024

How to Blend Concepts in Diffusion Models

For the last decade, there has been a push to use multi-dimensional (latent) spaces to represent concepts; and yet how to manipulate these concepts or reason with them remains largely unclear. Some recent methods exploit multiple latent representations and their connection, making this research question even more entangled. Our goal is to understand how operations in the latent space affect the underlying concepts. To that end, we explore the task of concept blending through diffusion models. Diffusion models are based on a connection between a latent representation of textual prompts and a latent space that enables image reconstruction and generation. This task allows us to try different text-based combination strategies, and evaluate easily through a visual analysis. Our conclusion is that concept blending through space manipulation is possible, although the best strategy depends on the context of the blend.

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arXiv2024

Implicit-ARAP: Efficient Handle-Guided Neural Field Deformation via Local Patch Meshing

Neural fields have emerged as a powerful representation for 3D geometry, enabling compact and continuous modeling of complex shapes. Despite their expressive power, manipulating neural fields in a controlled and accurate manner -- particularly under spatial constraints -- remains an open challenge, as existing approaches struggle to balance surface quality, robustness, and efficiency. We address this by introducing a novel method for handle-guided neural field deformation, which leverages discrete local surface representations to optimize the As-Rigid-As-Possible deformation energy. To this end, we propose the local patch mesh representation, which discretizes level sets of a neural signed distance field by projecting and deforming flat mesh patches guided solely by the SDF and its gradient. We conduct a comprehensive evaluation showing that our method consistently outperforms baselines in deformation quality, robustness, and computational efficiency. We also present experiments that motivate our choice of discretization over marching cubes. By bridging classical geometry processing and neural representations through local patch meshing, our work enables scalable, high-quality deformation of neural fields and paves the way for extending other geometric tasks to neural domains.

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arXiv2024

Reconstructing Curves from Sparse Samples on Riemannian Manifolds

Reconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive attention, primarily relying on human assistance, and where not, limited by very strict sampling conditions. In this work, we formally improve on the state-of-the-art requirements and introduce an innovative algorithm capable of reconstructing closed curves directly on surfaces from a given sparse set of sample points. We extend and adapt a state-of-the-art planar curve reconstruction method to the realm of surfaces while dealing with the challenges arising from working on non-Euclidean domains. We demonstrate the robustness of our method by reconstructing multiple curves on various surface meshes. We explore novel potential applications of our approach, allowing for automated reconstruction of curves on Riemannian manifolds.

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arXiv2023

Disentangled Latent Spaces Facilitate Data-Driven Auxiliary Learning

Auxiliary tasks facilitate learning in situations where data is scarce or the principal task of interest is extremely complex. This idea is primarily inspired by the improved generalization capability induced by solving multiple tasks simultaneously, which leads to a more robust shared representation. Nevertheless, finding optimal auxiliary tasks is a crucial problem that often requires hand-crafted solutions or expensive meta-learning approaches. In this paper, we propose a novel framework, dubbed Detaux, whereby a weakly supervised disentanglement procedure is used to discover a new unrelated auxiliary classification task, which allows us to go from a Single-Task Learning (STL) to a Multi-Task Learning (MTL) problem. The disentanglement procedure works at the representation level, isolating the variation related to the principal task into an isolated subspace and additionally producing an arbitrary number of orthogonal subspaces, each of which encourages high separability among projections. We generate the auxiliary classification task through a clustering procedure on the most disentangled subspace, obtaining a discrete set of labels. Subsequently, the original data, the labels associated with the principal task, and the newly discovered ones can be fed into any MTL framework. Experimental validation on both synthetic and real data, along with various ablation studies, demonstrates promising results, revealing the potential in what has been, so far, an unexplored connection between learning disentangled representations and MTL. The source code is available at https://github.com/intelligolabs/Detaux.

cs.LG↗

arXiv2023

Extracting a functional representation from a dictionary for non-rigid shape matching

Shape matching is a fundamental problem in computer graphics with many applications. Functional maps translate the point-wise shape-matching problem into its functional counterpart and have inspired numerous solutions over the last decade. Nearly all the solutions based on functional maps rely on the eigenfunctions of the Laplace-Beltrami Operator (LB) to describe the functional spaces defined on the surfaces and then convert the functional correspondences into point-wise correspondences. However, this final step is often error-prone and inaccurate in tiny regions and protrusions, where the energy of LB does not uniformly cover the surface. We propose a new functional basis Principal Components of a Dictionary (PCD) to address such intrinsic limitation. PCD constructs an orthonormal basis from the Principal Component Analysis (PCA) of a dictionary of functions defined over the shape. These dictionaries can target specific properties of the final basis, such as achieving an even spreading of energy. Our experimental evaluation compares seven different dictionaries on established benchmarks, showing that PCD is suited to target different shape-matching scenarios, resulting in more accurate point-wise maps than the LB basis when used in the same pipeline. This evidence provides a promising alternative for improving correspondence estimation, confirming the power and flexibility of functional maps.

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arXiv2023

ReMatching: Low-Resolution Representations for Scalable Shape Correspondence

We introduce \emph{ReMatching}, a novel shape correspondence solution based on the functional maps framework. Our method, by exploiting a new and appropriate \emph{re}-meshing paradigm, can target shape-\emph{matching} tasks even on meshes counting millions of vertices, where the original functional maps does not apply or requires a massive computational cost. The core of our procedure is a time-efficient remeshing algorithm which constructs a low-resolution geometry while acting conservatively on the original topology and metric. These properties allow translating the functional maps optimization problem on the resulting low-resolution representation, thus enabling efficient computation of correspondences with functional map approaches. Finally, we propose an efficient technique for extending the estimated correspondence to the original meshes. We show that our method is more efficient and effective through quantitative and qualitative comparisons, outperforming state-of-the-art pipelines in quality and computational cost.

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arXiv2022

Spectral Maps for Learning on Subgraphs

In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and modified graphs. Classically, these maps are represented as binary node-to-node correspondence matrices and used as-is to transfer node-wise features between the graphs. In this paper, we argue that simply changing this map representation can bring notable benefits to graph learning tasks. Drawing inspiration from recent progress in geometry processing, we introduce a spectral representation for maps that is easy to integrate into existing graph learning models. This spectral representation is a compact and straightforward plug-in replacement and is robust to topological changes of the graphs. Remarkably, the representation exhibits structural properties that make it interpretable, drawing an analogy with recent results on smooth manifolds. We demonstrate the benefits of incorporating spectral maps in graph learning pipelines, addressing scenarios where a node-to-node map is not well defined, or in the absence of exact isomorphism. Our approach bears practical benefits in knowledge distillation and hierarchical learning, where we show comparable or improved performance at a fraction of the computational cost.

cs.LG↗

arXiv2022

Explanatory Learning: Beyond Empiricism in Neural Networks

We introduce Explanatory Learning (EL), a framework to let machines use existing knowledge buried in symbolic sequences -- e.g. explanations written in hieroglyphic -- by autonomously learning to interpret them. In EL, the burden of interpreting symbols is not left to humans or rigid human-coded compilers, as done in Program Synthesis. Rather, EL calls for a learned interpreter, built upon a limited collection of symbolic sequences paired with observations of several phenomena. This interpreter can be used to make predictions on a novel phenomenon given its explanation, and even to find that explanation using only a handful of observations, like human scientists do. We formulate the EL problem as a simple binary classification task, so that common end-to-end approaches aligned with the dominant empiricist view of machine learning could, in principle, solve it. To these models, we oppose Critical Rationalist Networks (CRNs), which instead embrace a rationalist view on the acquisition of knowledge. CRNs express several desired properties by construction, they are truly explainable, can adjust their processing at test-time for harder inferences, and can offer strong confidence guarantees on their predictions. As a final contribution, we introduce Odeen, a basic EL environment that simulates a small flatland-style universe full of phenomena to explain. Using Odeen as a testbed, we show how CRNs outperform empiricist end-to-end approaches of similar size and architecture (Transformers) in discovering explanations for novel phenomena.

cs.LG↗

arXiv2021

Complex Functional Maps : a Conformal Link Between Tangent Bundles

In this paper, we introduce complex functional maps, which extend the functional map framework to conformal maps between tangent vector fields on surfaces. A key property of these maps is their orientation awareness. More specifically, we demonstrate that unlike regular functional maps that link functional spaces of two manifolds, our complex functional maps establish a link between oriented tangent bundles, thus permitting robust and efficient transfer of tangent vector fields. By first endowing and then exploiting the tangent bundle of each shape with a complex structure, the resulting operations become naturally orientationaware, thus favoring orientation and angle preserving correspondence across shapes, without relying on descriptors or extra regularization. Finally, and perhaps more importantly, we demonstrate how these objects enable several practical applications within the functional map framework. We show that functional maps and their complex counterparts can be estimated jointly to promote orientation preservation, regularizing pipelines that previously suffered from orientation-reversing symmetry errors.

cs.CV↗

arXiv2021

Smoothness and effective regularizations in learned embeddings for shape matching

Many innovative applications require establishing correspondences among 3D geometric objects. However, the countless possible deformations of smooth surfaces make shape matching a challenging task. Finding an embedding to represent the different shapes in high-dimensional space where the matching is easier to solve is a well-trodden path that has given many outstanding solutions. Recently, a new trend has shown advantages in learning such representations. This novel idea motivated us to investigate which properties differentiate these data-driven embeddings and which ones promote state-of-the-art results. In this study, we analyze, for the first time, properties that arise in data-driven learned embedding and their relation to the shape-matching task. Our discoveries highlight the close link between matching and smoothness, which naturally emerge from training. Also, we demonstrate the relation between the orthogonality of the embedding and the bijectivity of the correspondence. Our experiments show exciting results, overcoming well-established alternatives and shedding a different light on relevant contexts and properties for learned embeddings.

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