Davide Boscaini

Pietro Astolfi, Ruben Verhagen, Laurent Petit et al.

A tractogram is a virtual representation of the brain white matter. It is composed of millions of virtual fibers, encoded as 3D polylines, which approximate the white matter axonal pathways. To date, tractograms are the most accurate white matter representation and thus are used for tasks like presurgical planning and investigations of neuroplasticity, brain disorders, or brain networks. However, it is a well-known issue that a large portion of tractogram fibers is not anatomically plausible and can be considered artifacts of the tracking procedure. With Verifyber, we tackle the problem of filtering out such non-plausible fibers using a novel fully-supervised learning approach. Differently from other approaches based on signal reconstruction and/or brain topology regularization, we guide our method with the existing anatomical knowledge of the white matter. Using tractograms annotated according to anatomical principles, we train our model, Verifyber, to classify fibers as either anatomically plausible or non-plausible. The proposed Verifyber model is an original Geometric Deep Learning method that can deal with variable size fibers, while being invariant to fiber orientation. Our model considers each fiber as a graph of points, and by learning features of the edges between consecutive points via the proposed sequence Edge Convolution, it can capture the underlying anatomical properties. The output filtering results highly accurate and robust across an extensive set of experiments, and fast; with a 12GB GPU, filtering a tractogram of 1M fibers requires less than a minute. Verifyber implementation and trained models are available at https://github.com/FBK-NILab/verifyber.

Mohamed L. Mekhalfi, Davide Boscaini, Fabio Poiesi

Unsupervised domain adaptation (UDA) plays a crucial role in object detection when adapting a source-trained detector to a target domain without annotated data. In this paper, we propose a novel and effective four-step UDA approach that leverages self-supervision and trains source and target data concurrently. We harness self-supervised learning to mitigate the lack of ground truth in the target domain. Our method consists of the following steps: (1) identify the region with the highest-confidence set of detections in each target image, which serve as our pseudo-labels; (2) crop the identified region and generate a collection of its augmented versions; (3) combine these latter into a composite image; (4) adapt the network to the target domain using the composed image. Through extensive experiments under cross-camera, cross-weather, and synthetic-to-real scenarios, our approach achieves state-of-the-art performance, improving upon the nearest competitor by more than 2% in terms of mean Average Precision (mAP). The code is available at https://github.com/MohamedTEV/DACA.

Luigi Riz, Andrea Caraffa, Matteo Bortolon et al.

We present MONET, a new multimodal dataset captured using a thermal camera mounted on a drone that flew over rural areas, and recorded human and vehicle activities. We captured MONET to study the problem of object localisation and behaviour understanding of targets undergoing large-scale variations and being recorded from different and moving viewpoints. Target activities occur in two different land sites, each with unique scene structures and cluttered backgrounds. MONET consists of approximately 53K images featuring 162K manually annotated bounding boxes. Each image is timestamp-aligned with drone metadata that includes information about attitudes, speed, altitude, and GPS coordinates. MONET is different from previous thermal drone datasets because it features multimodal data, including rural scenes captured with thermal cameras containing both person and vehicle targets, along with trajectory information and metadata. We assessed the difficulty of the dataset in terms of transfer learning between the two sites and evaluated nine object detection algorithms to identify the open challenges associated with this type of data. Project page: https://github.com/fabiopoiesi/monet_dataset.

Jaime Corsetti, Davide Boscaini, Fabio Poiesi

Recent works on 6D object pose estimation focus on learning keypoint correspondences between images and object models, and then determine the object pose through RANSAC-based algorithms or by directly regressing the pose with end-to-end optimisations. We argue that learning point-level discriminative features is overlooked in the literature. To this end, we revisit Fully Convolutional Geometric Features (FCGF) and tailor it for object 6D pose estimation to achieve state-of-the-art performance. FCGF employs sparse convolutions and learns point-level features using a fully-convolutional network by optimising a hardest contrastive loss. We can outperform recent competitors on popular benchmarks by adopting key modifications to the loss and to the input data representations, by carefully tuning the training strategies, and by employing data augmentations suitable for the underlying problem. We carry out a thorough ablation to study the contribution of each modification. The code is available at https://github.com/jcorsetti/FCGF6D.

Anil Osman Tur, Alessandro Conti, Cigdem Beyan et al.

In smart retail applications, the large number of products and their frequent turnover necessitate reliable zero-shot object classification methods. The zero-shot assumption is essential to avoid the need for re-training the classifier every time a new product is introduced into stock or an existing product undergoes rebranding. In this paper, we make three key contributions. Firstly, we introduce the MIMEX dataset, comprising 28 distinct product categories. Unlike existing datasets in the literature, MIMEX focuses on fine-grained product classification and includes a diverse range of retail products. Secondly, we benchmark the zero-shot object classification performance of state-of-the-art vision-language models (VLMs) on the proposed MIMEX dataset. Our experiments reveal that these models achieve unsatisfactory fine-grained classification performance, highlighting the need for specialized approaches. Lastly, we propose a novel ensemble approach that integrates embeddings from CLIP and DINOv2 with dimensionality reduction techniques to enhance classification performance. By combining these components, our ensemble approach outperforms VLMs, effectively capturing visual cues crucial for fine-grained product discrimination. Additionally, we introduce a class adaptation method that utilizes visual prototyping with limited samples in scenarios with scarce labeled data, addressing a critical need in retail environments where product variety frequently changes. To encourage further research into zero-shot object classification for smart retail applications, we will release both the MIMEX dataset and benchmark to the research community. Interested researchers can contact the authors for details on the terms and conditions of use. The code is available: https://github.com/AnilOsmanTur/Zero-shot-Retail-Product-Classification.

Davide Boscaini, Fabio Poiesi

The recent trend in deep learning methods for 3D point cloud understanding is to propose increasingly sophisticated architectures either to better capture 3D geometries or by introducing possibly undesired inductive biases. Moreover, prior works introducing novel architectures compared their performance on the same domain, devoting less attention to their generalization to other domains. We argue that the ability of a model to transfer the learnt knowledge to different domains is an important feature that should be evaluated to exhaustively assess the quality of a deep network architecture. In this work we propose PatchMixer, a simple yet effective architecture that extends the ideas behind the recent MLP-Mixer paper to 3D point clouds. The novelties of our approach are the processing of local patches instead of the whole shape to promote robustness to partial point clouds, and the aggregation of patch-wise features using an MLP as a simpler alternative to the graph convolutions or the attention mechanisms that are used in prior works. We evaluated our method on the shape classification and part segmentation tasks, achieving superior generalization performance compared to a selection of the most relevant deep architectures.

Amir Hamza, Davide Boscaini, Weihang Li et al.

Existing methods for instance-level 6D pose estimation typically rely on neural networks that either directly regress the pose in $\mathrm{SE}(3)$ or estimate it indirectly via local feature matching. The former struggle with object symmetries, while the latter fail in the absence of distinctive local features. To overcome these limitations, we propose a novel formulation of 6D pose estimation as a conditional flow matching problem in $\mathbb{R}^3$. We introduce Flose, a generative method that infers object poses via a denoising process conditioned on local features. While prior approaches based on conditional flow matching perform denoising solely based on geometric guidance, Flose integrates appearance-based semantic features to mitigate ambiguities caused by object symmetries. We further incorporate RANSAC-based registration to handle outliers. We validate Flose on five datasets from the established BOP benchmark. Flose outperforms prior methods with an average improvement of +4.5 Average Recall. Project Website : https://tev-fbk.github.io/Flose/

Marco Garosi, Riccardo Tedoldi, Davide Boscaini et al.

Supervised 3D part segmentation models are tailored for a fixed set of objects and parts, limiting their transferability to open-set, real-world scenarios. Recent works have explored vision-language models (VLMs) as a promising alternative, using multi-view rendering and textual prompting to identify object parts. However, naively applying VLMs in this context introduces several drawbacks, such as the need for meticulous prompt engineering, and fails to leverage the 3D geometric structure of objects. To address these limitations, we propose COPS, a COmprehensive model for Parts Segmentation that blends the semantics extracted from visual concepts and 3D geometry to effectively identify object parts. COPS renders a point cloud from multiple viewpoints, extracts 2D features, projects them back to 3D, and uses a novel geometric-aware feature aggregation procedure to ensure spatial and semantic consistency. Finally, it clusters points into parts and labels them. We demonstrate that COPS is efficient, scalable, and achieves zero-shot state-of-the-art performance across five datasets, covering synthetic and real-world data, texture-less and coloured objects, as well as rigid and non-rigid shapes. The code is available at https://3d-cops.github.io.

Luigi Riz, Sergio Povoli, Andrea Caraffa et al.

Berry picking has long-standing traditions in Finland, yet it is challenging and can potentially be dangerous. The integration of drones equipped with advanced imaging techniques represents a transformative leap forward, optimising harvests and promising sustainable practices. We propose WildBe, the first image dataset of wild berries captured in peatlands and under the canopy of Finnish forests using drones. Unlike previous and related datasets, WildBe includes new varieties of berries, such as bilberries, cloudberries, lingonberries, and crowberries, captured under severe light variations and in cluttered environments. WildBe features 3,516 images, including a total of 18,468 annotated bounding boxes. We carry out a comprehensive analysis of WildBe using six popular object detectors, assessing their effectiveness in berry detection across different forest regions and camera types. WildBe is publicly available on HuggingFace at https://huggingface.co/datasets/FBK-TeV/WildBe.

Jaime Corsetti, Francesco Giuliari, Davide Boscaini et al.

Functionality understanding in 3D, which aims to identify the functional element in a 3D scene to complete an action (e.g., the correct handle to "Open the second drawer of the cabinet near the bed"), is hindered by the scarcity of real-world data due to the substantial effort needed for its collection and annotation. To address this, we introduce SynthFun3D, the first method for task-based 3D scene synthesis. Given the action description, SynthFun3D generates a 3D indoor environment using a furniture asset database with part-level annotation, ensuring the action can be accomplished. It reasons about the action to automatically identify and retrieve the 3D mask of the correct functional element, enabling the inexpensive and large-scale generation of high-quality annotated data. We validate SynthFun3D through user studies, which demonstrate improved scene-prompt coherence compared to other approaches. Our quantitative results further show that the generated data can either replace real data with minor performance loss or supplement real data for improved performance, thereby providing an inexpensive and scalable solution for data-hungry 3D applications. Project page: github.com/tev-fbk/synthfun3d.

Fabio Poiesi, Davide Boscaini

We present a simple but yet effective method for learning distinctive 3D local deep descriptors (DIPs) that can be used to register point clouds without requiring an initial alignment. Point cloud patches are extracted, canonicalised with respect to their estimated local reference frame and encoded into rotation-invariant compact descriptors by a PointNet-based deep neural network. DIPs can effectively generalise across different sensor modalities because they are learnt end-to-end from locally and randomly sampled points. Because DIPs encode only local geometric information, they are robust to clutter, occlusions and missing regions. We evaluate and compare DIPs against alternative hand-crafted and deep descriptors on several indoor and outdoor datasets consisting of point clouds reconstructed using different sensors. Results show that DIPs (i) achieve comparable results to the state-of-the-art on RGB-D indoor scenes (3DMatch dataset), (ii) outperform state-of-the-art by a large margin on laser-scanner outdoor scenes (ETH dataset), and (iii) generalise to indoor scenes reconstructed with the Visual-SLAM system of Android ARCore. Source code: https://github.com/fabiopoiesi/dip.

Jaime Corsetti, Francesco Giuliari, Alice Fasoli et al.

Understanding functionalities in 3D scenes involves interpreting natural language descriptions to locate functional interactive objects, such as handles and buttons, in a 3D environment. Functionality understanding is highly challenging, as it requires both world knowledge to interpret language and spatial perception to identify fine-grained objects. For example, given a task like 'turn on the ceiling light', an embodied AI agent must infer that it needs to locate the light switch, even though the switch is not explicitly mentioned in the task description. To date, no dedicated methods have been developed for this problem. In this paper, we introduce Fun3DU, the first approach designed for functionality understanding in 3D scenes. Fun3DU uses a language model to parse the task description through Chain-of-Thought reasoning in order to identify the object of interest. The identified object is segmented across multiple views of the captured scene by using a vision and language model. The segmentation results from each view are lifted in 3D and aggregated into the point cloud using geometric information. Fun3DU is training-free, relying entirely on pre-trained models. We evaluate Fun3DU on SceneFun3D, the most recent and only dataset to benchmark this task, which comprises over 3000 task descriptions on 230 scenes. Our method significantly outperforms state-of-the-art open-vocabulary 3D segmentation approaches. Project page: https://tev-fbk.github.io/fun3du/

Andrea Caraffa, Davide Boscaini, Fabio Poiesi

Estimating the 6D pose of objects from RGBD data is a fundamental problem in computer vision, with applications in robotics and augmented reality. A key challenge is achieving generalization to novel objects that were not seen during training. Most existing approaches address this by scaling up training on synthetic data tailored to the task, a process that demands substantial computational resources. But is task-specific training really necessary for accurate and efficient 6D pose estimation of novel objects? To answer No!, we introduce FreeZeV2, the second generation of FreeZe: a training-free method that achieves strong generalization to unseen objects by leveraging geometric and vision foundation models pre-trained on unrelated data. FreeZeV2 improves both accuracy and efficiency over FreeZe through three key contributions: (i) a sparse feature extraction strategy that reduces inference-time computation without sacrificing accuracy; (ii) a feature-aware scoring mechanism that improves both pose selection during RANSAC-based 3D registration and the final ranking of pose candidates; and (iii) a modular design that supports ensembles of instance segmentation models, increasing robustness to segmentation masks errors. We evaluate FreeZeV2 on the seven core datasets of the BOP Benchmark, where it establishes a new state-of-the-art in 6D pose estimation of unseen objects. When using the same segmentation masks, FreeZeV2 achieves a remarkable 8x speedup over FreeZe while also improving accuracy by 5%. When using ensembles of segmentation models, FreeZeV2 gains an additional 8% in accuracy while still running 2.5x faster than FreeZe. FreeZeV2 was awarded Best Overall Method at the BOP Challenge 2024.

Amir Hamza, Andrea Caraffa, Davide Boscaini et al.

Three-dimensional local descriptors are crucial for encoding geometric surface properties, making them essential for various point cloud understanding tasks. Among these descriptors, GeDi has demonstrated strong zero-shot 6D pose estimation capabilities but remains computationally impractical for real-world applications due to its expensive inference process. Can we retain GeDi's effectiveness while significantly improving its efficiency? In this paper, we explore this question by introducing a knowledge distillation framework that trains an efficient student model to regress local descriptors from a GeDi teacher. Our key contributions include: an efficient large-scale training procedure that ensures robustness to occlusions and partial observations while operating under compute and storage constraints, and a novel loss formulation that handles weak supervision from non-distinctive teacher descriptors. We validate our approach on five BOP Benchmark datasets and demonstrate a significant reduction in inference time while maintaining competitive performance with existing methods, bringing zero-shot 6D pose estimation closer to real-time feasibility. Project Website: https://tev-fbk.github.io/dGeDi/

Mohamed Lamine Mekhalfi, Davide Boscaini, Fabio Poiesi

Source-free domain-adaptive object detection is an interesting but scarcely addressed topic. It aims at adapting a source-pretrained detector to a distinct target domain without resorting to source data during adaptation. So far, there is no data augmentation scheme tailored to source-free domain-adaptive object detection. To this end, this paper presents a novel data augmentation approach that cuts out target image regions where the detector is confident, augments them along with their respective pseudo-labels, and joins them into a challenging target image to adapt the detector. As the source data is out of reach during adaptation, we implement our approach within a teacher-student learning paradigm to ensure that the model does not collapse during the adaptation procedure. We evaluated our approach on three adaptation benchmarks of traffic scenes, scoring new state-of-the-art on two of them.

Mattia Nardon, Stefano Messelodi, Antonio Granata et al.

Visual monitoring of industrial assembly tasks is critical for preventing equipment damage due to procedural errors and ensuring worker safety. Although commercial solutions exist, they typically require rigid workspace setups or the application of visual markers to simplify the problem. We introduce ViMAT, a novel AI-driven system for real-time visual monitoring of assembly tasks that operates without these constraints. ViMAT combines a perception module that extracts visual observations from multi-view video streams with a reasoning module that infers the most likely action being performed based on the observed assembly state and prior task knowledge. We validate ViMAT on two assembly tasks, involving the replacement of LEGO components and the reconfiguration of hydraulic press molds, demonstrating its effectiveness through quantitative and qualitative analysis in challenging real-world scenarios characterized by partial and uncertain visual observations. Project page: https://tev-fbk.github.io/ViMAT

Mattia Nardon, Mikel Mujika Agirre, Ander González Tomé et al.

Accurate 6D pose estimation of complex objects in 3D environments is essential for effective robotic manipulation. Yet, existing benchmarks fall short in evaluating 6D pose estimation methods under realistic industrial conditions, as most datasets focus on household objects in domestic settings, while the few available industrial datasets are limited to artificial setups with objects placed on tables. To bridge this gap, we introduce CHIP, the first dataset designed for 6D pose estimation of chairs manipulated by a robotic arm in a real-world industrial environment. CHIP includes seven distinct chairs captured using three different RGBD sensing technologies and presents unique challenges, such as distractor objects with fine-grained differences and severe occlusions caused by the robotic arm and human operators. CHIP comprises 77,811 RGBD images annotated with ground-truth 6D poses automatically derived from the robot's kinematics, averaging 11,115 annotations per chair. We benchmark CHIP using three zero-shot 6D pose estimation methods, assessing performance across different sensor types, localization priors, and occlusion levels. Results show substantial room for improvement, highlighting the unique challenges posed by the dataset. CHIP will be publicly released.

Jaime Corsetti, Davide Boscaini, Francesco Giuliari et al.

The generalisation to unseen objects in the 6D pose estimation task is very challenging. While Vision-Language Models (VLMs) enable using natural language descriptions to support 6D pose estimation of unseen objects, these solutions underperform compared to model-based methods. In this work we present Horyon, an open-vocabulary VLM-based architecture that addresses relative pose estimation between two scenes of an unseen object, described by a textual prompt only. We use the textual prompt to identify the unseen object in the scenes and then obtain high-resolution multi-scale features. These features are used to extract cross-scene matches for registration. We evaluate our model on a benchmark with a large variety of unseen objects across four datasets, namely REAL275, Toyota-Light, Linemod, and YCB-Video. Our method achieves state-of-the-art performance on all datasets, outperforming by 12.6 in Average Recall the previous best-performing approach.

Fabio Poiesi, Davide Boscaini

An effective 3D descriptor should be invariant to different geometric transformations, such as scale and rotation, robust to occlusions and clutter, and capable of generalising to different application domains. We present a simple yet effective method to learn general and distinctive 3D local descriptors that can be used to register point clouds that are captured in different domains. Point cloud patches are extracted, canonicalised with respect to their local reference frame, and encoded into scale and rotation-invariant compact descriptors by a deep neural network that is invariant to permutations of the input points. This design is what enables our descriptors to generalise across domains. We evaluate and compare our descriptors with alternative handcrafted and deep learning-based descriptors on several indoor and outdoor datasets that are reconstructed by using both RGBD sensors and laser scanners. Our descriptors outperform most recent descriptors by a large margin in terms of generalisation, and also become the state of the art in benchmarks where training and testing are performed in the same domain.

Levi O. Vasconcelos, Massimiliano Mancini, Davide Boscaini et al.

Recent unsupervised domain adaptation methods based on deep architectures have shown remarkable performance not only in traditional classification tasks but also in more complex problems involving structured predictions (e.g. semantic segmentation, depth estimation). Following this trend, in this paper we present a novel deep adaptation framework for estimating keypoints under domain shift}, i.e. when the training (source) and the test (target) images significantly differ in terms of visual appearance. Our method seamlessly combines three different components: feature alignment, adversarial training and self-supervision. Specifically, our deep architecture leverages from domain-specific distribution alignment layers to perform target adaptation at the feature level. Furthermore, a novel loss is proposed which combines an adversarial term for ensuring aligned predictions in the output space and a geometric consistency term which guarantees coherent predictions between a target sample and its perturbed version. Our extensive experimental evaluation conducted on three publicly available benchmarks shows that our approach outperforms state-of-the-art domain adaptation methods in the 2D keypoint prediction task.

Mohamed Ilyes Lakhal, Davide Boscaini, Fabio Poiesi et al.

Novel-View Human Action Synthesis aims to synthesize the movement of a body from a virtual viewpoint, given a video from a real viewpoint. We present a novel 3D reasoning to synthesize the target viewpoint. We first estimate the 3D mesh of the target body and transfer the rough textures from the 2D images to the mesh. As this transfer may generate sparse textures on the mesh due to frame resolution or occlusions. We produce a semi-dense textured mesh by propagating the transferred textures both locally, within local geodesic neighborhoods, and globally, across symmetric semantic parts. Next, we introduce a context-based generator to learn how to correct and complete the residual appearance information. This allows the network to independently focus on learning the foreground and background synthesis tasks. We validate the proposed solution on the public NTU RGB+D dataset. The code and resources are available at https://bit.ly/36u3h4K.

Antonio Alliegro, Davide Boscaini, Tatiana Tommasi

Point cloud processing and 3D shape understanding are very challenging tasks for which deep learning techniques have demonstrated great potentials. Still further progresses are essential to allow artificial intelligent agents to interact with the real world, where the amount of annotated data may be limited and integrating new sources of knowledge becomes crucial to support autonomous learning. Here we consider several possible scenarios involving synthetic and real-world point clouds where supervised learning fails due to data scarcity and large domain gaps. We propose to enrich standard feature representations by leveraging self-supervision through a multi-task model that can solve a 3D puzzle while learning the main task of shape classification or part segmentation. An extensive analysis investigating few-shot, transfer learning and cross-domain settings shows the effectiveness of our approach with state-of-the-art results for 3D shape classification and part segmentation.

Pietro Astolfi, Ruben Verhagen, Laurent Petit et al.

Tractograms are virtual representations of the white matter fibers of the brain. They are of primary interest for tasks like presurgical planning, and investigation of neuroplasticity or brain disorders. Each tractogram is composed of millions of fibers encoded as 3D polylines. Unfortunately, a large portion of those fibers are not anatomically plausible and can be considered artifacts of the tracking algorithms. Common methods for tractogram filtering are based on signal reconstruction, a principled approach, but unable to consider the knowledge of brain anatomy. In this work, we address the problem of tractogram filtering as a supervised learning problem by exploiting the ground truth annotations obtained with a recent heuristic method, which labels fibers as either anatomically plausible or non-plausible according to well-established anatomical properties. The intuitive idea is to model a fiber as a point cloud and the goal is to investigate whether and how a geometric deep learning model might capture its anatomical properties. Our contribution is an extension of the Dynamic Edge Convolution model that exploits the sequential relations of points in a fiber and discriminates with high accuracy plausible/non-plausible fibers.

Davide Boscaini, Fabio Poiesi

The semantic segmentation of 3D shapes with a high-density of vertices could be impractical due to large memory requirements. To make this problem computationally tractable, we propose a neural-network based approach that produces 3D augmented views of the 3D shape to solve the whole segmentation as sub-segmentation problems. 3D augmented views are obtained by projecting vertices and normals of a 3D shape onto 2D regular grids taken from different viewpoints around the shape. These 3D views are then processed by a Convolutional Neural Network to produce a probability distribution function (pdf) over the set of the semantic classes for each vertex. These pdfs are then re-projected on the original 3D shape and postprocessed using contextual information through Conditional Random Fields. We validate our approach using 3D shapes of publicly available datasets and of real objects that are reconstructed using photogrammetry techniques. We compare our approach against state-of-the-art alternatives.

Federico Monti, Davide Boscaini, Jonathan Masci et al.

Deep learning has achieved a remarkable performance breakthrough in several fields, most notably in speech recognition, natural language processing, and computer vision. In particular, convolutional neural network (CNN) architectures currently produce state-of-the-art performance on a variety of image analysis tasks such as object detection and recognition. Most of deep learning research has so far focused on dealing with 1D, 2D, or 3D Euclidean-structured data such as acoustic signals, images, or videos. Recently, there has been an increasing interest in geometric deep learning, attempting to generalize deep learning methods to non-Euclidean structured data such as graphs and manifolds, with a variety of applications from the domains of network analysis, computational social science, or computer graphics. In this paper, we propose a unified framework allowing to generalize CNN architectures to non-Euclidean domains (graphs and manifolds) and learn local, stationary, and compositional task-specific features. We show that various non-Euclidean CNN methods previously proposed in the literature can be considered as particular instances of our framework. We test the proposed method on standard tasks from the realms of image-, graph- and 3D shape analysis and show that it consistently outperforms previous approaches.

Davide Boscaini, Jonathan Masci, Emanuele Rodolà et al.

Establishing correspondence between shapes is a fundamental problem in geometry processing, arising in a wide variety of applications. The problem is especially difficult in the setting of non-isometric deformations, as well as in the presence of topological noise and missing parts, mainly due to the limited capability to model such deformations axiomatically. Several recent works showed that invariance to complex shape transformations can be learned from examples. In this paper, we introduce an intrinsic convolutional neural network architecture based on anisotropic diffusion kernels, which we term Anisotropic Convolutional Neural Network (ACNN). In our construction, we generalize convolutions to non-Euclidean domains by constructing a set of oriented anisotropic diffusion kernels, creating in this way a local intrinsic polar representation of the data (`patch'), which is then correlated with a filter. Several cascades of such filters, linear, and non-linear operators are stacked to form a deep neural network whose parameters are learned by minimizing a task-specific cost. We use ACNNs to effectively learn intrinsic dense correspondences between deformable shapes in very challenging settings, achieving state-of-the-art results on some of the most difficult recent correspondence benchmarks.

Jonathan Masci, Davide Boscaini, Michael M. Bronstein et al.

Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we introduce Geodesic Convolutional Neural Networks (GCNN), a generalization of the convolutional networks (CNN) paradigm to non-Euclidean manifolds. Our construction is based on a local geodesic system of polar coordinates to extract "patches", which are then passed through a cascade of filters and linear and non-linear operators. The coefficients of the filters and linear combination weights are optimization variables that are learned to minimize a task-specific cost function. We use GCNN to learn invariant shape features, allowing to achieve state-of-the-art performance in problems such as shape description, retrieval, and correspondence.

Davide Boscaini, Davide Eynard, Michael M. Bronstein

Shape-from-X is an important class of problems in the fields of geometry processing, computer graphics, and vision, attempting to recover the structure of a shape from some observations. In this paper, we formulate the problem of shape-from-operator (SfO), recovering an embedding of a mesh from intrinsic differential operators defined on the mesh. Particularly interesting instances of our SfO problem include synthesis of shape analogies, shape-from-Laplacian reconstruction, and shape exaggeration. Numerically, we approach the SfO problem by splitting it into two optimization sub-problems that are applied in an alternating scheme: metric-from-operator (reconstruction of the discrete metric from the intrinsic operator) and embedding-from-metric (finding a shape embedding that would realize a given metric, a setting of the multidimensional scaling problem).