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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., Comment: Pre-print. Under review at journal

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., Comment: Accepted at MICCAI2020

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.

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.

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).

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 propose ShapeNet, a generalization of the popular convolutional neural 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 ShapeNet to learn invariant shape feature descriptors that significantly outperform recent state-of-the-art methods, and show that previous approaches such as heat and wave kernel signatures, optimal spectral descriptors, and intrinsic shape contexts can be obtained as particular configurations of ShapeNet.