Synthetic Data Generation and Deep Learning for the Topological Analysis of 3D Data

Deformable objects present a formidable challenge for robotic manipulation due to the lack of canonical low-dimensional representations and the difficulty of capturing, predicting, and controlling such objects. We construct compact topological representations to capture the state of highly deformable objects that are topologically nontrivial. We develop an approach that tracks the evolution of this topological state through time. Under several mild assumptions, we prove that ...

3D data is a valuable asset the computer vision filed as it provides rich information about the full geometry of sensed objects and scenes. Recently, with the availability of both large 3D datasets and computational power, it is today possible to consider applying deep learning to learn specific tasks on 3D data such as segmentation, recognition and correspondence. Depending on the considered 3D data representation, different challenges may be foreseen in using existent deep ...

Topology matters. Despite the recent success of point cloud processing with geometric deep learning, it remains arduous to capture the complex topologies of point cloud data with a learning model. Given a point cloud dataset containing objects with various genera, or scenes with multiple objects, we propose an autoencoder, TearingNet, which tackles the challenging task of representing the point clouds using a fixed-length descriptor. Unlike existing works directly deforming p...

We present a comprehensive survey and benchmark of both traditional and learning-based methods for surface reconstruction from point clouds. This task is particularly challenging for real-world acquisitions due to factors like noise, outliers, non-uniform sampling, and missing data. Traditional approaches often simplify the problem by imposing handcrafted priors on either the input point clouds or the resulting surface, a process that can necessitate tedious hyperparameter tu...

Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often effective to incorporate global topological features, which are typically extracted by persistent homology. In the calculation of persistent homology for a point cloud, we choose a filtration for the point cloud, an increasing sequence of spaces. ...

We propose a deep autoencoder with graph topology inference and filtering to achieve compact representations of unorganized 3D point clouds in an unsupervised manner. Many previous works discretize 3D points to voxels and then use lattice-based methods to process and learn 3D spatial information; however, this leads to inevitable discretization errors. In this work, we handle raw 3D points without such compromise. The proposed networks follow the autoencoder framework with a ...

To endow machines with the ability to perceive the real-world in a three dimensional representation as we do as humans is a fundamental and long-standing topic in Artificial Intelligence. Given different types of visual inputs such as images or point clouds acquired by 2D/3D sensors, one important goal is to understand the geometric structure and semantics of the 3D environment. Traditional approaches usually leverage hand-crafted features to estimate the shape and semantics ...

Point cloud is point sets defined in 3D metric space. Point cloud has become one of the most significant data format for 3D representation. Its gaining increased popularity as a result of increased availability of acquisition devices, such as LiDAR, as well as increased application in areas such as robotics, autonomous driving, augmented and virtual reality. Deep learning is now the most powerful tool for data processing in computer vision, becoming the most preferred techniq...

Three-dimensional geometric data offer an excellent domain for studying representation learning and generative modeling. In this paper, we look at geometric data represented as point clouds. We introduce a deep AutoEncoder (AE) network with state-of-the-art reconstruction quality and generalization ability. The learned representations outperform existing methods on 3D recognition tasks and enable shape editing via simple algebraic manipulations, such as semantic part editing,...

Point cloud data has been extensively studied due to its compact form and flexibility in representing complex 3D structures. The ability of point cloud data to accurately capture and represent intricate 3D geometry makes it an ideal choice for a wide range of applications, including computer vision, robotics, and autonomous driving, all of which require an understanding of the underlying spatial structures. Given the challenges associated with annotating large-scale point clo...