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

The use of topological descriptors in modern machine learning applications, such as Persistence Diagrams (PDs) arising from Topological Data Analysis (TDA), has shown great potential in various domains. However, their practical use in applications is often hindered by two major limitations: the computational complexity required to compute such descriptors exactly, and their sensitivity to even low-level proportions of outliers. In this work, we propose to bypass these two bur...

The process of segmenting point cloud data into several homogeneous areas with points in the same region having the same attributes is known as 3D segmentation. Segmentation is challenging with point cloud data due to substantial redundancy, fluctuating sample density and lack of apparent organization. The research area has a wide range of robotics applications, including intelligent vehicles, autonomous mapping and navigation. A number of researchers have introduced various ...

Surface-based geodesic topology provides strong cues for object semantic analysis and geometric modeling. However, such connectivity information is lost in point clouds. Thus we introduce GeoNet, the first deep learning architecture trained to model the intrinsic structure of surfaces represented as point clouds. To demonstrate the applicability of learned geodesic-aware representations, we propose fusion schemes which use GeoNet in conjunction with other baseline or backbone...

Reconstructing the 3D mesh of a general object from a single image is now possible thanks to the latest advances of deep learning technologies. However, due to the nontrivial difficulty of generating a feasible mesh structure, the state-of-the-art approaches often simplify the problem by learning the displacements of a template mesh that deforms it to the target surface. Though reconstructing a 3D shape with complex topology can be achieved by deforming multiple mesh patches,...

3D segmentation is a fundamental and challenging problem in computer vision with applications in autonomous driving, robotics, augmented reality and medical image analysis. It has received significant attention from the computer vision, graphics and machine learning communities. Conventional methods for 3D segmentation, based on hand-crafted features and machine learning classifiers, lack generalization ability. Driven by their success in 2D computer vision, deep learning tec...

We introduce GEM3D -- a new deep, topology-aware generative model of 3D shapes. The key ingredient of our method is a neural skeleton-based representation encoding information on both shape topology and geometry. Through a denoising diffusion probabilistic model, our method first generates skeleton-based representations following the Medial Axis Transform (MAT), then generates surfaces through a skeleton-driven neural implicit formulation. The neural implicit takes into accou...

Point clouds are characterized by irregularity and unstructuredness, which pose challenges in efficient data exploitation and discriminative feature extraction. In this paper, we present an unsupervised deep neural architecture called Flattening-Net to represent irregular 3D point clouds of arbitrary geometry and topology as a completely regular 2D point geometry image (PGI) structure, in which coordinates of spatial points are captured in colors of image pixels. \mr{Intuitiv...

Remote sensing through unmanned aerial systems (UAS) has been increasing in forestry in recent years, along with using machine learning for data processing. Deep learning architectures, extensively applied in natural language and image processing, have recently been extended to the point cloud domain. However, the availability of point cloud datasets for training and testing remains limited. Creating forested environment point cloud datasets is expensive, requires high-precis...

We present a novel approach to learning a point-wise, meaningful embedding for point-clouds in an unsupervised manner, through the use of neural-networks. The domain of point-cloud processing via neural-networks is rapidly evolving, with novel architectures and applications frequently emerging. Within this field of research, the availability and plethora of unlabeled point-clouds as well as their possible applications make finding ways of characterizing this type of data appe...

The introduction of inexpensive 3D data acquisition devices has promisingly facilitated the wide availability and popularity of 3D point cloud, which attracts more attention to the effective extraction of novel 3D point cloud descriptors for accuracy of the efficiency of 3D computer vision tasks in recent years. However, how to develop discriminative and robust feature descriptors from 3D point cloud remains a challenging task due to their intrinsic characteristics. In this p...