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

Point cloud learning has lately attracted increasing attention due to its wide applications in many areas, such as computer vision, autonomous driving, and robotics. As a dominating technique in AI, deep learning has been successfully used to solve various 2D vision problems. However, deep learning on point clouds is still in its infancy due to the unique challenges faced by the processing of point clouds with deep neural networks. Recently, deep learning on point clouds has ...

In recent years, point cloud representation has become one of the research hotspots in the field of computer vision, and has been widely used in many fields, such as autonomous driving, virtual reality, robotics, etc. Although deep learning techniques have achieved great success in processing regular structured 2D grid image data, there are still great challenges in processing irregular, unstructured point cloud data. Point cloud classification is the basis of point cloud ana...

Over the past decade deep learning has driven progress in 2D image understanding. Despite these advancements, techniques for automatic 3D sensed data understanding, such as point clouds, is comparatively immature. However, with a range of important applications from indoor robotics navigation to national scale remote sensing there is a high demand for algorithms that can learn to automatically understand and classify 3D sensed data. In this paper we review the current state-o...

Transformers have been at the heart of the Natural Language Processing (NLP) and Computer Vision (CV) revolutions. The significant success in NLP and CV inspired exploring the use of Transformers in point cloud processing. However, how do Transformers cope with the irregularity and unordered nature of point clouds? How suitable are Transformers for different 3D representations (e.g., point- or voxel-based)? How competent are Transformers for various 3D processing tasks? As of...

Semantic segmentation of raw 3D point clouds is an essential component in 3D scene analysis, but it poses several challenges, primarily due to the non-Euclidean nature of 3D point clouds. Although, several deep learning based approaches have been proposed to address this task, but almost all of them emphasized on using the latent (global) feature representations from traditional convolutional neural networks (CNN), resulting in severe loss of spatial information, thus failing...

Point clouds are rich geometric data structures, where their three dimensional structure offers an excellent domain for understanding the representation learning and generative modeling in 3D space. In this work, we aim to improve the performance of point cloud latent-space generative models by experimenting with transformer encoders, latent-space flow models, and autoregressive decoders. We analyze and compare both generation and reconstruction performance of these models on...

This report surveys advances in deep learning-based modeling techniques that address four different 3D indoor scene analysis tasks, as well as synthesis of 3D indoor scenes. We describe different kinds of representations for indoor scenes, various indoor scene datasets available for research in the aforementioned areas, and discuss notable works employing machine learning models for such scene modeling tasks based on these representations. Specifically, we focus on the analys...

We introduce a method for training neural networks to perform image or volume segmentation in which prior knowledge about the topology of the segmented object can be explicitly provided and then incorporated into the training process. By using the differentiable properties of persistent homology, a concept used in topological data analysis, we can specify the desired topology of segmented objects in terms of their Betti numbers and then drive the proposed segmentations to con...

Comparison of data representations is a complex multi-aspect problem that has not enjoyed a complete solution yet. We propose a method for comparing two data representations. We introduce the Representation Topology Divergence (RTD), measuring the dissimilarity in multi-scale topology between two point clouds of equal size with a one-to-one correspondence between points. The data point clouds are allowed to lie in different ambient spaces. The RTD is one of the few TDA-based ...

This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competition asked participants to provide open-source implementations of topological neural networks from the literature by contributing to the python packages TopoNetX (data processing) and TopoModelX (deep learning). The challenge attracted twenty-eight qualifying submissions in its two-month duration. T...