Related papers: FILTR: Extracting Topological Features from Pretra…

Although accurate and fast point cloud classification is a fundamental task in 3D applications, it is difficult to achieve this purpose due to the irregularity and disorder of point clouds that make it challenging to achieve effective and…

This paper introduces a new method for 3D point cloud registration based on deep learning. The architecture is composed of three distinct blocs: (i) an encoder composed of a convolutional graph-based descriptor that encodes the immediate…

Unsupervised feature learning often finds low-dimensional embeddings that capture the structure of complex data. For tasks for which prior expert topological knowledge is available, incorporating this into the learned representation may…

Recent machine learning-based multi-object tracking (MOT) frameworks are becoming popular for 3-D point clouds. Most traditional tracking approaches use filters (e.g., Kalman filter or particle filter) to predict object locations in a time…

Persistent homology analysis provides means to capture the connectivity structure of data sets in various dimensions. On the mathematical level, by defining a metric between the objects that persistence attaches to data sets, we can…

There is a growing body of work that leverages features extracted via topological data analysis to train machine learning models. While this field, sometimes known as topological machine learning (TML), has seen some notable successes, an…

Tables organize valuable content in a concise and compact representation. This content is extremely valuable for systems such as search engines, Knowledge Graph's, etc, since they enhance their predictive capabilities. Unfortunately, tables…

We present an approach to learning features that represent the local geometry around a point in an unstructured point cloud. Such features play a central role in geometric registration, which supports diverse applications in robotics and 3D…

We introduce a framework for analyzing topological tipping in time-evolutionary point clouds by extending the recently proposed Topological Optimal Transport (TpOT) distance. While TpOT unifies geometric, homological, and higher-order…

We develop a novel deep contour detection algorithm with a top-down fully convolutional encoder-decoder network. Our proposed method, named TD-CEDN, solves two important issues in this low-level vision problem: (1) learning multi-scale and…

Extended persistence is a technique from topological data analysis to obtain global multiscale topological information from a graph. This includes information about connected components and cycles that are captured by the so-called…

Implicit neural networks have emerged as a crucial technology in 3D surface reconstruction. To reconstruct continuous surfaces from discrete point clouds, encoding the input points into regular grid features (plane or volume) has been…

We investigate topological descriptors for 3D surface analysis, i.e. the classification of surfaces according to their geometric fine structure. On a dataset of high-resolution 3D surface reconstructions we compute persistence diagrams for…

Point clouds data, as one kind of representation of 3D objects, are the most primitive output obtained by 3D sensors. Unlike 2D images, point clouds are disordered and unstructured. Hence it is not straightforward to apply classification…

Assessing the quality of 3D printed models before they are printed remains a challeng- ing problem, particularly when considering point cloud-based models. This paper introduces an approach to quality assessment, which uses techniques from…

As two fundamental representation modalities of 3D objects, 3D point clouds and multi-view 2D images record shape information from different domains of geometric structures and visual appearances. In the current deep learning era,…

Topological features play an essential role in ensuring geometric plausibility and structural consistency in image analysis tasks such as segmentation and skeletonization. However, integrating topology-preserving learning based on simple…

In the area of 3D shape analysis, the geometric properties of a shape have long been studied. Instead of directly extracting representative features using expert-designed descriptors or end-to-end deep neural networks, this paper is…

Topological methods, including persistent homology, are powerful tools for analysis of high-dimensional data sets but these methods rely almost exclusively on thresholding techniques. In noisy data sets, thresholding does not always allow…

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of…