Related papers: Topological descriptors for 3D surface analysis

This paper describes new techniques for learning atlas-like representations of 3D surfaces, i.e. homeomorphic transformations from a 2D domain to surfaces. Compared to prior work, we propose two major contributions. First, instead of…

We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…

We represent 3D shape by structured 2D representations of fixed length making it feasible to apply well investigated 2D convolutional neural networks (CNN) for both discriminative and geometric tasks on 3D shapes. We first provide a general…

Feature descriptors of point clouds are used in several applications, such as registration and part segmentation of 3D point clouds. Learning discriminative representations of local geometric features is unquestionably the most important…

In this paper, we design linear time algorithms to recognize and determine topological invariants such as the genus and homology groups in 3D. These properties can be used to identify patterns in 3D image recognition. This has tremendous…

This work proposes a new method for place recognition based on the scene architecture. From depth video, we compute the 3D model and we derive and describe geometrically the 2D map from which the scene descriptor is deduced to constitute…

The persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space.…

We propose SDFDiff, a novel approach for image-based shape optimization using differentiable rendering of 3D shapes represented by signed distance functions (SDFs). Compared to other representations, SDFs have the advantage that they can…

In this paper we present a new methodology for edge detection in digital images. The first originality of the proposed method is to consider image content as a parametric surface. Then, an original parametric local model of this surface…

Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes…

3D asymmetric tensor fields have found many applications in science and engineering domains, such as fluid dynamics and solid mechanics. 3D asymmetric tensors can have complex eigenvalues, which makes their analysis and visualization more…

Three-dimensional (3D) point cloud analysis has become one of the attractive subjects in realistic imaging and machine visions due to its simplicity, flexibility and powerful capacity of visualization. Actually, the representation of scenes…

Three-dimensional data have become increasingly present in earth observation over the last decades. However, many 3D surveys are still underexploited due to the lack of accessible and explainable automatic classification methods, for…

Microstructure reconstruction is an important cornerstone to the inverse materials design concept. In this work, a general algorithm is developed to reconstruct a three-dimensional microstructure from given descriptors. Based on…

Accurate structural analysis is essential to gain physical knowledge and understanding of atomic-scale processes in materials from atomistic simulations. However, traditional analysis methods often reach their limits when applied to…

The analysis of 3D symmetric second-order tensor fields often relies on topological features such as degenerate tensor lines, neutral surfaces, and their generalization to mode surfaces, which reveal important structural insights into the…

Fractured surfaces carry unique details that can provide an accurate quantitative comparison to support comparative forensic analysis of those fractured surfaces. In this study, a statistical analysis comparison protocol was applied to a…

3D shape models are naturally parameterized using vertices and faces, \ie, composed of polygons forming a surface. However, current 3D learning paradigms for predictive and generative tasks using convolutional neural networks focus on a…

Shape is an important physical property of natural and manmade 3D objects that characterizes their external appearances. Understanding differences between shapes and modeling the variability within and across shape classes, hereinafter…

Topological descriptors have been increasingly utilized for capturing multiscale structural information in relational data. In this work, we consider various filtrations on the (box) product of graphs and the effect on their outputs on the…