Topological Descriptors for 3D Surface Analysis

Zeppelzauer, Matthias; Zieliński, Bartosz; Juda, Mateusz; Seidl, Markus

doi:10.1007/978-3-319-39441-1_8

Cited by 12 publications

(12 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, we verify the validity of our results on an extended large-scale dataset [11]. To provide the complete picture of our analysis we include the results from [9] in this paper.…”

Section: Introductionsupporting

confidence: 63%

“…For both descriptors we select those parameters for which they have yielded best results in our previous investigation [9]. See Tab.…”

Section: Topological Baseline Descriptorsmentioning

confidence: 99%

“…In other situations, it is possible to avoid instability issues with PI by using another approach for constructing PI, such as the one described by Eqn. (9) in [31], which reduces the influence of the low-persistence points close to the diagonal when the scale σ increases.…”

Section: Discriminativitymentioning

confidence: 99%

See 2 more Smart Citations

A study on topological descriptors for the analysis of 3D surface texture

Zeppelzauer

Zieliński

Juda

et al. 2018

Computer Vision and Image Understanding

Self Cite

View full text Add to dashboard Cite

Methods from computational topology are becoming more and more popular in computer vision and have shown to improve the state-of-the-art in several tasks. In this paper, we investigate the applicability of topological descriptors in the context of 3D surface analysis for the classification of different surface textures. We present a comprehensive study on topological descriptors, investigate their robustness and expressiveness and compare them with state-of-the-art methods including Convolutional Neural Networks (CNNs). Results show that class-specific information is reflected well in topological descriptors. The investigated descriptors can directly compete with non-topological descriptors and capture complementary information. As a consequence they improve the state-of-the-art when combined with non-topological descriptors.

show abstract

“…Moreover, we verify the validity of our results on an extended large-scale dataset [11]. To provide the complete picture of our analysis we include the results from [9] in this paper.…”

Section: Introductionsupporting

confidence: 63%

“…For both descriptors we select those parameters for which they have yielded best results in our previous investigation [9]. See Tab.…”

Section: Topological Baseline Descriptorsmentioning

confidence: 99%

See 1 more Smart Citation

A study on topological descriptors for the analysis of 3D surface texture

Zeppelzauer

Zieliński

Juda

et al. 2018

Computer Vision and Image Understanding

Self Cite

View full text Add to dashboard Cite

show abstract

“…Kramár et al (2016) use sublevel set persistence to summarize the complicated spatiotemporal patterns that arise from dynamical systems modeling fluid flow, including turbulence (Kolmogorov flow) and heat convection (Rayleigh-Bénard convection). With sublevel set persistence, Zeppelzauer et al (2016) improve 3D surface classification, including on an archaeology task of segmenting engraved regions of rock from the surrounding natural rock surface. In a task of tracking automobiles, Bendich et al (2016a) use the sublevel set persistent homology of driver speeds in order to characterize driver behaviors and prune out improbable paths from their multiple hypothesis tracking framework.…”

Section: Examples Measuring Local Geometrymentioning

confidence: 99%

Topology Applied to Machine Learning: From Global to Local

Adams

Moy

2021

Front. Artif. Intell.

View full text Add to dashboard Cite

Through the use of examples, we explain one way in which applied topology has evolved since the birth of persistent homology in the early 2000s. The first applications of topology to data emphasized the global shape of a dataset, such as the three-circle model for 3 × 3 pixel patches from natural images, or the configuration space of the cyclo-octane molecule, which is a sphere with a Klein bottle attached via two circles of singularity. In these studies of global shape, short persistent homology bars are disregarded as sampling noise. More recently, however, persistent homology has been used to address questions about the local geometry of data. For instance, how can local geometry be vectorized for use in machine learning problems? Persistent homology and its vectorization methods, including persistence landscapes and persistence images, provide popular techniques for incorporating both local geometry and global topology into machine learning. Our meta-hypothesis is that the short bars are as important as the long bars for many machine learning tasks. In defense of this claim, we survey applications of persistent homology to shape recognition, agent-based modeling, materials science, archaeology, and biology. Additionally, we survey work connecting persistent homology to geometric features of spaces, including curvature and fractal dimension, and various methods that have been used to incorporate persistent homology into machine learning.

show abstract

“…They showed that estimated standard deviations of the errors indicate the robustness and classification results. Zeppelzauer et al [24] investigated different topological descriptors and measured their ability to discriminate structurally different 3D surface patches. The study revealed that topological descriptors are (i) robust, (ii) yield state-of-the-art performance for the task of 3D surface analysis, and (iii) improve classification performance when combined with non-topological descriptors.…”

Section: Introductionmentioning

confidence: 99%

Texture Analysis of Hydrophobic Polycarbonate and Polydimethylsiloxane Surfaces via Persistent Homology

et al. 2017

View full text Add to dashboard Cite

Due to recent climate change-triggered, regular dust storms in the Middle East, dust mitigation has become the critical issue for solar energy harvesting devices. One of the methods to minimize and prevent dust adhesion and create self-cleaning abilities is to generate hydrophobic characteristics on surfaces. The purpose of this study is to explore the topological features of hydrophobic surfaces. We use non-standard techniques from topological data analysis to extract morphological features from the AFM images. Our method recovers most of the previous qualitative observations in a robust and quantitative way. Persistence diagrams, which is a summary of topological structures, witness quantitatively that the crystallized polycarbonate (PC) surface possesses spherulites, voids, and fibrils, and the texture height and spherulite concentration increases with the increased immersion period. The approach also shows that the polydimethylsiloxane (PDMS) exactly copied the structures at the PC surface but 80 to 90 percent of the nanofibrils were not copied at PDMS surface. We next extract a feature vector from each persistence diagram to show which experiments hold features with similar variance using principal component analysis (PCA). The K-means clustering algorithm is applied to the matrix of feature vectors to support the PCA result, grouping experiments with similar features.

show abstract

Topological Descriptors for 3D Surface Analysis

Cited by 12 publications

References 26 publications

A study on topological descriptors for the analysis of 3D surface texture

A study on topological descriptors for the analysis of 3D surface texture

Topology Applied to Machine Learning: From Global to Local

Texture Analysis of Hydrophobic Polycarbonate and Polydimethylsiloxane Surfaces via Persistent Homology

Contact Info

Product

Resources

About