Add to ORKGAccurate delineation of fine-scale structures is a very important yet challenging problem. Existing methods use topological information as an additional training loss, but are ultimately making pixel-wise predictions. In this paper, we propose the first deep learning based method to learn topological/structural representations. We use discrete Morse theory and persistent homology to construct an one-parameter family of structures as the topological/structural representation space. Furthermore, we learn a probabilistic model that can perform inference tasks in such a topological/structural representation space. Our method generates true structures rather than pixel-maps, leading to better topological integrity in automatic segmentation tasks...
Accurate segmentation of tubular, network-like structures, such as vessels, neurons, or roads, is re...
23 pages, 4 figuresThe use of topological descriptors in modern machine learning applications, such ...
We address the problem of generating navigation roadmaps for uncertain and cluttered environments re...
Besides per-pixel accuracy, topological correctness is also crucial for the segmentation of images w...
Curvilinear structure segmentation plays an important role in many applications. The standard formul...
Generalization is challenging in small-sample-size regimes with over-parameterized deep neural netwo...
We show how discrete Morse theory provides a rigorous and unifying foundation for defining skeletons...
Topological Data Analysis (TDA) with its roots embedded in the field of algebraic topology has succe...
This paper proposes a novel topological learning framework that integrates networks of different siz...
The rising field of Topological Data Analysis (TDA) provides a new approach to learning from data th...
Recovering hidden graph-like structures from potentially noisy data is a fundamental task in modern ...
168 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001.The thesis also gives algorit...
Topology and machine learning are two actively researched topics not only in condensed matter physic...
The last decade saw an enormous boost in the field of computational topology: methods and concepts f...
Persistent Homology (PH) has been successfully used to train networks to detect curvilinear structur...
Accurate segmentation of tubular, network-like structures, such as vessels, neurons, or roads, is re...
23 pages, 4 figuresThe use of topological descriptors in modern machine learning applications, such ...
We address the problem of generating navigation roadmaps for uncertain and cluttered environments re...
Besides per-pixel accuracy, topological correctness is also crucial for the segmentation of images w...
Curvilinear structure segmentation plays an important role in many applications. The standard formul...
Generalization is challenging in small-sample-size regimes with over-parameterized deep neural netwo...
We show how discrete Morse theory provides a rigorous and unifying foundation for defining skeletons...
Topological Data Analysis (TDA) with its roots embedded in the field of algebraic topology has succe...
This paper proposes a novel topological learning framework that integrates networks of different siz...
The rising field of Topological Data Analysis (TDA) provides a new approach to learning from data th...
Recovering hidden graph-like structures from potentially noisy data is a fundamental task in modern ...
168 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2001.The thesis also gives algorit...
Topology and machine learning are two actively researched topics not only in condensed matter physic...
The last decade saw an enormous boost in the field of computational topology: methods and concepts f...
Persistent Homology (PH) has been successfully used to train networks to detect curvilinear structur...
Accurate segmentation of tubular, network-like structures, such as vessels, neurons, or roads, is re...
23 pages, 4 figuresThe use of topological descriptors in modern machine learning applications, such ...
We address the problem of generating navigation roadmaps for uncertain and cluttered environments re...