Related papers: Efficient Betti Matching Enables Topology-Aware 3D…

Image segmentation is a largely researched field where neural networks find vast applications in many facets of technology. Some of the most popular approaches to train segmentation networks employ loss functions optimizing pixel-overlap,…

Segmentation algorithms are prone to make topological errors on fine-scale structures, e.g., broken connections. We propose a novel method that learns to segment with correct topology. In particular, we design a continuous-valued loss…

Topological accuracy in medical image segmentation is a highly important property for downstream applications such as network analysis and flow modeling in vessels or cell counting. Recently, significant methodological advancements have…

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…

Segmenting multiple objects (e.g., organs) in medical images often requires an understanding of their topology, which simultaneously quantifies the shape of the objects and their positions relative to each other. This understanding is…

We present a novel method to explicitly incorporate topological prior knowledge into deep learning based segmentation, which is, to our knowledge, the first work to do so. Our method uses the concept of persistent homology, a tool from…

Persistent homology is a common technique in topological data analysis providing geometrical and topological information about the sample space. All this information, known as topological features, is summarized in persistence diagrams, and…

We describe an approach to bounded-memory computation of persistent homology and betti barcodes, in which a computational state is maintained with updates introducing new edges to the underlying neighbourhood graph and percolating the…

Topological correctness is critical for segmentation of tubular structures, which pervade in biomedical images. Existing topological segmentation loss functions are primarily based on the persistent homology of the image. They match the…

Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust…

Comparison between multidimensional persistent Betti numbers is often based on the multidimensional matching distance. While this metric is rather simple to define and compute by considering a suitable family of filtering functions…

In this paper we study a new metric for comparing Betti numbers functions in bidimensional persistent homology, based on coherent matchings, i.e. families of matchings that vary in a continuous way. We prove some new results about this…

Accurate and interpretable brain tumor classification from medical imaging remains a challenging problem due to the high dimensionality and complex structural patterns present in magnetic resonance imaging (MRI). In this study, we propose a…

This paper proposes a novel topological learning framework that integrates networks of different sizes and topology through persistent homology. Such challenging task is made possible through the introduction of a computationally efficient…

Persistent homology is a fundamental tool in topological data analysis; however, it lacks methods to quantify the fragility or fineness of cycles, anticipate their formation or disappearance, or evaluate their stability beyond persistence.…

Success of deep neural networks in diverse tasks across domains of computer vision, speech recognition and natural language processing, has necessitated understanding the dynamics of training process and also working of trained models. Two…

Accurate segmentation of tubular and curvilinear structures, such as blood vessels, neurons, and road networks, is crucial in various applications. A key challenge is ensuring topological correctness while maintaining computational…

Blood vessel segmentation is one of the most studied topics in computer vision, due to its relevance in daily clinical practice. Despite the evolution the field has been facing, especially after the dawn of deep learning, important…

Topology is the foundation for many industrial applications ranging from CAD to simulation analysis. Computational topology mostly focuses on structured data such as mesh, however unstructured dataset such as point set remains a virgin land…

In recent years, cosmic shear has emerged as a powerful tool to study the statistical distribution of matter in our Universe. Apart from the standard two-point correlation functions, several alternative methods like peak count statistics…