Related papers: The Gestalt Computational Model by Persistent Homo…
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…
Incompatibility of image descriptor and ranking is always neglected in image retrieval. In this paper, manifold learning and Gestalt psychology theory are involved to solve the incompatibility problem. A new holistic descriptor called…
Hand gesture recognition has been granted as one of the emerging fields in research today providing a natural way of communication between man and a machine. Gestures are some forms of body motions which a person expresses when doing a work…
Algorithms for persistent homology and zigzag persistent homology are well-studied for persistence modules where homomorphisms are induced by inclusion maps. In this paper, we propose a practical algorithm for computing persistence under…
One of the primary areas of interest in applied algebraic topology is persistent homology, and, more specifically, the persistence diagram. Persistence diagrams have also become objects of interest in topological data analysis. However,…
Image representation is an important topic in computer vision and pattern recognition. It plays a fundamental role in a range of applications towards understanding visual contents. Moment-based image representation has been reported to be…
Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this…
Force-directed layouts belong to a popular class of methods used to position nodes in a node-link diagram. However, they typically lack direct consideration of global structures, which can result in visual clutter and the overlap of…
User's intentions may be expressed through spontaneous gesturing, which have been seen only a few times or never before. Recognizing such gestures involves one shot gesture learning. While most research has focused on the recognition of the…
We define persistent homology groups over any set of spaces which have inclusions defined so that the corresponding directed graph between the spaces is acyclic, as well as along any subgraph of this directed graph. This method…
We present a topological pipeline for automated multiclass emotion recognition from eye-tracking data. Delay embeddings of gaze trajectories are analyzed using persistent homology. From the resulting persistence diagrams, we extract…
Tracking multiple objects is a challenging task when objects move in groups and occlude each other. Existing methods have investigated the problems of group division and group energy-minimization; however, lacking overall object-group…
Clustering artworks based on style can have many potential real-world applications like art recommendations, style-based search and retrieval, and the study of artistic style evolution of an artist or in an artwork corpus. We introduce and…
Solving optimization tasks based on functions and losses with a topological flavor is a very active, growing field of research in data science and Topological Data Analysis, with applications in non-convex optimization, statistics and…
We present SCULPT, a novel 3D generative model for clothed and textured 3D meshes of humans. Specifically, we devise a deep neural network that learns to represent the geometry and appearance distribution of clothed human bodies. Training…
Persistent (co)homology is a central construction in topological data analysis, where it is used to quantify prominence of features in data to produce stable descriptors suitable for downstream analysis. Persistence is challenging to…
Image segmentation is a central topic in image processing and computer vision and a key issue in many applications, e.g., in medical imaging, microscopy, document analysis and remote sensing. According to the human perception, image…
We propose a functorial framework for persistent homology based on finite topological spaces and their associated posets. Starting from a finite metric space, we associate a filtration of finite topologies whose structure maps are…
The Gapminder project set out to use statistics to dispel simplistic notions about global development. In the same spirit, we use persistent homology, a technique from computational algebraic topology, to explore the relationship between…
We propose a general technique for extracting a larger set of stable information from persistent homology computations than is currently done. The persistent homology algorithm is usually viewed as a procedure which starts with a filtered…