131 research outputs found
Topological features for monitoring human activities at distance
In this paper, a topological approach for monitoring human activities is presented. This approach makes possible to protect the person’s privacy hiding details that are not essential for processing a security alarm. First, a stack of human silhouettes, extracted by background subtraction and thresholding, are glued through their gravity centers, forming a 3D digital binary image I. Secondly, different orders of the simplices are applied on a simplicial complex obtained from I, which capture relations among the parts of the human body when walking. Finally, a topological signature is extracted from the persistence diagrams according to each order. The measure cosine is used to give a similarity value between topological signatures. In this way, the powerful topological tool known as persistent homology is novelty adapted to deal with gender classification, person identification, carrying bag detection and simple action recognition. Four experiments show the strength of the topological feature used; three of they use the CASIA-B database, and the fourth use the KTH database to present the results in the case of simple actions recognition. In the first experiment the named topological signature is evaluated, obtaining 98.8% (lateral view) of correct classification rates for gender identification. In the second one are shown results for person identification, obtaining an average of 98.5%. In the third one the result obtained is 93.8% for carrying bag detection. And in the last experiment the results were 97.7% walking and 97.5% running, which were the actions took from the KTH database
Persistent Homology Over Directed Acyclic Graphs
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
simultaneously generalizes standard persistent homology, zigzag persistence and
multidimensional persistence to arbitrary directed acyclic graphs, and it also
allows the study of more general families of topological spaces or point-cloud
data. We give an algorithm to compute the persistent homology groups
simultaneously for all subgraphs which contain a single source and a single
sink in arithmetic operations, where is the number of vertices in
the graph. We then demonstrate as an application of these tools a method to
overlay two distinct filtrations of the same underlying space, which allows us
to detect the most significant barcodes using considerably fewer points than
standard persistence.Comment: Revised versio
Towards Emotion Recognition: A Persistent Entropy Application
Emotion recognition and classification is a very active area of research. In
this paper, we present a first approach to emotion classification using
persistent entropy and support vector machines. A topology-based model is
applied to obtain a single real number from each raw signal. These data are
used as input of a support vector machine to classify signals into 8 different
emotions (calm, happy, sad, angry, fearful, disgust and surprised)
Simplicial complex entropy.
We propose an entropy function for simplicial complices. Its value gives the expected cost of the optimal encoding of sequences of vertices of the complex, when any two vertices belonging to the same simplex are indistinguishable. We focus on the computational properties of the entropy function, showing that it can be computed efficiently. Several examples over complices consisting of hundreds of simplices show that the proposed entropy function can be used in the analysis of large sequences of simplicial complices that often appear in computational topology applications
Designing a topological algorithm for 3D activity recognition
Voxel carving is a non-invasive and low-cost technique that is used for the reconstruction of a 3D volume from images captured from a set of cameras placed around the object of interest. In this paper we propose a method to topologically analyze a video sequence of 3D reconstructions representing a tennis player performing different forehand and backhand strokes with the aim of providing an approach that could be useful in other sport activities
Incremental-Decremental Algorithm for Computing AT-Models and Persistent Homology
In this paper, we establish a correspondence between the incremental algorithm for computing AT-models [8,9] and the one for computing persistent homology [6,14,15]. We also present a decremental algorithm for computing AT-models that allows to extend the persistence computation to a wider setting. Finally, we show how to combine incremental and decremental techniques for persistent homology computation
Optimal topological simplification of discrete functions on surfaces
We solve the problem of minimizing the number of critical points among all
functions on a surface within a prescribed distance {\delta} from a given input
function. The result is achieved by establishing a connection between discrete
Morse theory and persistent homology. Our method completely removes homological
noise with persistence less than 2{\delta}, constructively proving the
tightness of a lower bound on the number of critical points given by the
stability theorem of persistent homology in dimension two for any input
function. We also show that an optimal solution can be computed in linear time
after persistence pairs have been computed.Comment: 27 pages, 8 figure
Recommended from our members
Uniaxial Tensile Stress-Strain Relationships of RC Elements Strengthened with FRP Sheets
The shear behavior of fiber-reinforced-polymer–strengthened reinforced concrete (FRP-strengthened RC) members is not fully developed and accurately predicted because of the lack of accurate constitutive laws for the components of the composite members. This paper presents experimental and analytical investigations of tensile stress-strain relationships of concrete and steel in FRP-strengthened RC members. These stress-strain relationships are required in formulations of softened truss models to predict the shear behavior of the FRP-strengthened RC element. Thirteen full-scale FRP-strengthened RC prismatic specimens with different FRP reinforcement ratios, steel reinforcement ratios, and FRP wrapping schemes were tested under uniaxial tension loading. The results show that the tensile behavior of the concrete and steel is altered because of the externally bonded FRP sheets. Modified constitutive laws are proposed and incorporated in the softened membrane model (SMM) to demonstrate through two tests the behavior of FRP-strengthened RC element subjected to pure shear. Moreover, crack spacing and crack width were studied and compared with existing code provisions
Towards Minimal Barcodes
In the setting of persistent homology computation, a useful tool is the persistence barcode representation in which pairs of birth and death times of homology classes are encoded in the form of intervals. Starting from a polyhedral complex K (an object subdivided into cells which are polytopes) and an initial order of the set of vertices, we are concerned with the general problem of searching for filters (an order of the rest of the cells) that provide a minimal barcode representation in the sense of having minimal number of “k-significant” intervals, which correspond to homology classes with life-times longer than a fixed number k. As a first step, in this paper we provide an algorithm for computing such a filter for k = 1 on the Hasse diagram of the poset of faces of K
- …