Topological Methods of Analysis in Behavioral Analytics Systems

Purpose of the article: development of a methodology for the application of methods for analyzing big data based on topological constructions in relation to behavioral analytics systems to ensure corporate and cyber-physical security. Method: the technique is based on the algebraic theory of persistent homology. Along with algebraic topology, embedology (Takens-Mane embedding theory) and the theory of metric spaces are used. Result: the necessary concepts of algebraic topology are given, which underlie the analysis of user / entity behavior profiles: Vietoris-Rips simplicial complex, filtering by a set of cloud points, homology groups, persistence modules, topological characteristics and dependencies. At the first stage of the technique, the time series that describe the time-varying behavior of the user / entity are transformed into a cloud of points in the topological space. For this transformation, the methods of the Takens-Mane embedding theory and the algorithm of the method of false neighbors are used. At the subsequent stages of the methodology for the base and current point clouds, topological dependencies, diagrams (persistence, bar codes) characterizing the base and current behavior profiles, respectively, are built. At the final stage, the deviation of the current behavior profile from the baseline is revealed. To estimate the deviation, the Wasserstein, Chebyshev, bottleneck metrics and scaling based on the generalized Harrington desirability function are used. The results of practical testing of the proposed method of applying topological algorithms to the data of the monitoring system for the work of corporate network users with information resources are presented

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Accuracy Analysis of Fringe Projection Systems Based on Blue Light Technology

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.615.9 ◽

2014 ◽

Vol 615 ◽

pp. 9-14 ◽

Cited By ~ 3

Author(s):

Claudio Bernal ◽

Beatriz de Agustina ◽

Marta María Marín ◽

Ana Maria Camacho

Keyword(s):

Blue Light ◽

Point Clouds ◽

Fringe Projection ◽

Accuracy Analysis ◽

Scanning Procedure ◽

Structured Light Scanner ◽

Cloud Of Points ◽

3D Digitizing

Some manufacturers of 3D digitizing systems are developing and market more accurate, fastest and affordable systems of fringe projection based on blue light technology. The aim of the present work is the determination of the quality and accuracy of the data provided by the LED structured light scanner Comet L3D (Steinbichler). The quality and accuracy of the cloud of points produced by the scanner is determined by measuring a number of gauge blocks of different sizes. The accuracy range of the scanner has been established through multiple digitizations showing the dependence on different factors such as the characteristics of the object and scanning procedure. Although many factors influence, accuracies announced by manufacturer have been achieved under optimal conditions and it has been noted that the quality of the point clouds (density, noise, dispersion of points) provided by this system is higher than that obtained with laser technology devices.

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A topological characterization of DNA sequences based on chaos geometry and persistent homology

10.1101/2021.01.31.429071 ◽

2021 ◽

Author(s):

Dong Quan Ngoc Nguyen ◽

Phuong Dong Tan Le ◽

Lin Xing ◽

Lizhen Lin

Keyword(s):

Dna Sequences ◽

Algebraic Topology ◽

Influenza A ◽

Graphical Representation ◽

Dimensional Space ◽

Persistent Homology ◽

Point Clouds ◽

Influenza A Viruses ◽

Topological Characterization ◽

Topological Features

AbstractMethods for analyzing similarities among DNA sequences play a fundamental role in computational biology, and have a variety of applications in public health, and in the field of genetics. In this paper, a novel geometric and topological method for analyzing similarities among DNA sequences is developed, based on persistent homology from algebraic topology, in combination with chaos geometry in 4-dimensional space as a graphical representation of DNA sequences. Our topological framework for DNA similarity analysis is general, alignment-free, and can deal with DNA sequences of various lengths, while proving first-of-the-kind visualization features for visual inspection of DNA sequences directly, based on topological features of point clouds that represent DNA sequences. As an application, we test our methods on three datasets including genome sequences of different types of Hantavirus, Influenza A viruses, and Human Papillomavirus.

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Topological pattern recognition for point cloud data

Acta Numerica ◽

10.1017/s0962492914000051 ◽

2014 ◽

Vol 23 ◽

pp. 289-368 ◽

Cited By ~ 73

Author(s):

Gunnar Carlsson

Keyword(s):

Pattern Recognition ◽

Algebraic Topology ◽

Point Cloud ◽

Metric Spaces ◽

Persistent Homology ◽

Topological Spaces ◽

Data Sets ◽

Point Cloud Data ◽

Cloud Data ◽

Finite Metric Spaces

In this paper we discuss the adaptation of the methods of homology from algebraic topology to the problem of pattern recognition in point cloud data sets. The method is referred to aspersistent homology, and has numerous applications to scientific problems. We discuss the definition and computation of homology in the standard setting of simplicial complexes and topological spaces, then show how one can obtain useful signatures, called barcodes, from finite metric spaces, thought of as sampled from a continuous object. We present several different cases where persistent homology is used, to illustrate the different ways in which the method can be applied.

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Terrestrial laser scanning in monitoring of anthropogenic objects

Geodesy and Cartography ◽

10.1515/geocart-2017-0011 ◽

2017 ◽

Vol 66 (2) ◽

pp. 347-364

Author(s):

Janina Zaczek-Peplinska ◽

Maria Kowalska

Keyword(s):

Laser Scanning ◽

Incidence Angle ◽

Geometric Analysis ◽

Laser Scanner ◽

Terrestrial Laser Scanning ◽

Point Clouds ◽

Angle Of Incidence ◽

Point Distribution ◽

Common Coordinate System ◽

Cloud Of Points

Abstract The registered xyz coordinates in the form of a point cloud captured by terrestrial laser scanner and the intensity values (I) assigned to them make it possible to perform geometric and spectral analyses. Comparison of point clouds registered in different time periods requires conversion of the data to a common coordinate system and proper data selection is necessary. Factors like point distribution dependant on the distance between the scanner and the surveyed surface, angle of incidence, tasked scan’s density and intensity value have to be taken into consideration. A prerequisite for running a correct analysis of the obtained point clouds registered during periodic measurements using a laser scanner is the ability to determine the quality and accuracy of the analysed data. The article presents a concept of spectral data adjustment based on geometric analysis of a surface as well as examples of geometric analyses integrating geometric and physical data in one cloud of points: cloud point coordinates, recorded intensity values, and thermal images of an object. The experiments described here show multiple possibilities of usage of terrestrial laser scanning data and display the necessity of using multi-aspect and multi-source analyses in anthropogenic object monitoring. The article presents examples of multisource data analyses with regard to Intensity value correction due to the beam’s incidence angle. The measurements were performed using a Leica Nova MS50 scanning total station, Z+F Imager 5010 scanner and the integrated Z+F T-Cam thermal camera.

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Poincaré inequalities, embeddings, and wild groups

Compositio Mathematica ◽

10.1112/s0010437x11005343 ◽

2011 ◽

Vol 147 (5) ◽

pp. 1546-1572 ◽

Cited By ~ 31

Author(s):

Assaf Naor ◽

Lior Silberman

Keyword(s):

Fixed Point ◽

Metric Spaces ◽

Isometric Action ◽

Metric Embedding ◽

Random Group ◽

Cartesian Products ◽

Poincaré Inequalities ◽

Embedding Theory ◽

Geometric Conditions ◽

Poincare Inequalities

AbstractWe present geometric conditions on a metric space (Y,dY) ensuring that, almost surely, any isometric action onYby Gromov’s expander-based random group has a common fixed point. These geometric conditions involve uniform convexity and the validity of nonlinear Poincaré inequalities, and they are stable under natural operations such as scaling, Gromov–Hausdorff limits, and Cartesian products. We use methods from metric embedding theory to establish the validity of these conditions for a variety of classes of metric spaces, thus establishing new fixed point results for actions of Gromov’s ‘wild groups’.

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SLAM-OR: Simultaneous Localization, Mapping and Object Recognition Using Video Sensors Data in Open Environments from the Sparse Points Cloud

Sensors ◽

10.3390/s21144734 ◽

2021 ◽

Vol 21 (14) ◽

pp. 4734

Author(s):

Patryk Mazurek ◽

Tomasz Hachaj

Keyword(s):

Neural Network ◽

Deep Neural Network ◽

Clustering Algorithm ◽

State Of The Art ◽

Point Clouds ◽

Video Frame ◽

Current Frame ◽

Visual Sensors ◽

Open Environments ◽

Cloud Of Points

In this paper, we propose a novel approach that enables simultaneous localization, mapping (SLAM) and objects recognition using visual sensors data in open environments that is capable to work on sparse data point clouds. In the proposed algorithm the ORB-SLAM uses the current and previous monocular visual sensors video frame to determine observer position and to determine a cloud of points that represent objects in the environment, while the deep neural network uses the current frame to detect and recognize objects (OR). In the next step, the sparse point cloud returned from the SLAM algorithm is compared with the area recognized by the OR network. Because each point from the 3D map has its counterpart in the current frame, therefore the filtration of points matching the area recognized by the OR algorithm is performed. The clustering algorithm determines areas in which points are densely distributed in order to detect spatial positions of objects detected by OR. Then by using principal component analysis (PCA)—based heuristic we estimate bounding boxes of detected objects. The image processing pipeline that uses sparse point clouds generated by SLAM in order to determine positions of objects recognized by deep neural network and mentioned PCA heuristic are main novelties of our solution. In contrary to state-of-the-art approaches, our algorithm does not require any additional calculations like generation of dense point clouds for objects positioning, which highly simplifies the task. We have evaluated our research on large benchmark dataset using various state-of-the-art OR architectures (YOLO, MobileNet, RetinaNet) and clustering algorithms (DBSCAN and OPTICS) obtaining promising results. Both our source codes and evaluation data sets are available for download, so our results can be easily reproduced.

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Alternative method of analysis of results of 3D terrestrial laser scanning (comment to the article “Contribution to a rock block slide examination by a model of mutual transformation of point clouds”, Acta Carsologica 38,1)

Acta Carsologica ◽

10.3986/ac.v41i1.55 ◽

2012 ◽

Vol 41 (1) ◽

Author(s):

Matija Perne

Keyword(s):

Affine Transformation ◽

Laser Scanning ◽

Terrestrial Laser Scanning ◽

Point Clouds ◽

Rock Block ◽

Translation Vector ◽

Mutual Transformation ◽

Original Hypothesis ◽

Cloud Of Points ◽

Block Slide

The article Konic et al. (2009) describes efforts to find out if the rock block on which the castle of Črni kal is situated slid away from the Kraški rob wall. 3D terrestrial laser scanning has been used to determine positions of many points on both presumed contact surfaces and 12-parameter affine transformation that transforms the cloud of points from one wall into another has been found. The deviation between matching point clouds has been used as a test of the original hypothesis. It has been concluded that the rock block did slide. Some of the data from the article are re-analysed using another numerical method. A 6-parameter translation composed with rotation that best transforms the 12 published points from the rock block wall into their counterparts on the Kraški rob wall is found. The original hypothesis is confirmed and some additional insight into the block slide is revealed.Keywords: rock block slide, 12-parameter affine transformation, rotation matrix, translation vector.

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Laparoscopic Image Guidance via Conoscopic Holography

Journal of Medical Devices ◽

10.1115/1.3136754 ◽

2009 ◽

Vol 3 (2) ◽

Cited By ~ 1

Author(s):

R. A. Lathrop ◽

T. T. Cheng ◽

R. J. Webster

Keyword(s):

Standard Deviation ◽

Laser Beam ◽

Point Cloud ◽

Point Clouds ◽

Optical Tracking ◽

Operating Table ◽

Laparoscopic Port ◽

Conoscopic Holography ◽

Cloud Of Points ◽

The Way

Spatially registered 3D preoperative medical images can improve surgical accuracy and reduce reliance on memory and hand-eye coordination by the surgeon. They enable visualization of internal structures within the anatomy of a patient on the operating table. In the case of biopsy, for example, this would allow the surgeon to guide the needle tip to a tumor though opaque tissue. It has been well established that for soft tissues, image registration can be performed by aligning the preoperative image with a cloud of points that describe the surface of an organ [1]. Collecting this point cloud can be challenging, generally requiring open surgery to permit line-of-sight access for laser triangulation (e.g., the system of Pathfinder Therapeutics, Inc.). We present a conoscopic holography-based system for collecting a point cloud less invasively-through a laparoscopic port. The system consists of a commercial conoscope (Optimet, Inc., Probe Head Mk3), designed for precision machine-shop linear measurements, that is tracked (the surgical tool is also tracked) with an optical tracking system (Claron Micron Tracker H3-60). The conoscope laser beam can, in principle, be aimed through a laparoscopic port. The 1 degree of freedom linear distance measurements it returns are converted into a point cloud using optical tracker information. Proof-of-concept for obtaining point clouds via conoscopic holography and registering them to known shapes is provided in [2]. However, the procedure for collecting these point clouds requires the surgeon to manually `paint' the surface of the organ with the laser beam, aiming it at many points on the surface by manipulating the conoscope base unit, thus pivoting the tube in the laparoscopic port. It would be desirable to relieve the surgeon of this task by creating a system for automatically aiming the laser beam from a stationary conoscope. We hypothesize that this can be done with a suitably designed actuated mirror assembly at the tip of the laparoscopic tube. To assess whether a conoscope can make an accurate distance measurement when reflected by a mirror, we conducted a set of experiments. We placed a front-silvered mirror at a fixed 45 degree angle relative to the conoscope, 12 cm in front of it. Total beam length was 185-315 mm measured in 10 mm increments. The results were similar to direct measurements of the same distance without a mirror. We recorded a standard deviation of error of less than 0.01 mm in each 10 mm increment. A second experiment was then carried out to assess the effect of mirror angle. The laser was swept across a flat surface 105 mm from the mirror by rotating the mirror. The standard deviation of the data points from a true line was less than 0.1 mm along a 175 mm line segment. These experiments indicate the feasibility of using a mirror to aim a conoscopic holographic laser, paving the way for an automatic laparoscopic laser, paving the way for an automatic laparoscopic point cloud collection device to be developed in future work.

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Roadway Stability Evaluation on the Basis of Modern Monitoring of Displacement

Studia Geotechnica et Mechanica ◽

10.1515/sgem-2015-0006 ◽

2015 ◽

Vol 37 (1) ◽

pp. 45-52 ◽

Cited By ~ 2

Author(s):

Tadeusz Majcherczyk ◽

Zbigniew Niedbalski ◽

Artur Ulaszek

Keyword(s):

Laser Scanning ◽

Three Dimensional ◽

Point Clouds ◽

Measurement Technology ◽

Stability Evaluation ◽

3D Laser Scanning ◽

Roadway Stability ◽

Measurement Results ◽

Comparison Of The Results ◽

Cloud Of Points

Abstract The paper presents the application of a 3D laser measurement technology in a modern monitoring of roadways. The authors analyze the possibility of using a three-dimensional scanning measurement of longwall working dimensions. The measurement results are presented in the form of a cloud of points obtained from a 3D laser scanning. The paper also presents a comparison of the results obtained from the convergence of traditionally-made measurements with the measurements derived from the threedimensional scanning and discusses possible methods of comparing different point clouds.

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The Lorenz convection model's random attractor (LORA) and its robust topology

10.5194/egusphere-egu2020-10973 ◽

2020 ◽

Author(s):

Michael Ghil ◽

Gisela D. Charó ◽

Denisse Sciamarella ◽

Mickael D. Chekroun

Keyword(s):

Algebraic Topology ◽

Random Attractor ◽

Chaotic Flows ◽

Model Driven ◽

Closed Sets ◽

Local Approximations ◽

Convection Model ◽

Parameter Values ◽

Cloud Of Points ◽

First Time

Chekroun et al. (Physica D, 240, 2011) studied the global&#160;random attractor associated&#160;with the Lorenz (1963) model driven by multiplicative noise; they dubbed this time-evolving attractor LORA for short. The present talk examines the topological structure of the snapshots that approximate LORA&#8217;s evolution in time.&#160;Sciamarella & Mindlin (Phys. Rev. Lett., 82, 1999; Phys. Rev. E, 64, 2001) introduced the methodology of Branched Manifold Analysis through Homologies (BraMAH) to the study of chaotic flows. Here, the BraMAH methodology is extended for the first time, to the best of our knowledge, from deterministically chaotic flows to nonlinear noise-driven systems.&#160;The BraMAH algorithm starts from a cloud of points given by a large number of orbits and it builds a rough skeleton of the underlying branched manifold on which the points lie. This construction is achieved by local approximations of the manifold that use Euclidean closed sets; the nature of these sets depends on their topological dimension, e.g., segments or disks.&#160; The skeleton is mathematically expressed as a complex of cells, whose algebraic topology is analyzed by computing its homology groups.&#160;The analysis is performed for a fixed realization of the driving noise at different time instants. We show that the topology of LORA changes in time and that it is quite distinct from the time-independent one of the classical Lorenz (1963) convection model, for the same values of the parameters. Topological tipping points are also studied by varying the parameter values from the classical ones.

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