Random sampling of random processes - Stationary point processes.
Randomly sampled random processes, discussing sampling time statistics and stationary point processes
STATISTICAL ANALYSIS↗
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Results for “point processes”
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The theory of stationary point processes.
Axiomatic formulation for stationary point processes interpreted as ordered sequences of points randomly located on real line, noting relation to set theory
SET THEORY↗
Unsupervised Detection of Planetary Craters by a Marked Point Process
With the launch of several planetary missions in the last decade, a large amount of planetary images is being acquired. Preferably, automatic and robust processing techniques need to be used for data analysis because of the huge amount of the acquired data. Here, the aim is to achieve a robust and general methodology for crater detection. A novel technique based on a marked point process is proposed. First, the contours in the image are extracted. The object boundaries are modeled as a configuration of an unknown number of random ellipses, i.e., the contour image is considered as a realization of a marked point process. Then, an energy function is defined, containing both an a priori energy and a likelihood term. The global minimum of this function is estimated by using reversible jump Monte-Carlo Markov chain dynamics and a simulated annealing scheme. The main idea behind marked point processes is to model objects within a stochastic framework: Marked point processes represent a very promising current approach in the stochastic image modeling and provide a powerful and methodologically rigorous framework to efficiently map and detect objects and structures in an image with an excellent robustness to noise. The proposed method for crater detection has several feasible applications. One such application area is image registration by matching the extracted features.
Troglio, G.↗
Morphostatistical characterization of the spatial galaxy distribution through Gibbs point processes
ABSTRACT This paper proposes a morphostatistical characterization of the galaxy distribution through spatial statistical modelling based on inhomogeneous Gibbs point processes. The galaxy distribution is supposed to exhibit two components. The first one is related to the major geometrical features exhibited by the observed galaxy field, here, its corresponding filamentary pattern. The second one is related to the interactions exhibited by the galaxies. Gibbs point processes are statistical models able to integrate these two aspects in a probability density, controlled by some parameters. Several such models are fitted to real observational data via the ABC shadow algorithm. This algorithm provides simultaneous parameter estimation and posterior-based inference, hence allowing the derivation of the statistical significance of the obtained results.
79 ASTRONOMY AND ASTROPHYSICS↗
Marked point process models of raindrop-size distributions
The principal process considered in this paper is the flux of raindrops through a volume of the atmosphere. This process is of fundamental importance for a wide variety of engineering and environmental problems, notably remote sensing of precipitation, infiltration of rainfall, soil erosion, atmospheric deposition of pollutants, and design of microwave communication systems. A marked point process model is developed in which the point process represents the arrival times of drops at the upper surface of a sample volume and the mark associated with a drop is its diameter. In the model, both the rate of occurrence of raindrops and the distribution of drop diameters vary randomly over time. Results that relate the drop-size distribution within the sample volume to the probability law of the drop-arrival process are presented. These results allow straightforward comparisons between temporal characterizations of drop-size distributions and spatial characterizations. Representations for derived processes such as rainfall rate and reflectivity are shown to be quite accurate using raindrop data from North Carolina.
Smith, James A.↗
The detection and analysis of point processes in biological signals
A pragmatic approach to the detection and analysis of discrete events in biomedical signals is taken. Examples from both clinical and basic research are provided. Introductory sections discuss not only discrete events which are easily extracted from recordings by conventional threshold detectors but also events embedded in other information carrying signals. The primary considerations are factors governing event-time resolution and the effects limits to this resolution have on the subsequent analysis of the underlying process. The analysis portion describes tests for qualifying the records as stationary point processes and procedures for providing meaningful information about the biological signals under investigation. All of these procedures are designed to be implemented on laboratory computers of modest computational capacity.
Anderson, D. J.↗
Point process algorithm: a new Bayesian approach for TPF-I planet signal extraction
TPF-I capability for planetary signal extraction, including both detection and spectral characterization, can be optimized by taking proper account of instrumental characteristics and astrophysical prior information. We have developed the Point Process Algorithm, a Bayesian technique for estracting planetary signals using the sine/cosine chopped outputs of a dual nulling interferometer.
stars↗
Planetary Crater Detection and Registration Using Marked Point Processes, Graph Cut Algorithms, and Wavelet Transforms
This paper addresses the problem of semi-automatic image registration on planetary images. A joint feature-based and area-based approach is proposed. Firstly, the most relevant craters are extracted from the two images to register, and then, registration is performed in two steps. The first step matches the craters extracted from the images based on a generalized Hausdorff distance. In the second step, the mutual information between the two images is maximized to achieve high registration accuracy. Craters are detected by a stochastic-geometry approach based on a marked point process model and of a multiple-birth-and-cut energy minimization algorithm. The experimental validation is carried out with 13 images for the crater extraction stage, and with 20 semi-synthetic pairs of images with ground truth and several images extracted from actual multi-temporal lunar scenes for the registration phase.
Image Processing; Pattern Recognition↗
Analysis of spatial arrangement of fractures in two dimensions using point process statistics
Not Available
58 GEOSCIENCES↗
Planetary Crater Detection and Registration Using Marked Point Processes, Multiple Birth and Death Algorithms, and Region-Based Analysis
Because of the large variety of sensors and spacecraft collecting data, planetary science needs to integrate various multi-sensor and multi-temporal images. These multiple data represent a precious asset, as they allow the study of targets spectral responses and of changes in the surface structure; because of their variety, they also require accurate and robust registration. A new crater detection algorithm, used to extract features that will be integrated in an image registration framework, is presented. A marked point process-based method has been developed to model the spatial distribution of elliptical objects (i.e. the craters) and a birth-death Markov chain Monte Carlo method, coupled with a region-based scheme aiming at computational efficiency, is used to find the optimal configuration fitting the image. The extracted features are exploited, together with a newly defined fitness function based on a modified Hausdorff distance, by an image registration algorithm whose architecture has been designed to minimize the computational time.
Image Processing; Pattern Recognition↗
Planetary Crater Detection and Registration Using Marked Point Processes, Multiple Birth and Death Algorithms, and Region-Based Analysis
Because of the large variety of sensors and spacecraft collecting data, planetary science needs to integrate various multi-sensor and multi-temporal images. These multiple data represent a precious asset, as they allow the study of targets spectral responses and of changes in the surface structure; because of their variety, they also require accurate and robust registration. A new crater detection algorithm, used to extract features that will be integrated in an image registration framework, is presented. A marked point process-based method has been developed to model the spatial distribution of elliptical objects (i.e. the craters) and a birth-death Markov chain Monte Carlo method, coupled with a region-based scheme aiming at computational efficiency, is used to find the optimal configuration fitting the image. The extracted features are exploited, together with a newly defined fitness function based on a modified Hausdorff distance, by an image registration algorithm whose architecture has been designed to minimize the computational time.
Image Processing:Pattern Recognition↗
Stochastic reconstruction of fracture network pattern using spatial point processes
Fracture spatial patterns can strongly affect fluid flow in the subsurface. Proximity and distribution of fractures control reservoir flow behavior over various length scales. In many studies, however, simplified geometrical patterns are generated for fractures which may lead to unrealistic subsurface models. Here we introduce a new method for characterization and modeling of fracture spatial patterns based on outcrop observations. We use Ripley's K-function to characterize the arrangement of fracture barycenters and intersection points over various length scales. In addition, we use semivariograms to quantify spatial correlation in fracture intensity maps. Using this information, we develop a stochastic algorithm that generates two-dimensional fracture network realizations with spatial properties similar to those of a real fracture network measured in the field. Numerical simulation models indicate that the generated fracture realizations exhibit similar flow behaviors as that of the original fracture network. Furthermore, such modeling tools expand and improve our capability in building representative fracture models and in quantification of uncertainty in naturally and hydraulically fractured reservoirs.
58 GEOSCIENCES↗
Bayesian Modeling of Self-Exciting Marked Point Processes with Missing Histories
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Tucker, James Derek [Sandia National Laboratories ↗
Deep Sigma Point Processes-Assisted Chance-Constrained Power System Transient Stability Preventive Control
Here this paper proposes a deep sigma point processes (DSPP)-assisted chance-constrained power system transient stability preventive control method to deal with uncertain renewable energy and loads-induced stability risk. The traditional transient stability-constrained preventive control is reformulated as a chance-constrained optimization problem. To deal with the computational bottleneck of the time-domain simulation-based probabilistic transient stability assessment, the DSPP is developed. DSPP is a parametric Bayesian approach that allows us to predict system transient stability with high computational efficiency while accurately quantifying the confidence intervals of the predictions that can be used to inform system instability risk. To this end, with a given preset confidence probability, we embed DSPP into the primal dual interior point method to help solve the chance-constrained preventive control problem, where the corresponding Jacobian and Hessian matrices are derived. Comparison results with other existing methods show that the proposed method can significantly speed up preventive control while maintaining high accuracy and convergence
97 MATHEMATICS AND COMPUTING↗
3D point cloud processing
Methods for processing a 3D point cloud of a building into polygons using an electronic computing device are presented, the methods including: causing the electronic computing device to receive the 3D point cloud; causing the electronic computing device to segment the 3D point cloud into a number of facades; and causing the electronic computing device to generate a number of polygons representing the number of facades. In some embodiments, the causing the electronic computing device to segment the 3D point cloud into a number of facades includes: performing voxel downsampling operation on the 3D point cloud; calculating a point normal for every point in the voxel downsampled 3D point cloud; and performing region growing to find each of the number of facades.
Wang, Richard↗
Numerical analysis of a time discretized method for nonlinear filtering problem with Lévy process observations
Abstract In this paper, we consider a nonlinear filtering model with observations driven by correlated Wiener processes and point processes. We first derive a Zakai equation whose solution is an unnormalized probability density function of the filter solution. Then, we apply a splitting-up technique to decompose the Zakai equation into three stochastic differential equations, based on which we construct a splitting-up approximate solution and prove its half-order convergence. Furthermore, we apply a finite difference method to construct a time semi-discrete approximate solution to the splitting-up system and prove its half-order convergence to the exact solution of the Zakai equation. Finally, we present some numerical experiments to demonstrate the theoretical analysis.
Mathematics↗
Discrimination of shot-noise-driven Poisson processes by external dead time - Application of radioluminescence from glass
Ways in which dead time can be used to constructively enhance or diminish the effects of point processes that display bunching in the shot-noise-driven doubly stochastic Poisson point process (SNDP) are discussed. Interrelations between photocount bunching arising in the SNDP and the antibunching character arising from dead-time effects are investigated. It is demonstrated that the dead-time-modified count mean and variance for an arbitrary doubly stochastic Poisson point process can be obtained from the Laplace transform of the single-fold and joint-moment-generating functions for the driving rate process. The theory is in good agreement with experimental values for radioluminescence radiation in fused silica, quartz, and glass, and the process has many applications in pulse, particle, and photon detection.
Saleh, B. E. A.↗