scholarly journals EXPLORATORY SPECTRAL ANALYSIS IN THREE-DIMENSIONAL SPATIAL POINT PATTERNS

2021 ◽  
Vol 39 (1) ◽  
pp. 177
Author(s):  
Edmary Silveira Barreto ARAÚJO ◽  
João Domingos SCALON ◽  
Lurimar Smera BATISTA
Keyword(s):  
Spectral Analysis ◽  
Point Processes ◽  
Three Dimensional ◽  
Dependence Structure ◽  
Point Pattern ◽  
Spatial Point Pattern ◽  
Space Domain ◽  
Point Patterns ◽  
Spatial Point ◽  
Spatial Point Patterns

A spatial point pattern is a collection of points irregularly located within a bounded area (2D) or space (3D) that have been generated by some form of stochastic mechanism. Examples of point patterns include locations of trees in a forest, of cases of a disease in a region, or of particles in a microscopic section of a composite material. Spatial Point pattern analysis is used mostly to determine the absence (completely spatial randomness) or presence (regularity and clustering) of spatial dependence structure of the locations. Methods based on the space domain are widely used for this purpose, while methods conducted in the frequency domain (spectral analysis) are still unknown to most researchers. Spectral analysis is a powerful tool to investigate spatial point patterns, since it does not assume any structural characteristics of the data (ex. isotropy), and uses only the autocovariance function, and its Fourier transform. There are some methods based on the spectral frameworks for analyzing 2D spatial point patterns. There is no such methods available for the 3D situation and, therefore, the aim of this work is to develop new methods based on spectral framework for the analysis of three-dimensional point patterns. The emphasis is on relating periodogram structure to the type of stochastic process which could have generated a 3D observed pattern. The results show that the methods based on spectral analysis developed in this work are able to identify patterns of three typical three-dimensional point processes, and can be used, concurrently, with analyzes in the space domain for a better characterization of spatial point patterns.

Multitype Markov point processes: some approximations

1984 ◽  
Vol 391 (1800) ◽  
pp. 39-53 ◽  
Keyword(s):  
Statistical Analysis ◽  
Point Processes ◽  
Boundary Effects ◽  
Point Interactions ◽  
Point Patterns ◽  
Spatial Point ◽  
Spatial Point Patterns ◽  
Markov Point Processes ◽  
Moment Measure ◽  
Reduced Second Moment Measure

Approximations are derived for some simple properties of a Strauss-type spatial point process with two types of point, on the assumption that the interactions between points are fairly weak and that boundary effects are negligible. In particular, expansions are obtained of the reduced second moment measure K ij used in the statistical analysis of spatial point patterns. It is found that these expansions may be useful in the estimation of the inter-point interactions and their ranges.

Testing the Stability of Crime Patterns: Implications for Theory and Policy

2010 ◽  
Vol 48 (1) ◽  
pp. 58-82 ◽  
Author(s):  
Martin A. Andresen ◽  
Nicolas Malleson
Keyword(s):  
Spatial Scales ◽  
Theoretical Development ◽  
Point Pattern ◽  
Crime Patterns ◽  
Point Patterns ◽  
Spatial Point ◽  
Spatial Point Patterns ◽  
Spatial Criminology ◽  
The Stability ◽  
Street Segments

Recent research in the ‘‘crime at places’’ literature is concerned with smaller units of analysis than conventional spatial criminology. An important issue is whether the spatial patterns observed in conventional spatial criminology focused on neighborhoods remain when the analysis shifts to street segments. In this article, the authors use a new spatial point pattern test that identifies the similarity in spatial point patterns. This test is local in nature such that the output can be mapped showing where differences are present. Using this test, the authors investigate the stability of crime patterns moving from census tracts to dissemination areas to street segments. The authors find that general crime patterns are somewhat similar at all spatial scales, but finer scales of analysis reveal significant variations within larger units. This result demonstrates the importance of analyzing crime patterns at small scales and has important implications for further theoretical development and policy implementation.

Exploratory Point Pattern Analysis for Modeling Biological Data

2013 ◽  
Vol 2 (1) ◽  
pp. 1-13
Author(s):  
Stelios Zimeras
Keyword(s):  
Biological Process ◽  
Biological Data ◽  
Point Pattern ◽  
Data Sets ◽  
Similar Data ◽  
Point Patterns ◽  
Spatial Point ◽  
Spatial Point Patterns ◽  
Statistical Measures ◽  
Physical Scale

Data in the form of sets of points, irregular distributed in a region of space could be identified in varies biological applications for examples the cell nuclei in a microscope section of tissue. These kinds of data sets are defined as spatial point patterns and the presentation of the positions in the space are defined as points. The spatial pattern generated by a biological process, can be affected by the physical scale on which the process is observed. With these spatial maps, the biologists will usually want a detailed description of the observed patterns. One way to achieve this is by forming a parametric stochastic model and fitting it to the data. The estimated values of the parameters could be used to compare similar data sets providing statistical measures for fitting models. Also a fitted model can provide an explanation of the biological processes. Model fitting especially for large data sets is difficult. For that reason, statistical methods can apply with main purpose to formulate a hypothesis for the implementation of biological process. Spatial statistics could be implemented using advance statistical techniques that explicitly analyses and simulates point structures data sets. Typically spatial point patterns are data that explain the location of point events. The author’s interest is the investigation of the significance of these patterns. In this work, an investigation of biological spatial data is analyzed, using advance statistical modeling techniques like kriging.

scholarly journals Does fluvial channel-belt clustering predict net sand to gross rock volume? Architectural metrics and point-pattern analysis of a digital outcrop model

2019 ◽  
Vol 89 (11) ◽  
pp. 1109-1126
Author(s):  
Alexander R. Koch ◽  
Cari L. Johnson ◽  
Lisa Stright
Keyword(s):  
Large Scale ◽  
Small Scale ◽  
Point Pattern ◽  
Point Patterns ◽  
Spatial Point ◽  
Channel Belt ◽  
John Henry Member ◽  
Scale Point ◽  
Belt Width ◽  
Digital Outcrop

ABSTRACT Spatial point-pattern analyses (PPAs) are used to quantify clustering, randomness, and uniformity of the distribution of channel belts in fluvial strata. Point patterns may reflect end-member fluvial architecture, e.g., uniform compensational stacking and avulsion-generated clustering, which may change laterally, especially at greater scales. To investigate spatial and temporal changes in fluvial systems, we performed PPA and architectural analyses on extensive outcrops of the Cretaceous John Henry Member of the Straight Cliffs Formation in southern Utah, USA. Digital outcrop models (DOMs) produced using unmanned aircraft system-based stereophotogrammetry form the basis of detailed interpretations of a 250-m-thick fluvial succession over a total outcrop length of 4.5 km. The outcrops are oriented roughly perpendicular to fluvial transport direction. This transverse cross-sectional exposure of the fluvial system allows a study of the system's variation along depositional strike. We developed a workflow that examines spatial point patterns using the quadrat method, and architectural metrics such as net sand to gross rock volume (NTG), amalgamation index, and channel-belt width and thickness within moving windows. Quadrat cell sizes that are ∼ 50% of the average channel-belt width-to-thickness ratio (16:1 aspect ratio) provide an optimized scale to investigate laterally elongate distributions of fluvial-channel-belt centroids. Large-scale quadrat point patterns were recognized using an array of four quadrat cells, each with 237× greater area than the median channel belt. Large-scale point patterns and NTG correlate negatively, which is a result of using centroid-based PPA on a dataset with disparately sized channel belts. Small-scale quadrat point patterns were recognized using an array of 16 quadrat cells, each with 21× greater area than the median channel belt. Small-scale point patterns and NTG correlate positively, and match previously observed stratigraphic trends in the fluvial John Henry Member, suggesting that these are regional trends. There are deviations from these trends in architectural statistics over small distances (hundreds of meters) which are interpreted to reflect autogenic avulsion processes. Small-scale autogenic processes result in architecture that is difficult to correlate between 1D datasets, for example when characterizing a reservoir using well logs. We show that 1D NTG provides the most accurate prediction for surrounding 2D architecture.

scholarly journals Filtering spatial point patterns using kernel densities

2021 ◽  
Vol 41 ◽  
pp. 100487
Author(s):  
Brian E. Vestal ◽  
Nichole E. Carlson ◽  
Debashis Ghosh
Keyword(s):  
Point Patterns ◽  
Spatial Point ◽  
Spatial Point Patterns

scholarly journals Envelope tests for spatial point patterns with and without simulation

Ecosphere ◽  
2016 ◽  
Vol 7 (6) ◽  
Author(s):  
Thorsten Wiegand ◽  
Pavel Grabarnik ◽  
Dietrich Stoyan
Keyword(s):  
Point Patterns ◽  
Spatial Point ◽  
Spatial Point Patterns

scholarly journals Spatial point-pattern analysis as a powerful tool in identifying pattern-process relationships in plant ecology: an updated review

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Mariem Ben-Said
Keyword(s):  
Spatial Patterns ◽  
Pattern Analysis ◽  
Biotic Interactions ◽  
Plant Ecology ◽  
Point Pattern Analysis ◽  
Point Pattern ◽  
Summary Statistics ◽  
Spatial Point Pattern ◽  
Spatial Point ◽  
Spatial Point Pattern Analysis

Abstract Background Ecological processes such as seedling establishment, biotic interactions, and mortality can leave footprints on species spatial structure that can be detectable through spatial point-pattern analysis (SPPA). Being widely used in plant ecology, SPPA is increasingly carried out to describe biotic interactions and interpret pattern-process relationships. However, some aspects are still subjected to a non-negligible debate such as required sample size (in terms of the number of points and plot area), the link between the low number of points and frequently observed random (or independent) patterns, and relating patterns to processes. In this paper, an overview of SPPA is given based on rich and updated literature providing guidance for ecologists (especially beginners) on summary statistics, uni-/bi-/multivariate analysis, unmarked/marked analysis, types of marks, etc. Some ambiguities in SPPA are also discussed. Results SPPA has a long history in plant ecology and is based on a large set of summary statistics aiming to describe species spatial patterns. Several mechanisms known to be responsible for species spatial patterns are actually investigated in different biomes and for different species. Natural processes, plant environmental conditions, and human intervention are interrelated and are key drivers of plant spatial distribution. In spite of being not recommended, small sample sizes are more common in SPPA. In some areas, periodic forest inventories and permanent plots are scarce although they are key tools for spatial data availability and plant dynamic monitoring. Conclusion The spatial position of plants is an interesting source of information that helps to make hypotheses about processes responsible for plant spatial structures. Despite the continuous progress of SPPA, some ambiguities require further clarifications.

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