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Stefan Sommer - One of the best experts on this subject based on the ideXlab platform.

  • Currents and K-Functions for Fiber Point Processes.
    arXiv: Methodology, 2021
    Co-Authors: Pernille Eh. Hansen, Jon Sporring, Rasmus Waagepetersen, Anne Marie Svane, Hans Jt. Stephensen, Stine Hasselholt, Stefan Sommer
    Abstract:

    Analysis of images of sets of fibers such as myelin sheaths or sKeletal muscles must account for both the spatial distribution of fibers and differences in fiber shape. This necessitates a combination of point process and shape analysis methodology. In this paper, we develop a K-Function for shape-valued point processes by embedding shapes as currents, thus equipping the point process domain with metric structure inherited from a reproducing Kernel Hilbert space. We extend Ripley's K-Function which measures deviations from spatial homogeneity of point processes to fiber data. The paper provides a theoretical account of the statistical foundation of the K-Function and its extension to fiber data, and we test the developed K-Function on simulated as well as real data sets. This includes a fiber data set consisting of myelin sheaths, visualizing the spatial and fiber shape behavior of myelin configurations at different debts.

  • IPMI - Generalizations of Ripley's K-Function with Application to Space Curves.
    Lecture Notes in Computer Science, 2019
    Co-Authors: Jon Sporring, Rasmus Waagepetersen, Stefan Sommer
    Abstract:

    The intensity Function and Ripley’s K-Function have been used extensively in the literature to describe the first and second moment structure of spatial point sets. This has many applications including describing the statistical structure of synaptic vesicles. Some attempts have been made to extend Ripley’s K-Function to curve pieces. Such an extension can be used to describe the statistical structure of muscle fibers and brain fiber tracKs. In this paper, we taKe a computational perspective and construct new and very general variants of Ripley’s K-Function for curves pieces, surface patches etc. We discuss the method from [3] and compare it with our generalizations theoretically, and we give examples demonstrating the difference in their ability to separate sets of curve pieces.

  • Generalizations of Ripley's K-Function with Application to Space Curves.
    arXiv: Methodology, 2018
    Co-Authors: Jon Sporring, Rasmus Waagepetersen, Stefan Sommer
    Abstract:

    The intensity Function and Ripley's K-Function have been used extensively in the literature to describe the first and second moment structure of spatial point sets. This has many applications including describing the statistical structure of synaptic vesicles. Some attempts have been made to extend Ripley's K-Function to curve pieces. Such an extension can be used to describe the statistical structure of muscle fibers and brain fiber tracKs. In this paper, we taKe a computational perspective and construct new and very general variants of Ripley's K-Function for curves pieces, surface patches etc. We discuss the method from [Chiu, Stoyan, Kendall, & MecKe 2013] and compare it with our generalizations theoretically, and we give examples demonstrating the difference in their ability to separate sets of curve pieces.

Patrik Krieger - One of the best experts on this subject based on the ideXlab platform.

  • Spatial Point Pattern Analysis of Neurons Using Ripley's K-Function in 3D
    Frontiers in neuroinformatics, 2010
    Co-Authors: Mehrdad Jafari-mamaghani, Mikael Andersson, Patrik Krieger
    Abstract:

    The aim of this paper is to apply a non-parametric statistical tool, Ripley’s KFunction, to analyze the 3-dimensional distribution of pyramidal neurons. Ripley’s K-Function is a widely used tool in spatial point pattern analysis. There are several approaches in 2D domains in which this Function is executed and analyzed. Drawing consistent inferences on the underlying 3D point pattern distributions in various applications is of great importance as the acquisition of 3D biological data poses lesser of challenge due to technological progress. As of now, most of the applications of Ripley’s K-Function in 3D domains do not focus on the phenomenon of edge correction, which is discussed thoroughly in this paper. The main goal is to extend the theoretical and practical utilization of Ripley’s K-Function and corresponding tests based on bootstrap resampling from 2D to 3D domains.

Jean-claude Thill - One of the best experts on this subject based on the ideXlab platform.

  • Flow Cross K-Function: A Bivariate Flow Analytical Method
    International Journal of Geographical Information Science, 2019
    Co-Authors: Ran Tao, Jean-claude Thill
    Abstract:

    ABSTRACTSpatial flow data represent meaningful interaction activities between pairs of corresponding locations, such as daily commuting, animal migration, and merchandise shipping. Despite recent a...

  • IF&GIS - Detecting Clustering Scales with the Incremental K-Function: Comparison Tests on Actual and Simulated Geospatial Datasets
    Lecture Notes in Geoinformation and Cartography, 2015
    Co-Authors: Ran Tao, Jean-claude Thill, Ikuho Yamada
    Abstract:

    The detection of so-called hot-spots in point datasets is important to generalize the spatial structures and properties in geospatial datasets. This is all the more important when spatial big data analytics is concerned. The K-Function is regarded as one of the most effective methods to detect departures from randomness, high concentrations of point events and to examine the scale properties of a spatial point pattern. However, when applied to a pattern exhibiting local clusters, it can hardly determine the true scales of an observed pattern. We use a variant of the K-Function that examines the number of events within a particular distance increment rather than the total number of events within a distance range. We compare the Incremental K-Function to the standard K-Function in terms of its fundamental properties and demonstrate the differences using several simulated point processes, which allow us to explore the range of conditions under which differences are obtained, as well as on a real-world geospatial dataset.

  • Local Indicators of NetworK-Constrained Clusters in Spatial Point Patterns
    Geographical Analysis, 2007
    Co-Authors: Ikuho Yamada, Jean-claude Thill
    Abstract:

    The detection of clustering in a spatial phenomenon of interest is an important issue in spatial pattern analysis. While traditional methods mostly rely on the planar space assumption, many spatial phenomena defy the logic of this assumption. For instance, certain spatial phenomena related to human activities are inherently constrained by a transportation networK because of our strong dependence on the transportation system. This article thus introduces an exploratory spatial data analysis method named local indicators of networK-constrained clusters (LINCS), for detecting local-scale clustering in a spatial phenomenon that is constrained by a networK space. The LINCS method presented here applies to a set of point events distributed over the networK space. It is based on the networK K-Function, which is designed to determine whether an event distribution has a significant clustering tendency with respect to the networK space. First, an incremental K-Function is developed so as to identify cluster size more explicitly than the original K-Function does. Second, to enable identification of cluster locations, a local K-Function is derived by decomposing and modifying the original networK K-Function. The local K-Function LINCS, which is referred to as KLINCS, is tested on the distribution of 1997 highway vehicle crashes in the Buffalo, NY area. Also discussed is an adjustment of the KLINCS method for the nonuniformity of the population at risK over the networK. As traffic volume can be seen as a surrogate of the population exposed to a risK of vehicle crashes, the spatial distribution of vehicle crashes is examined in relation to that of traffic volumes on the networK. The results of the KLINCS analysis are validated through a comparison with priority investigation locations (PILs) designated by the New YorK State Department of Transportation.

  • comparison of planar and networK K Functions in traffic accident analysis
    Journal of Transport Geography, 2004
    Co-Authors: Ikuho Yamada, Jean-claude Thill
    Abstract:

    The networK and planar K-Function methods are applied to traffic accident data to illustrate the risK of false positive detection associated with the use of a statistic designed for a planar space to analyze a networK-constrained phenomenon. We also demonstrate the benefits of using a method specifically designed for a networK space. The results clearly indicate that the planar K-Function analysis is problematic since it entails a significant chance of over-detecting clustered patterns. Analyses are implemented based on Monte Carlo simulation and applied to 1997 traffic accident data in the Buffalo, NY area.

Zousen Cui - One of the best experts on this subject based on the ideXlab platform.

  • Optimizing and accelerating space–time Ripley ’s K Function based on Apache SparK for distributed spatiotemporal point pattern analysis
    Future Generation Computer Systems, 2020
    Co-Authors: Yuan Wang, Zhipeng Gui, Dehua Peng, Zousen Cui
    Abstract:

    Abstract With increasing point of interest (POI) datasets available with fine-grained spatial and temporal attributes, space–time Ripley’s K Function has been regarded as a powerful approach to analyze spatiotemporal point process. However, space–time Ripley’s K Function is computationally intensive for point-wise distance comparisons, edge correction and simulations for significance testing. Parallel computing technologies liKe OpenMP, MPI and CUDA have been leveraged to accelerate the K Function, and related experiments have demonstrated the substantial acceleration. Nevertheless, previous worKs have not extended optimization of Ripley’s K Function from space dimension to space–time dimension. Without sophisticated spatiotemporal query and partitioning mechanisms, extra computational overhead can be problematic. Meanwhile, these researches were limited by the restricted scalability and relative expensive programming cost of parallel frameworKs and impeded their applications for large POI dataset and Ripley’s K Function variations. This paper presents a distributed computing method to accelerate space–time Ripley’s K Function upon state-of-the-art distributed computing frameworK Apache SparK, and four strategies are adopted to simplify calculation procedures and accelerate distributed computing respectively: (1) spatiotemporal index based on R-tree is utilized to retrieve potential spatiotemporally neighboring points with less distance comparison; (2) spatiotemporal edge correction weights are reused by 2-tier cache to reduce repetitive computation in L value estimation and simulations; (3) spatiotemporal partitioning using KDB-tree is adopted to decrease ghost buffer redundancy in partitions and support near-balanced distributed processing; (4) customized serialization with compact representations of spatiotemporal objects and indexes is developed to lower the cost of data transmission. Based on the optimized method, a web-based visual analytics frameworK prototype has been developed. Experiments prove the feasibility and time efficiency of the proposed method, and also demonstrate its value on promoting applications of space–time Ripley’s K Function in ecology, geography, sociology, economics, urban transportation and other fields.

F. Goreaud - One of the best experts on this subject based on the ideXlab platform.

  • ads pacKage for r a fast unbiased implementation of the K Function family for studying spatial point patterns in irregular shaped sampling windows
    Journal of Statistical Software, 2015
    Co-Authors: R. Pelissier, F. Goreaud
    Abstract:

    ads is an R pacKage that performs multi-scale spatial point pattern analyses through methods derived from Ripley's K-Function. These methods apply to univariate, multivariate or marKed point data mapped in a rectangular, circular or irregular-shaped sampling window. Specific tests of statistical significance based on Monte Carlo simulations are associated to these methods. The main features of ads is to call fast C subroutines for computing Ripley's unbiased local correction of edge effects for various sampling window configurations and for performing Monte Carlo simulations. It thus allows one to analyze large datasets and to compute robust confidence envelopes. This paper is an introduction to ads version 1.5, focusing on its complementarity with the other R pacKages for spatial point pattern analysis, and on recent original developments towards the introduction of multivariate Functions for analyzing spatial pattern of species diversity.

  • On explicit formulas of edge effect correction for Ripley' s K-Function
    Journal of Vegetation Science, 1999
    Co-Authors: F. Goreaud, R. Pelissier
    Abstract:

    The analysis of spatial pattern in plant ecology usually implies the solution of some edge effect problems. We present in this paper some explicit formulas of edge effect correction that should enable plant ecologists to analyse a wider range of real field data. We consider the local correcting factor of edge effect for Ripley's K-Function, that can also be used for other statistics of spatial analysis based on the counting of neighbours within a given distance. For both circular and rectangular study areas, we provide a review of explicit formulas and an extension of these formulas for long and narrow plots. In the case of irregular-shaped study plots, we propose a generalization of the method that computes edge effect correction by excluding triangular surfaces from a simple (rectangular or circular) initial shape. A short example in forest ecology, where the soil characteristics determine a study plot of complex shape, illustrate how this edge effect correction can be effective to avoid misinterpretations.

  • On explicit formulas of edge effect correction for Ripley's K‐Function
    Journal of Vegetation Science, 1999
    Co-Authors: F. Goreaud, R. Pelissier
    Abstract:

    . The analysis of spatial pattern in plant ecology usually implies the solution of some edge effect problems. We present in this paper some explicit formulas of edge effect correction that should enable plant ecologists to analyse a wider range of real field data. We consider the local correcting factor of edge effect for Ripley's K-Function, that can also be used for other statistics of spatial analysis based on the counting of neighbours within a given distance. For both circular and rectangular study areas, we provide a review of explicit formulas and an extension of these formulas for long and narrow plots. In the case of irregular-shaped study plots, we propose a generalization of the method that computes edge effect correction by excluding triangular surfaces from a simple (rectangular or circular) initial shape. An example in forest ecology, where the soil characteristics determine a study plot of complex shape, illustrates how this edge effect correction can be effective in avoiding misinterpretations.