Beyond the epsilon band: polygonal modeling of gradation/uncertainty in area-class maps

A spatial modeling technique is proposed to represent boundary uncertainty or gradation on area-class maps using a simple polygon tessellation with designated zones of indeterminacy or transition zones. The transition zone can be conceptualized as a dual of the epsilon band, but is more flexible and allows for a wide range of polygonal configurations, including polygons with sinuous boundaries, spurs, three-way transition zones, and null polygons. The model is specified using the medial axis to capture the general shape characteristics of a transition zone. Graph theoretic representation of an extended version of the medial axis captures key junctions in both shape and classification and is used to identify well-formed transition zones that can be logically and unambiguously handled by the model. A multivariate classification surface is specified by first defining degrees or probabilities of membership at every point on the medial axis and transition zone boundary. Degrees or probabilities of membership at all other points are defined by linear interpolation. The technique is illustrated with an example of a complex transition zone, and a simple isoline representation that can be derived from the model is presented. The proposed modeling technique promises to facilitate expert characterization of soil formations, ecological systems, and other types of areal units where gradation and/or boundary uncertainty are prevalent

A Plotless Density Estimator based on the Asymptotic Limit of Ordered Distance Estimation Values

Estimation of tree density from point-tree distances is an attractive option for quick inventory of new sites, but estimators that are unbiased in clustered and dispersed situations have not been found. Noting that bias of an estimator derived from distances to the kth nearest neighbor from a random point tends to decrease with increasing k, a method is proposed for estimating the limit of an asymptotic function through a set of ordered distance estimators. A standard asymptotic model is derived from the limiting case of a clustered distribution. The proposed estimator is evaluated against 13 types of simulated generating processes, including random, clustered, dispersed and mixed. Performance is compared with ordered distance estimation of the same rank, and with fixed-area sampling with the same number of trees tallied. The proposed estimator consistently performs better than ordered distance estimation, and nearly as well as fixed area sampling in all but the most clustered situations. The estimator also provides information regarding the degree of clustering or dispersion

A Sketch-based Language for Representing Uncertainty in the Locations of Origin of Herbarium Specimens

Uncertainty fields have been suggested as an appropriate model for retrospective georeferencing of herbarium specimens. Previous work has focused only on automated data capture methods, but techniques for manual data specification may be able to harness human spatial cognition skills to quickly interpret complex spatial propositions. This paper develops a formal modeling language by which location uncertainty fields can be derived from manually sketched features. The language consists of low-level specification of critical probability isolines from which a surface can be uniquely derived, and high-level specification of features and predicates from which low-level isolines can be derived. In a case study, five specimens of Kolsteletzkya pentacarpos housed in the Ted Bradley Herbarium at George Mason University are retrospectively georeferenced, and locational uncertainties of error distance, possibility region and uncertainty field representations are compared

A Sketch-based Language for Representing Uncertainty in the Locations of Origin of Herbarium Specimens

Uncertainty fields have been suggested as an appropriate model for retrospective georeferencing of herbarium specimens. Previous work has focused only on automated data capture methods, but techniques for manual data specification may be able to harness human spatial cognition skills to quickly interpret complex spatial propositions. This paper develops a formal modeling language by which location uncertainty fields can be derived from manually sketched features. The language consists of low-level specification of critical probability isolines from which a surface can be uniquely derived, and high-level specification of features and predicates from which low-level isolines can be derived. In a case study, five specimens of Kolsteletzkya pentacarpos housed in the Ted Bradley Herbarium at George Mason University are retrospectively georeferenced, and locational uncertainties of error distance, possibility region and uncertainty field representations are compared

Restricted random labeling: testing for between-group interaction after controlling for joint population and within-group spatial structure

Statistical measures of spatial interaction between multiple types of entities are commonly assessed against a null model of either toroidal shift (TS), which controls for spatial structure of individual subpopulations, or random labeling (RL), which controls for spatial structure of the joint population. Neither null model controls for both types of spatial structure simultaneously, although this may sometimes be desirable when more than two subpopulations are present. To address this, we propose a flexible framework for specifying null models that we refer to as restricted random labeling (rRL). Under rRL, a specified subset of individuals is restricted and other individuals are randomly relabeled. Within this framework, two specific null models are proposed for pairwise analysis within populations consisting of three or more subpopulations, to simultaneously control for spatial structure in the joint population and one or the other of the two subpopulations being analyzed. Formulas are presented for calculating expected nearest neighbor counts and co-location quotients within the proposed framework. Differences between TS, RL and rRL are illustrated by application to six types of generating processes in a simulation study, and to empirical datasets of tree species in a forest and crime locations in an urban setting. These examples show that rRL null models are typically stricter than either TS or RL, which often detect “interactions” that are an expected consequence either of the joint population pattern or of individual subpopulation patterns

Co-Location Analysis Engine

Software to support analysis of spatial interaction. Calculates the neighbor contingency table and co-location quotient (CLQ), and runs Monte Carlo simulation to test for significance under different null models including restricted random labeling (RRL)

A Plotless Density Estimator based on the Asymptotic Limit of Ordered Distance Estimation Values

Estimation of tree density from point-tree distances is an attractive option for quick inventory of new sites, but estimators that are unbiased in clustered and dispersed situations have not been found. Noting that bias of an estimator derived from distances to the kth nearest neighbor from a random point tends to decrease with increasing k, a method is proposed for estimating the limit of an asymptotic function through a set of ordered distance estimators. A standard asymptotic model is derived from the limiting case of a clustered distribution. The proposed estimator is evaluated against 13 types of simulated generating processes, including random, clustered, dispersed and mixed. Performance is compared with ordered distance estimation of the same rank, and with fixed-area sampling with the same number of trees tallied. The proposed estimator consistently performs better than ordered distance estimation, and nearly as well as fixed area sampling in all but the most clustered situations. The estimator also provides information regarding the degree of clustering or dispersion

Presettlement Surveyor Bias Estimator

Estimates bearing tree selection bias in the General Land Office (GLO) surveys, and similar surveys where distance to the nearest individual (tree) was calculated at each survey location (corner). Developed in Visual Basic.Net using MS Excel functions to calculate ANOVA and student T test

Co-Location Analysis Engine

Software to support analysis of spatial interaction. Calculates the neighbor contingency table and co-location quotient (CLQ), and runs Monte Carlo simulation to test for significance under different null models including restricted random labeling (RRL)

Georeferenced Image of William Morgan\u27s 1682 Map of London, England

Georeferencing performed by Ali AkbariMoghaddam, Paul Bocian, Jason Fachie, Alexander Goldstein, Brandon Haggerty, Ryan Kermicle, Joseph Lenhardt, Ryne Robertson, Lynn Schofield, Melinda Swinford, Srikanth Vykuntapu, Alicia Waller, Jeremy Wells The original image of Morgan’s 1682 map of London was downloaded in JPEG format from Wikimedia (http://commons.wikimedia.org/wiki/File:London_actually_surveyed_by_Wm_Morgan_1682.jpg). Georeferencing was accomplished in the spring of 2015 as a group project by the students of GEG 3860/5860: GIS II at Eastern Illinois University. Over 100 control points were identified by locating prominent landmarks and road intersections on both Morgan\u27s original map and OpenStreetMap (OSM) data for modern London. These points were then merged into a single file and examined for reliability, and the 68 control points considered most reliable were retained. Georeferencing was performed in a transverse Mercator projection with central meridian 0.09 degrees west of the Greenwich meridian. The map image was then rectified to the web Mercator projection for compatibility with web mapping services. Spatial accuracy with respect to the OSM data is estimated to be within 15-20 meters in the main portion of the map, including the area north and northwest of London Bridge and on the west side of the Thames near Buckingham Palace. Spatial error may be 50 meters or more in the southern and eastern portions and on the edges of the map. A full-detail zoomable preview of the map can be seen here: http://arcg.is/1QEoj2g For more information, contact [email protected]