--- jupytext: text_representation: extension: .md format_name: myst format_version: 0.13 jupytext_version: 1.11.5 kernelspec: display_name: Python 3 language: python name: python3 --- # Neighborhood Relation Operations, Connectivity, and Distance Analysis Topics: * Neighborhood Relation Operations * Spatial Connectivity Analysis * Distance Analysis ## Map Compute Framework * Three kinds of analysis/mapping units (MUs) in maps: * Cells, raster zones, and features * Four kinds of operations: * Local, focal, and global operations based on the spatial scope of the neighborhood * Neighborhood relation operations | Mapping Units | Neighborhood Relation: Local | Neighborhood Relation: Focal | Neighborhood Relation: Global | | :--- | :--- | :--- | :--- | | Cells | Local | Focal | Global | | Raster zones | Local | Focal | Global | | Features (vectors) | Local | | | ## Neighborhood Relation Operations * Local, focal, and global operations manipulate the data within the neighborhood associated with a focus MU. * Neighborhood relation operations characterize all the neighborhoods associated with the MUs on a map. * Example: **NbrLocation** represents the location covered by all the neighborhoods of a set of features (points, lines, or polygons). ## Siren Population Coverage Analysis (Vector Data Model) * Circle neighborhood is created for each siren point. * Location covered by all neighborhoods is found by combining all circle neighborhoods into a multi-part coverage polygon. * This is a neighborhood relation operation (NbrLocation). * Local sum is performed using combined buffers as the mapping unit. * Effective neighbors are found by intersecting the coverage polygon with census blocks. ## NbrLocation with Raster Distance Neighborhoods * The operation can be performed with raster data using distance-based neighborhoods. * Example: A neighborhood defined by distance d <= 3 cell units. ## Buffer Tool as a Neighborhood Relation Operation * The Buffer tool in GIS is a neighborhood relation operation where the buffer is the neighborhood of each feature. * It creates an output map as a single multi-part polygon representing the location covered by at least one neighborhood. * Alternatively, it can create a set of isolated polygons, each with a unique ID. ## NbrLocationFrequency Operation * For features: Calculates the frequency of a location that belongs to overlapping neighborhoods. * ArcGIS Pro Tool: "Count Overlapping Features" generates planarized overlapping features with a count written to the output. * For cells: A value raster specifies MUs. * Neighborhoods can include "+", 3x3 window, zonal, or watershed neighborhoods. ## Degree of Neighborhood Overlapping (NbrOverlapDegree) * Quantifies the degree of neighborhood overlapping. * For 2 neighborhoods: (Area of Intersection) / (Area of Union), resulting in a value between 0 and 1. * For more than 2 neighborhoods: (Frequency weighted area of locations with frequency >=2) / (Area of locations with frequency >=1). * Typical values: * Local neighborhoods: 0 (no overlap). * Focal neighborhoods (3x3 window): approximately 0.27. * Zonal neighborhoods: example value of 0.52. * Global neighborhoods: always 1. ## MU Graph Through Neighborhoods (NbrGraph) * An NbrGraph operation forms a mapping unit spatial graph through MU neighborhoods. * A neighborhood defines a relationship where a MU is "connected" to its neighbors, forming a link. * Interactions can occur: * When a MU is in another MU's neighborhood. * When a MU's neighborhood co-locates with the neighborhood of another MU (e.g., buffers overlap). * MUs act as nodes with geographical locations, and links among MUs have weights characterizing their relation. ## Spatial Connectivity Analysis * Connectivity analysis identifies groups of connected MUs, known as sub-graphs or components. * MU graphs can be formed by various neighborhoods: * Spatial adjacency (4- or 8-connectivity). * Distance-based neighborhoods. * Watershed or Viewshed. ## Spatial Adjacency as Neighborhood * A cell is spatially adjacent to its immediate neighbors. * 4-adjacency ("+" neighborhood): Cells sharing an edge. * 8-adjacency (3x3 window neighborhood): Cells sharing an edge or a point. * Adjacency usually exists between cells with the same value (e.g., foreground vs. background). ## Identifying Connected Regions (RegionGroup) * RegionGroup identifies and groups connected cells with the same value into regions. * A zone consists of all cells with the same value. * A region (or component) consists of cells that have the same value AND are spatially connected. * Each unique region is assigned a unique ID number. ## Connectivity with Distance-Based Neighborhoods * Connectivity can be defined by distance rather than just adjacency. * A 1-cell radius circle is equivalent to 4-adjacency. * A square root of 2 cell size radius is equivalent to 8-adjacency. * Cells may be connected even if not immediately adjacent, depending on the neighborhood radius used. ## Nearest Neighbor Connectivity for Features * The nearest point can be defined as the neighborhood of a point. * This forms a directed graph since nearness is not always symmetric. * Sub-graph analysis then groups these points, lines, or polygons based on these connections. ## Euclidean Distance and Direction * Euclidean Distance: Calculates the straight-line distance to the nearest source. * Euclidean Direction: Calculates the direction (in degrees) to the nearest source. * These are treated as Global Operations within the framework. ## Cost Distance Analysis * Movement cost varies across a friction surface. * Accumulated Cost Surface: A global operation determining the minimum cost to reach a source. * Identify the least-cost path based on the accumulated surface. ## Proximity Regions (Thiessen Polygons) * A neighborhood relation operation where the study area is divided into regions based on the nearest source feature. * Boundaries are the perpendicular bisectors of the lines connecting neighboring source points. ## Identity of the Nearest Source Zone * Every cell receives the ID of the nearest source feature. * This is also referred to as "Allocation" in GIS software. * In this operation, cells are the mapping units and the neighborhood is the nearest source zone.