The Map Compute Framework

5. The Map Compute Framework#

5.1. Topics#

  • Overview of spatial data analysis

  • Overview of Map Compute Framework (MCF)

  • MCF vs Map Algebra (Cartographic Modelling)

5.2. Spatial Data Analysis: A Continuum of Sophistication#

  • Measure/Mapping

    • Systematically collecting geospatial data (location + attributes)

    • Create regular maps ({location: {attributes}})

  • Visualize

    • Present geospatial data for human interpretation and understanding

    • Show maps (variation in space)

  • Query

    • Maps as stored functions

    • Attribute, spatial and compound queries

    • {location: {attributes}}

    • Linkage between location and attributes

  • Predict/estimate value at a location/MU

    • \(a = f(l)\)

    • Entanglement between location and attributes (population)

5.3. Spatial Data Analysis: A Continuum of Sophistication#

  • Model geospatial interactional relationships and processes

    • Exchange of matter, energy and information in space

    • Create meta-maps ({location: {(location: {attributes})})

  • Fundamental geospatial interactional relationships

    • Co-locational relationship

    • Distance as a proxy of interactional relationship

      • Euclidean and non-Euclidean distance (cost distance)

  • Spatial auto-correlation

    • How attribute is self-correlated in space

    • First law of geography

  • Domain geospatial interactional relationships

    • Physical, biological and social processes involved in the exchange of matter, energy and information on or close to earth surface

    • Hydrology, ATM, etc.

5.4. Map Compute Framework (MCF)#

  • A comprehensive framework for analyzing geospatial data

    • Based on the concept of “Map as Function”

    • Focuses on the “Compute” part of GIS

  • Two components

    • Data model: How to represent geospatial data (MUs and attributes)

    • Computational model: How to manipulate and analyze geospatial data

  • Key elements

    • Mapping Units (MU)

    • Attributes

    • Spatial relationships (neighborhoods)

    • Operations (local, focal, zonal, global)

5.5. Mapping Units (MU)#

  • Discrete divisions of space

  • Used as the domain of the map function

  • Types of MUs

    • Regular: Raster cells (squares, hexagons, etc.)

    • Irregular: Points, lines, polygons (vector features)

  • Resolution and precision

    • Size and shape of MUs affect the quality of data and analysis

5.6. Attributes#

  • Qualitative or quantitative characteristics of a MU

  • Used as the co-domain of the map function

  • Levels of measurement

    • Nominal, ordinal, interval, ratio

  • Single-valued vs. multi-valued maps

5.7. Spatial Relationships (Neighborhoods)#

  • How MUs are related to each other in space

  • Used to model interactional processes

  • Types of neighborhoods

    • Immediate: Adjacent MUs (topology)

    • Proximity: MUs within a certain distance

    • Domain-specific: Watersheds, viewsheds, network connectivity

  • Neighborhood is a mapping: \(MU \to \{MU\}\)

5.8. Map Operations#

  • Mathematical or logical operations applied to maps

  • Classified by their spatial scope (Tomlin, 1990)

  • Local operations

    • Output value at a location depends only on the input value(s) at the same location

  • Focal operations

    • Output value depends on the input values within a neighborhood of the location

  • Zonal operations

    • Output value depends on the input values within a predefined zone

  • Global operations

    • Output value depends on the input values of the entire map

5.9. Local Operations#

  • \(Value_{new} = f(Value_{old})\)

  • Cell-by-cell or feature-by-feature processing

  • Examples:

    • Scalar math (e.g., \(map \times 2\))

    • Map overlay (e.g., \(map_A + map_B\))

    • Reclassification

5.10. Focal Operations#

  • \(Value_{new} = f(Values\ in\ neighborhood)\)

  • Also known as neighborhood operations

  • Requires a predefined neighborhood (kernel/window)

  • Examples:

    • Smoothing (mean), edge detection, slope, aspect

    • Focal flow (hydrology)

5.11. Zonal Operations#

  • \(Value_{new} = f(Values\ in\ zone)\)

  • Two input maps:

    • Zone map: Defines the zones

    • Value map: Contains the attributes to be summarized

  • Examples:

    • Average elevation per watershed

    • Total population per county

5.12. Global Operations#

  • \(Value_{new} = f(Values\ in\ entire\ map)\)

  • Examples:

    • Global mean, maximum, or minimum

    • Euclidean distance (from a source to all other points)

    • Least cost path analysis

5.13. Tomlin’s Map Algebra#

  • Simple but powerful approach/tools for analyzing geospatial raster data

    • Primary way of analyzing raster data

    • Implemented in commercial/open source GIS software

  • All the existing extensions followed the original framework

    • Local, focal, zonal

  • Remaining issues

    • Inconsistent structure (focal vs zonal)

    • Limited (enumerated) neighborhoods

    • Only available for raster data

5.14. Map Algebra Operations in the MC Framework#

  • Local operations

    • Cells as MUs

  • Focal operations

    • Cells as MUs

    • Predefined (and limited) neighborhoods

    • Doesn’t distinguish using and modeling geospatial interactional relationships

  • Zonal operations

    • Zones as neighborhoods (focal operations)

    • Zones as analysis units (local operations)

  • Concepts in MC but labs and tools are still using MA!

    • Map Compute Engine (MCE) is not entirely implemented yet

Mapping Units

Neighborhood Relation: Local

Neighborhood Relation: Focal

Neighborhood Relation: Global

Cells

Local

Focal

Global

Raster zones

Zonal

Features (vectors)

5.15. Readings#

  • Tomlin, 2017 Cartographic modeling, The International Encyclopedia of Geography

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