Models of Spatial Information
Introduction
In the previous lecture, a discussion on cartography was initiated. The focus was on the abstraction of real-world objects into representations such as points, lines, and areas for map usage.
The process outlined in the previous lecture involved transitioning from geographic data to geometric classes, feature characteristics, and measurement levels.
Today's lecture aims to expand on this discussion by examining models of spatial information, moving from conceptual models to data models, to logical models.
The two most common model types discussed will be vector and raster models.
Conceptual Models of Spatial Information
Spatial information can be modeled in two standard ways:
Object-Based Models:
Treat spatial information as populated by discrete entities (objects) that possess georeferenced coordinates.
The focus is on individual objects, leading to data models and structures that are object-oriented.
Field-Based Models:
Treat spatial information as collections of spatial distributions formalized as mathematical functions from a spatial framework.
Key terms for understanding field-based models include:
Spatial Framework: Divides an area into a finite tessellation of spatial units.
Mathematical Function: Consists of values in a numerical format.
These models typically segment an area into a grid, populating each cell with numerical values. Field-based models focus on location, resulting in data models and structures that are location-based.
Data Models
From the conceptual models arise spatial data models, which fall into two categories: vector and raster.
Vector Data Models:
Originating from object-based models, vector data models use basic units of objects such as points, lines, and polygons.
Objects have clear definitions, making their identification implicit, but their locations require explicit encoding.
Spatial locations are expressed in Cartesian coordinates on a Euclidean plane (refer to Figure 1A).
Raster Data Models:
In raster models, the fundamental data unit is spatial, usually represented as a cell in a tessellated array (rows and columns).
Each cell has implicit x and y coordinates due to known size and origin, but object information requires explicit designation through numeric codes (refer to Figure 1B).
Logical Models
Transitioning to logical models focuses on specific data structures and management of how objects are stored and manipulated within various hardware/software platforms.
While different GIS (Geographic Information System) software may employ distinct logical models, there are critical similarities across all platforms.
In this course, the specifics of ArcGIS software will be examined during lab sessions.
Vector Data Structure
Vector structures are tailored to organize point, line, and polygon objects alongside their attribute data.
A typical setup involves tables containing ID numbers for each object, allowing for connection to a variety of tabular attribute data (see Figure 2).
This connection method, which integrates geometric data with tabular data, is known as the georelational model.
Coordinate storage can occur in different ways:
Often as BLOBs (Binary Large Objects) in standard attribute tables.
Alternatively as hidden files linked to attribute tables through ID numbers.
Vector analysis typically employs overlays of georeferenced data themes, producing new combined data themes that retain attributes from the original datasets (see Figure 3).
Raster Data Structure
Raster data are organized in a grid format consisting of rows and columns, with each intersection termed a cell.
Each cell possesses specific x and y coordinates corresponding to real-world locations and contains a z value representing various data types (e.g., elevation, census data, land cover).
Color assignments when displaying raster data are derived from the numeric values held in each cell (refer to Figure 4).
Analysis within a raster context involves mathematical manipulation of cell values, which can focus on individual or neighborhood cell operations guided by equations or statistical models (see Figure 5).
Strengths in Structures
Both raster and vector data structures exhibit unique strengths and weaknesses. Table 1 offers a concise comparison:
Raster Strengths:
Geographic position is implicit, eliminating the need for explicit storage of x,y coordinates for objects.
Neighboring locations are easily analyzed since neighboring cells represent adjacent geographic areas.
Can handle both discrete and continuous data effectively.
Simplified data storage due to only individual objects needing retrieval for processing.
Analytical algorithms are easier to design and apply due to numeric representation.
Can incorporate diverse descriptive data in tabular format linked to single features.
Compatibility with remotely sensed data, yielding superior cartographic outputs.
Vector Strengths:
The familiar point-line-polygon format facilitates understanding by users.
Smaller storage demands arise from only needing to store individual objects instead of grid cells.
Summary
This lecture explored prevalent methods for spatial information representation, detailing the progression from conceptual models, through data models, to logical models.
In the upcoming labs, students will delve into the specific data structures utilized in ESRI software.
Bonus Section: Early Raster Map
A historical example of raster data is illustrated by the mosaic map from the Byzantine period located in a church in Madaba, Jordan. The map delineates the known world during that time, displaying key urban features such as Jerusalem’s primary streets, significant buildings, and gates.
This mosaic exemplifies an early non-digital raster data structure, forming an intricate pattern of colored stone tesserae that interpret spatial information narratively.
References Cited
Bolstad, P. (2002). GIS fundamentals: a first text on geographic information systems. White Bear Lake, Minn., Eider Press.