Representation and Data Models

Introduction

Field-Based Model

• Raster
• Quadtree

Polygon-Based Model

• Arc/Node
• Triangulated Irregular Network (TIN)

Figure 9-2.1  Vector Data Structure

Field-Based Model

The field-based model is sometimes referred to as being "map-oriented" since the management of attributes is handled by an a pre-defined sampling scheme, regardless of the shape of the objects in a map.

This emphasis on a systematic spatial sampling framework makes field-based data structures most effective for those data whose attributes vary continuously over space. There is no explicit identification of the contiguity of neighboring attributes in the field-based model.

Polygon-Based Model

The polygon-based model is sometimes referred to as being "object-oriented" since attribute data are tagged directly to homogenous objects whose shape has no predetermined limits.

The focus on homogenous regions in the polygon based model allows the attributes of extensive, homogenous features to be managed more efficiently than the field-based approach. Attributes of a feature can be tracked using a single identification code, and the contiguity of these attributes over space is explicit in the data model.

• Vector based systems are often joined to a relational database management system (RDBMS)
• The RDBMS may be used to keep track of the topological relationships which join points into lines and lines into polygons.
• Systems using an RDBMS allow tabular data from other sources to be linked to map features.
• A RDBMS allows sophisticated queries regarding the multiple attributes of features in the GIS.

The logical basis for determining connectivity of points, lines, and areas in the GIS. Polygon-based data models must rigidly enforce topology in order to determine whether arbitrarily located points are located inside or outside of a given polygon.

• The most accurate data structure is dependent on the features being sampled.
• The polygon model is most useful in cases where changes in land characteristics occur along well defined boundaries between relatively homogenous spatial units.
• Because vector-based systems define objects by their boundaries, geometric representations of homogenous targets are generally more accurate than raster systems.
• Mapped boundaries are often rough approximations of broad zones of transition and the regions they define are often far from homogenous.
• Those features which display continuous variation over space, or for which the scale of observation makes precise taxonomic determination impossible, might be quantified most effectively with the systematic sampling of the raster structure.

Problems with converting vector maps to a raster structure include:

• The creation of stair-stepped boundaries
• Small shifts in the position of objects
• The deletion of small features

• Potentially massive data volumes
• Difficulties in line generalization
• Topological confusion

Vector-to-Raster Conversion

• The fixed grid of the raster data structure invariably leads to a jagged, or stair-stepped, representation of polygon boundaries which are oriented at an angle to the grid.
• By forcing real world features into a fixed raster grid, feature boundaries will shift by as much as half the dimension of the grid cells.
• The typical conversion rule of assigning values using that class which occupies the greatest proportion of the grid cell may result in the deletion of features which are smaller than a grid cell in either the X or Y dimension.
• Not only might small patches be deleted, but extensive narrow features such as roads or streams may drop out as well.

Figure 9-2.2  Vector-to-Raster Conversion Errors

Raster-to-Vector Conversion: Data Volumes

In the extreme, a single pixel with a value different from all its neighbors may require a single byte in a raster structure. In a vector structure there would be:

• 4 sets of X,Y coordinates for each corner,
• Each X and Y would require at least a 4 byte floating point value
• Depending on the implementation, the database might require additional fields to:
• Link these points into line segments
• Link the line segments into a single polygon
• Create an extra record in at least one attribute table.

Figure 10-2.3  Data Volume Problems

Raster-to-Vector Conversion: Line Generalization

• The degree of generalization in the boundaries of features in vector based maps is generally tied to the scale of data acquisition.
• Raster-to-vector conversion routines may have difficulty in identifying the those points along a raster boundary which best define a shape.
• If all points are used in the conversion, data volumes will be larger than required, and features will retain an undesirable stair-stepped artifact along angled lines.
• Vector based GIS packages usually provide functions for line generalization.

Figure 9-2.4  Line Generalization

Raster-to-Vector Conversion: Topological Confusion

Two problems may cause ambiguity regarding the connectivity of pixels in the conversion process:

• The space between two similar objects may be less than a pixel in width, so there will be no obvious boundary between them in a raster file. After conversion the vector based GIS will treat these two objects as a single feature.
• There may be multiple ways in which pixels might be connected when features are a single pixel in width or are only connected across a diagonal.

Figure 9-2.5  Topological Errors

Methods for mitigating problems in data conversion

• Filter raster data prior to performing a conversion to vector data, so that there are no single pixel polygons or ambiguous connections between proximate features.
• Use a weighting scheme when converting vector maps to a raster structure so that important classes do not drop out when they cover small areas. This will unfortunately bias the area statistics of the resulting map.
• Select the class located at the center of each pixel location when converting from vector to raster. This will tend to maintain smaller features and will preserve overall area statistics. However, this method in no way guarantees that the label of a specific pixel corresponds to the predominant class at that location.
• Use line generalization functions in the GIS after converting a raster file to a vector data structure. This will reduce unnecessary points, but may also distort shapes in undesirable ways if not used with caution.
• Use additional data layers in the GIS to provide guidance when editing topology of features after raster-to-vector conversion (feature snapping).