Lecture 09: Data Structure Transformations

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Lecture 09 Data Structure Transformations

• Geography 128
• Analytical and Computer Cartography
• Spring 2007
• Department of Geography
• University of California, Santa Barbara

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Why Transform Between Structures?

• "In virtually all mapping applications it becomes
  necessary to convert from one cartographic data
  structure to another. The ability to perform
  these object-to-object transformations often is
  the single most critical determinant of a mapping
  system's flexibility" (Clarke, 1995)
• Geocoding stamps coordinate system, resolution
  and projection onto objects
• Data usually in generic formats at first
• Can save space, gain flexibility, decrease
  processing time
• Suit demands of analysis and modeling
• Suit demands of map symbolization (e.g. fonts)

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Generalization Transformations- Why Generalize?

• Conversion of data collected at higher
  resolutions to lower resolution. Less data and
  less detail.
• Simplicity -gt clarity
• Information will be lost

John Krygier and Denis Wood, Making Maps a
visual guide to map design for GIS
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Generalization Transformations - Point-to-Point

• Centroid
• Map projections
• Usually be seen as a part of Geocoding process

USGS 1250,000 3-arc second DEM format (1-degree
block)
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Generalization Transformations - Line-to-Line
Generalization

• N-th Point retention
• Equidistant re-sampling
• Douglas-Peucker

Douglas-Peucker line generalization
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Generalization Transformations - Line-to-Line
Enhancement

• Splines
• Bezier Curves
• Polynomial Functions
• Trigonometric Functions (Fourier-based)

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Generalization Transformations - Area-to-Area
Population at counties

• Problem is given one set of regions, convert to
  another
• Example Convert census tract data to zip codes
  for marketing
• Example Convert crime data by police precinct to
  school district
• May require dividing non-divisible measures, e.g
  population
• Areal Interpolation
• Greatest common geographic units Full overlap
  set for reassignment

Population at watersheds?
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Generalization Transformations - Area-to-Area

• Algorithm for Overlay
• 1. Intersections
• 2. Chain splitting
• 3. Polygon reassembly
• 4. Labeling and attribution

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Generalization Transformations Volume-to-Volume

• Common conversion between two major data
  structures, vector (TIN) and grid
• Often via points and interpolation
• Change cell size
• Generate a new grid
• Compute the intersect
• Interpolate from neighboring cells
• Problem of VIPs

www.soi.city.ac.uk/jwo/phd/04param.php
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Vector-to-Raster Transformations

• Easy compared to inverse, a form of re-sampling
• Grid must relate to coordinates (extent, bounds,
  resolution, orientation)
• Rasters can be square, rectangular, hexagonal.
• Resample at minimum r/2

• Problem What value goes into the cell?
• Dominant criterion
• Center-point criterion
• Separate arrays for dimensions and binary data?
• Index entries look up tables

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Vector-to-Raster Transformations (cnt.)-
Algorithm

• Convert form of vectors (e.g. to slope intercept)
  
• Sample and convert to grid indices
• Thin fat lines
• Compute implicit inclusion (anti-alias)

www.inf.u-szeged.hu/palagyi/skel/skel.html
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Vector-to-Raster Transformations (cnt.)- Example
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Raster-to-Vector Transformations

• Much harder, more error prone.
• May involve cartographer intervention
• Importance of alignment
• Can do points, lines, area

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Raster-to-Vector Transformations- Algorithm

• Skeletonization and Thinning
• Peeling
• Expanding
• Medial Axis
• Feature Extraction
• Topological Reconstruction

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Raster-to-Vector Transformations- Edge Detection

• Grid Scan
• Matrix Algebra - filtering

fourier.eng.hmc.edu/.../gradient/node9.html
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Data Structure Transformations

• Scale transformations are lossy
• (re)storage produce error
• algorithmic error, systematic and random
• Types are scale, structural (data structure),
  dimensional, vector-to-raster

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The Role of Error

• Kate Beard Source error, use error, process
  error
• Morrison Method-produced error
• Error is inherent, can it be predicted,
  controlled or minimized?
• XT X'
• X' T-1 X E

• Errors are
• positional
• attribute
• systematic
• random
• known
• uncertain
• Errors can be attributed to poor choice of
  transformations
• Incompatible sequences of T's (non-invertible)
• "Hidden" Erroruse error, not process error

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Next Lecture

• Map Design