Geometric Coordinate Transformations

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Geography 3150Geographic Information Systems I
GEOG 3150

• Chapter 7
• Geometric (Coordinate) Transformations
• (a.k.a. Georeferencing)

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Geometric Transformations
GEOG 3150

• Digitizing and Scanning are used to Convert
  Hardcopy Documents to a Digital Format

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Geometric Transformations
GEOG 3150

• Digitized Documents have Digitizer Coordinates

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Geometric Transformations
GEOG 3150

• Scanned Documents have Scanner Coordinates

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Geometric Transformations
GEOG 3150

• Images often contain Spatial Data

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Geometric Transformations
GEOG 3150

• ArcMap cant Project this Image on-the-fly

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Geometric Transformations
GEOG 3150

• Images acquired by Digital Techniques need
  Geometric Transformation

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Geometric Transformations
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• GIS Layers based on unknown Coordinate
• Systems may need Geometric Transformation

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Geometric Transformations
GEOG 3150

• Geometric transformation is also used to correct
  geometric errors that result from
• The design of digital scanners,
• Movements of the imaging platform and the Earth
  during image acquisition, and
• Uncorrected variations in the position and
  altitude of the platform.

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Geometric Transformations
GEOG 3150

• Geometric transformation produces new coordinate
  values from the original coordinate values.

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Geometric Transformations
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• The Transformation Process is governed
• by Control Points

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Geometric Transformations
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• Map-to-Map vs. Image-to-Map
• Coordinate Transformation

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Geometric Transformations
GEOG 3150

• Available Transformation Methods
• Equiarea (rotation and translation),
• Similarity (rotation, translation and scaling),
• Affine (rotation, translation, scaling and
  skewing while preserving line parallelism),
• Projective (similar to affine, but allows
  differential skewing),
• General Polynomial (systematic warping), and
• Rubbersheeting (non-systematic warping).

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Geometric Transformations
GEOG 3150

• Appropriate GIS Transformation Methods
• Affine for map-to-map and image-to-map
  transformations,
• Projective transformation for georeferencing of
  aerial photographs (and projection of 3-D
  coordinates to create perspective views),
• General Polynomial for systematic distortions,
  and
• Rubbersheeting for non-systematic distortions.

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Geometric Transformations
GEOG 3150

• Distortions allowed by an Affine Transformation

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Geometric Transformations
GEOG 3150

• Distortions allowed by a Projective Transformation

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Geometric Transformations
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• A Projective Transformation does not correct
  geometric errors introduced by relief
  displacement.

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Geometric Transformations
GEOG 3150

• The correction of non-systematic distortion
  requires rubbersheeting.

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Geometric Transformations
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• Affine Transformation Equations
• X Ax By C
• Y Dx Ey F

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Geometric Transformations
GEOG 3150

• The affine transformation process consists of
  three steps
• Establish control point coordinates,
• Transform the control points to determine the
  transformation parameters, and
• Use the parameters derived from the control
  points in the transformation equation to
  transform all of the remaining points.

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Geometric Transformations
GEOG 3150

• Control Points

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Geometric Transformations
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• Control Points

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Geometric Transformations
GEOG 3150

• Calculating Transformation Parameters
• X Ax By C
• Y Dx Ey F
• Section 7.1.4 discusses the effect of each
  transformation parameter, and Equations 7.3
  through 7.6 show how they are applied.

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Geometric Transformations
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• The meanings of the Transformation Parameters

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Geometric Transformations
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• Estimating the Accuracy of a
• Geometric Transformation

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Geometric Transformations
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• Performing the Transformation

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Geography 3150Geographic Information Systems I
GEOG 3150

• Next
• Chapter 8