1. Lecture 09: Coordinate Transformation II
Topics:
Planar coordinate transformation (2D to 2D)
3) Curvilinear transformation
4) Statistical transformation
5) Geocoding (address matching)
References:
Chapter 1 & 2 in Maling’s (1992), pp. 1-46
Chapter 5 in Maling’s (1992), pp
Maling, D.H. “Coordinate Systems and Map Projections
For GIS” In Mqguire, Goodchild, and Rhind
Goodchild, M.F., “Geocoding and Geosampling,”
In Gaile and Willmott.
Chapter 6 in Noble and Daniel (Applied Linear Algebra,
1977), pp

2. Outlines 3. Planar map transformation (2D to 2D):
3.1 Simple Affine Transformations
3.2 Complex Affine Transformation
3.3 Curvilinear transformations
3.3.1 Forms:
3.3.2 Applications:
3.4 Statistical Transformation:
3.4.1 Statistical Affine Transformation
1) Basic Assumption:
relationship is linear and complex affine
can model it
2) Statistical approach
(The Statistical Approach PDF)

3. 3. Planar map transformation (2D to 2D):
3.4 Statistical Transformation: (continued…)
3.4.1 Statistical Affine Transformation (continued…)
3) Measure of transformation errors
a) For each point:
In the U (X) direction
In the V (Y) direction
Total for the point
b) RMSE for all points
In the Y (Y) direction
4) Example
(The Statistical Affine Transformation Spreadsheet)

4. 3. Planar map transformation (2D to 2D):
3.4 Statistical Transformation: (continued…)
3.4.2 Other forms of statistical transformations
3.4.3 Revisiting selection of control points
(1) Number of control points:
(2) Spatial Distribution of control points
(3) Identifiable and stable locations
(4) Final determination of control points
3.5 Geocoding (Address Matching)

5. Questions
In which way is statistical affine transformation advantageous
over complex affine transformation?
2. What is the basic assumption under the statistical affine
transformation? What do you need to make it statistical?
3. How are the errors about a transformation is reported?
4. What does it mean to be statistical?
5. In light of statistical affine transformation, discuss the three
criteria used for selecting control points.