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. 80-99 Maling, D.H. “Coordinate Systems and Map Projections For GIS” In Mqguire, Goodchild, and Rhind Goodchild, M.F., 1984. “Geocoding and Geosampling,” In Gaile and Willmott. Chapter 6 in Noble and Daniel (Applied Linear Algebra, 1977), pp. 177-212

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. 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)

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)

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.