Positional Accuracy

Objectives of Lecture:

1. Basic concepts
2. Deductive estimates
3. Registration techniques

Positional Accuracy comes down to numbers.

Are the coordinates for the data close (enough) to the "correct location"?

Some distinctions:

• Absolute accuracy: each position evaluated on its own.
• Relative accuracy: accuracy in reference to neighboring values (other features)

Pulling apart the numbers

Total error is the deviation between a position and a position considered to be true.

Components of error:

• Systematic error: whole data set "biased" (a uniform amount)
• Random error: each position has some inherent deviation (see Gauss)
• "Blunders": huge deviations from external sources

How did the coordinates get into the database?

From graphic material to coordinate system: the direct approach
· Affine: To translate, simply add (subtract) from X and Y; to scale multiply (either by the same value or by differential scales (removes a tilt from an airphoto, often, but not always...); rotation involves cross products.
alternatives to affine: projective (removes "barrel" distortion based on distance from a focal point (deals with lens distortions); higher order equations (usually impractical); piecewise transformations
ONLY transforms into original projection of graphic material, really

Ground control: Registration involves transforming the coordinates of some collection of data into a desired coordinate system. This is usually based on having a key to the transformation by identifying some set of points ("control") on both sources. Some systems (eg. ARC/INFO) build this into the process immediately. I disagree, since I think the original space is needed to perform quality control, then transform later (with more ability to select how it happens)
How many points? ARC suggests 4, barely enough to cross-check an affine! 16 or 20?
Least squares: (regression) Compute transformation between the input X,Ys and the desired "control" values that minimizes the squared deviations. R2 measure of goodness of fit, distances (variances) of the residuals are interesting too.
Outliers: regression can be affected (sometimes heavily) by some single bad value. Common method: examine outliers, remove points, refit equation

"Robust" Alternative: Least-Median Squares (can be up to 50% contaminated)

Version of 4 February 2004