GeoPDF and Georegistration

One of the key concepts behind GeoPDF is georegistration. We define georegistration as a specific form of georeferencing in which a projected Cartesian coordinate system is registered to a page Cartesian coordinate system using a linear transformation. That is, the relationship between a point in a map to a point in a projected coordinate system is given by:

x = a h + c v + H
y = b h + d v + V

where (x, y) is the projected coordinate, (h, v) is the page coordinate and a, b, c, d, H, and V are the parameters that define the linear relationship. In matrix notation, this can be represented as:

|a c H||h|   |x|
|b d V||v| = |y|
|0 0 1||1|   |1|

We call the matrix a coordinate transformation matrix, or CTM. We encode this in a more compact form in PDF object notation as:

[ a b c d H V ]

where the square brackets delimit an array. More on PDF object notation later, but Adobe's PDF Architect and Senior Principal Scientist Jim King's tutorials give a nice overview.