Question

The minimum number of 2-dimensional ground control points (GCPs) required for second-order polynomial mapping for image georeferencing is:

• A. 4
• B. 5
• C. 6
• D. 7

Hint:

For 2D polynomial georeferencing, a $k$th-order model has $\frac{(k+1)(k+2)}{2}$ terms per coordinate. Multiply by 2 (for $X'$ and $Y'$) to get the number of unknowns, then divide by 2 to get the minimum GCPs.

Answer 1

The Correct Option is C

A 2D second-order polynomial transformation is \[ X' = a_0 + a_1X + a_2Y + a_3X^2 + a_4XY + a_5Y^2,\qquad Y' = b_0 + b_1X + b_2Y + b_3X^2 + b_4XY + b_5Y^2. \] There are $6$ coefficients for $X'$ and $6$ for $Y'$ $⇒$ 12 unknowns.
Each GCP supplies two equations (one for $X'$, one for $Y'$), so the minimum number of GCPs is \[ \frac{12\ \text{unknowns}}{2\ \text{equations/GCP}}=6. \]