Mailinglist: | proj-imim |

Sender: | Helmut Dersch |

Date/Time: | 2001-Jan-05 21:48:56 |

Subject: | Number of Control Points, was Re: |

proj-imim:
**Number of Control Points, was Re:**
**Helmut Dersch** 2001-Jan-05 21:48:56

John Blommers wrote: > > > Haw! Your are right. Each control point represents two variables to be > optimized. No. Each control point represents one equation. The number of variables to solve is set in the 'v'-line of the script. If the equations to solve were linear equations of the variables, then you would need as many equations (ie control points) as variables (most of the time). Unfortunately, this is (a) a set of highly nonlinear equations, and (b) this is an optimisation, ie we're not solving the equations, because an exact solution doesn't exist, but only seeking the best approximation. You can visualize the problem by looking at an example: Suppose you want to stitch two images without any remapping, and optimize yaw, roll and pitch. Setting control points is like pinning a needle through both images at that point. Obviously, two needles fix the relative position. However, the optimizer will find an exact solution only if the distance between the two control points is the same in both images, otherwise the problem is unsolvable, and you get just an approximate solution. Mathematically, setting a third point doesn't help, or might make things worse, but practically, the solution will improve. Setting just one point always yields an exact solution, but it is worthless. Things get more complicated if you include more variables, remapping etc. Using at least as many control points as variables to optimize is a rule of thumb, and there may be cases where you need more or where less are sufficient. Regards Helmut Dersch