Difficulties

• Different lightning conditions
• Different framings
• Several displacements ($\Rightarrow$ occlusions)
• Multiple similar shapes
• Noise...

Actually $u_2(\mathbf{x})\:\backsimeq\:\chi_{D}(\mathbf{x})\;g\circ u_1\circ A(\mathbf{x})$
Framework $A$ is a rotation of unknown center or a similarity $A\mathbf{x} = s R_\theta \mathbf{x} + \mathbf{t}$
4 parameters: $s$, $\theta$, $t_x$, $t_y$
Classical method: correlation ($\rightarrow$ fast computation in frequency domain) [Reddy, Chatterji 96]

Summer School on Mathematical Problems in Image Processing, Trieste, Italy, September 4th-18th 2000