• aperture problem [page 78]

Briefing

Corners

• What are distinctive points in the image?
• Distinctive points can (to some extent) be matched in two different images.

More Images

Corner Correspondence

• Two images of the same scene \(I_1,I_2: \Omega\subset\mathbb{R}^3\to\R_+ ; \mathbf{x}\mapsto I_1(\mathbf{x}),I_2(\mathbf{x})\)
• Different in general

Why are they different?

Brightness Constancy Constraint

• Suppose we photograph empty space except for a single point \(p\)
  • Brightness Constancy Constraint

\[I_1(\mathbf{x}_1) = I_2(\mathbf{x}_2) \sim \mathcal{R}(p)\]

• Simple dislocation from \(\mathbf{x}_1\) to \(\mathbf{x}_2\)
• Problem: Globally, it is an infinite-dimentional transformation