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title: Corner Detection
categories: session
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- aperture problem [page 78]
# Briefing
## Corners
![Universitetsområdet i Ålesund](Images/ntnuaes1.jpg)
![Universitetsområdet i Ålesund (ny vinkel)](Images/ntnuaes2.jpg)
+ What are distinctive points in the image?
+ Distinctive points can (to some extent) be matched in two different images.
[More Images](https://www.flickr.com/photos/ntnu-trondheim/collections/72157632165205007/)
## 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