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Corner Detection

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---
title: Corner Detection
categories: session
---

- 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