Epipolar Geometry
1. Epipolar Geometry
Two images taken at the same time, in different positions, by different cameras.
2. The fundamental matrix
在I1及 I2上相對應的特徵點，滿足:
which is:
We can build an linear system with n corresponding feature points located on two images:
找到最佳解f即為Fundamental matrix。
Basic algorithm: normalized 8-points algorithm
重要觀念：
Two images taken at the same time, in different positions, by different cameras.
- Don't need to search across the entire image to estimate the motion vector
- Only one degree of freedom for the possible correspondence
假設有兩張連續拍攝的影像I1, I2，則物體P在I2上的成像點必落在一條線上，稱之為Epipolar line(因為不知道P與I1的距離)，而I2上所有的Epipolar line會相交在一點，稱之為epipole。
在I1及 I2上相對應的特徵點，滿足:
which is:
Basic algorithm: normalized 8-points algorithm
重要觀念：
- Normalized特徵點。
- 雖然無法找到唯一解使得Af = 0，但可對A做SVD特異值分解，D之中最小eigenvalue對應的eigenvector即為使Af最小的向量。(Af = 0 => Af = λf = 0, satisfied when λ=0 )
- 到Step4算出來的F可能不是Rank2，所以需要再做一次SVD，令D之中最小eigenvalue為0，使F變為Rank2。
- RANSAC可用來濾掉outliers。
- Image rectification可用來對齊兩張影像的epipolar line，方便我們搜尋特徵點。(homography transformation) 參: Hartley.
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