CSE 559A: Computer Vision

Fall 2018: T-R: 11:30-1pm @ Lopata 101

Instructor: Ayan Chakrabarti (ayan@wustl.edu).

Course Staff: Zhihao Xia, Charlie Wu, Han Liu

Oct 9, 2018

- Problem Set 2 Due 11:59pm tonight.

- My office hours switched to by appointment
- Make a private post on Piazza to setup a time
- Let me know a list of times that work for you over the next two days
- Don't wait till the day before a deadline

- Problem Set 3 out and ready to clone

- Due two weeks from Thursday.

**Szeliski Section 2.1**

**Szeliski Chapter 6**

- Other means of camera calibration
- Minimizing other error metrics
- Lens Distortions and Dealing with them

\[p_l^T F p_r = 0\]

- \(p_l, p_r\) are 2D homogenous co-ordinates of left and right points.
- Co-ordinates in "image space". \(F\) is called the
**fundamental matrix**.

- So given a specific point \(p_r\), says \(p_l^T (F p_r) = 0\).
- This is the equation of a line !

- Same for the other way round.

- Has rank 2. Why ?

- Vector \(p\) such that \(Fp = [0,0,0]^T\).

- Means that this vector \(p\) will satisfy \(p_l^T F p\) for every \(p_l\).

- \(p\) is the homogeneous co-ordinate for the epipole in the right image.

- Fundamental matrix has seven free parameters.
- One free parameter from scale.

- Fundamental matrix has seven free parameters.
- One free parameter from scale.
- Require that \(\text{det}(F)=0\)

- Estimate using correspondences.
- (see "eight point algorithm" in Szeliski 7.2 / Wikipedia)

- If both cameras are calibrated, then only five unknowns

- Three for rotation

- Only two for translation !

- Only direction of translation matters. Epipolar lines stay the same irrespective of magnitude (how far you move the second camera in the same direction).

- Going back, we want to express the fact that our disparity map is smooth.

- Cost volume filtering is an ad-hoc way of doing that.
- Still making independent decisions at each pixel.

- Averaging each disparity level promotes disparity maps where values are "equal" not close.
- If \(C[x,y,d]\) is a good match, then \(C[x+1,y,d\pm 1]\) gets no benefit from filtering.
- Not good for slanted surfaces.

- Could be fixed by smoothing

\[\min_{\delta = \{-1,0,1\}} C[x,y,d+\delta]\]

- But generally, would prefer expressing this as optimizing a well-defined cost.