L5: SFM

Question 1

★ What is SFM?

Answer 1

Estimating 3D reconstruction from different 2D images.
Have few assumptions:
- where the camera is placed in relation to each other
- what the scene would look like (no control points available)
- (general-case) we don’t have calibrated cameras, we might have different cameras for each image

Question 2

★ What is the most challenging part of visual SFM?

Answer 2

Finding the initial guesses

Question 3

★ What is the problem in SFM?

Answer 3

Given: m images of n fixed 3D points.
x_ij =P_iX_j, i=1,…,m, j=1,…,n

Problem: Estimate m projection matrices P_i and n 3D points X_j from the mn correspondences x_ij

Question 4

★ What is SFM ambiguity? MANGLER

Answer 4

Consider what we know geometrically, there must be some uncertainty/ambiguity. We cant solve for everything

Question 5

★ What is scale ambiguity?

Answer 5

When we don’t know the projection matrices (non-calibrated) the ambiguity is worse.

Question 6

★ What different kinds of ambiguity is there?

Question 7

What is projective and ambiguity and where does it arise in SfM?

Question 8

How can we use orthographic projection approximations in SfM?

Question 9

How is a zero-skew constraint introduced in SfM reconstruction?

Question 10

How can we reconstruct 3d geometry from uncalibrated cameras?

Question 11

★ The starting points of ambiguity

Answer 11

With no constraints on teh camera calibration matrix or on the scene, we get projective reconstruction. We need addition info to upgrade the reconstruction:

Projective (15 dof)
Affine (12 dof)
Similarity (7 dof)
Euclidean (6 dof)

Question 12

★ Hvad bruger vi de her transforms til?????

Question 13

★ What is a affine camera?

Answer 13

Assumes there are no vanishing points (perspective). The 3D scene that is projected is directly into the camera with parallel rays (weak perspective).
- Increase focal length and distance from camera.

Question 14

★ What does the affine camera do?

Answer 14

P = [3x3]OP[4x4] = [A b; 0 1]
[3x3]: affine transformation of the image
orthographic projection with a focal length of 1
[4x4]: affine transformation by the 3D space

Question 15

★ Difference between orthographic- and parallel projection

Answer 15

Orthographic projection
Parallel projection

Question 16

Hvordan fra projective bevæger vi os til affine?

Answer 16

Bruger ortographic?

Question 17

Hvad er D matricen?

Question 18

Hvordan bevæger vi os fra affine til similarity?

Question 19

Hvordan bevæger vi so fra similarity til euclidean?

Question 20

★ What is missing data

Answer 20

If not all of the points are visible in all views.

Question 21

★ What is Orthographic projection?

Answer 21

The distance from the center of projection to the image plane is infinite. The focal length is set to 1 in the matrix
[1, 0, 0, 0;
0, 1, 0, 0;
0, 0, 0, 1]