CV Chapter 7 3D Reconstruction
Questions about the lecture 'Computer Vision' of the RWTH Aachen Chapter 7 3D Reconstruction
Questions about the lecture 'Computer Vision' of the RWTH Aachen Chapter 7 3D Reconstruction
Fichier Détails
| Cartes-fiches | 108 |
|---|---|
| Langue | English |
| Catégorie | Informatique |
| Niveau | Université |
| Crée / Actualisé | 04.02.2017 / 23.02.2017 |
| Lien de web |
https://card2brain.ch/box/20170204_cv_chapter_7_3d_reconstruction
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What are cues for 3D recovery? [5]
1. Shading
2. Texture
3. Focus
4. Perspective
5. Motion
Which kind of geometry is necessary for stereo vision?
Multi-view geometry
What is the generic problem formulation for stereo vision?
“Given several images of an object or scene, compute 3D shape”
What is the narrower problem formulation for stereo vision?
“Given calibrated binocular stereo pair, fuse it to depth image”
What is the definition of triangulation in epipolar geometry?
Reconstruction as intersection of two rays
What is required for triangulation in epipolar geometry? [2]
1. Point correspondence
2. Camera pose or calibration
What are the two different set of parameters for camera calibration in triangulation in epipolar geometry? [2]
1. Extrinsic and 2. intrinsic
What does the extrinsic parameters describe for camera calibration in triangulation in epipolar geometry?
Camera ↔ reference frame
What does the intrinsic parameters describe for camera calibration in triangulation in epipolar geometry?
Image ↔ pixel coordinates // relative
What are the extrinsic parameters for camera calibration in triangulation in epipolar geometry? [2]
1. Rotation matrix
2. Translation vector
What are the intrinsic parameters for camera calibration in triangulation in epipolar geometry? [6]
1. Focal length
2. Pixel sizes [mm]
3. Image center point
4. Radial distortion
5. Pixel magnification factors
6. Skew (non-rectangular pixels)
Name the list of attributes necessary if we have parallel optical axes and known camera parameters in a simple stereo system? [6]
1. World point p and image point left pl and right pr
2. xl and xr
3. Focal length f
4. Optical center left Ol and right Or
5. Baseline T
6. Depth Z of p
How does triangulation works if we have parallel optical axes and known camera parameters in a simple stereo system? [4]
1. (pl, p, pr) and (Ol, p, Or)
2. (T-(xr-xl))/(Z-f) = T/Z
3. Z = f*T/(xr-xl) with (xr-xl) disparity
4. Update (x’,y’) with disparity map (x+D(x,y), y)
How do we proceed if optical axes are not parallel in a simple stereo system? [3]
1. Image scanlines are epipolar lines
2. Re-project image on plane parallel to optical centers // Stereo image rectification
3. Two homographies (3x3 transforms) are necessary
What is the definition of a baseline T in epipolar geometry?
Line joining camera centers
What is the definition of a epipole e in epipolar geometry?
Intersection of baseline and image plane
What is the definition of a epipolar plane p in epipolar geometry?
Plane containing baseline and world point
What is the definition of a epipolar line l in epipolar geometry?
Intersection of p and image plane
What is the stereo correspondence constraint and its problem? [2]
1. Reduce to 1D search along conjugate epipolar lines
2. But still multiple match hypotheses satisfy constraint
How is the rotational 3x3 R matrix defined for epipolar geometry? [3]
1. 3D rotation as series of rotations around three axes
2. Axis column and row filled with 1 and 0
3. Other entries are cos, *sin, °sin, cos with *=- for x,z and °=- for y
How is the cross product defined for epipolar geometry? [2]
1. a x b = c with c perpendicular to a and b
2. [ax]*b with [ax] = [0,-az,ay;az,0,-ax;-ay,ax,0]
How is 3D rigid transformation defined for epipolar geometry? [5]
1. x’ = R*x + t
2. 0 = x’*(T x R*x) via cross product
3. 0 = x’*([Tx]*R*x) with essential matrix E=[Tx]*R
4. 0 = x’T*E*x
5. l’ = E*p and l = ET*p’ representing epipolar lines
What are the examples calculations for parallel cameras in epipolar geometry? [4]
1. R = I
2. T = [-d,0,0]T
3. E = (0…0;0,0,d;0,-d,0)
4. p’T*E*p = 0 → y = y’ // All points lie on same horizontal line
What are the methods how to react on multiple match hypotheses in epipolar geometry? [2]
1. Dense and 2. sparse
What is the definition of the dense method to find correct match hypotheses in epipolar geometry? [4]
1. Examine all pixels on epipolar line
2. Pick best match with e.g. SSD or correlation
3. Triangulate matches to get depth information
4. Easier with rectified images
What are the advantages of the dense method to find correct match hypotheses in epipolar geometry? [3]
1. Simple
2. More depth estimates
3. Useful for surface reconstruction
What are the disadvantages of the dense method to find correct match hypotheses in epipolar geometry? [3]
1. Breaks down in textureless regions
2. Raw pixel distances can be brittle
3. Bad with different viewpoints
What is the definition of the sparse method to find correct match hypotheses in epipolar geometry? [2]
1. Restrict search to sparse set of detected features
2. Perform narrow search further by epipolar geometry
What are the advantages of the sparse method to find correct match hypotheses in epipolar geometry? [3]
1. Efficient
2. More reliable features
3. Less sensitive to illumination
What is the disadvantage of the sparse method to find correct match hypotheses in epipolar geometry? [1]
Needs information for good features
What are sources of errors while finding correct match hypotheses in epipolar geometry? [5]
1. Low-contrast/ textureless image regions
2. Occlusions
3. Wrong camera calibration
4. Violations of brightness constancy (Specular reflections)
5. Large motions
What are the sub topics of two-view geometry?
[stereo vision.3D reconstruction, 3]
1. Scene geometry (structure)
2. Correspondence (stereo matching)
3. Camera geometry (motion)
What is the definition of scene geometry?
[two view.stereo vision.3D reconstruction]
Given corresponding points where is the pre-image in 3D
What is the definition of correspondence?
[two view.stereo vision.3D reconstruction]
How does a point in one image restrict the position in another
What is the definition of camera geometry?
[two view.stereo vision.3D reconstruction]
Get cameras of corresponding points
What is a difficulty?
[triangulation.epipolar geometry.3D reconstruction]
Noise and numerical errors prohibit exact calculation
What are the formulas?
[pinhole camera model.camera calibration.3D reconstruction, 3]
1. (x,y,z) → (fX/Z,fY/Z)
2. (x;y;z;1) → x= (fX;fY;Z) = [f;0,f;0,0,1,0]*(X;Y;Z;1) = P*X
3. P = diag(f,f,1)*[I|0]
What are the degrees of freedom of cameras?
[camera calibration.3D reconstruction, 3]
1. 9 DoF for pinhole camera
2. 10 DoF for CCD camera with square pixels
3. 11 DoF for general camera
What are the definitions?
[camera coordinate system.camera calibration.3D reconstruction, 7]
1. Principal axis (PA) from camera center (CC) to image plane
2. Principal point p is intersection of PA and image plane
3. Origin is p
4. Origin is CC and PA the z-axis → Called normalized CCS
5. Origin is image corner → Called image coordinate system
6. Calibration matrix K
7. Camera projection matrix (CPM) P
What are the formulas?
[camera coordinate system.camera calibration.3D reconstruction, 2]
1. (x,y,z) → (fX/Z+px,fY/Z+py)
2. (x;y;z;1) → x = (fX+Zpx;fY+Zpy;Z) = [f,0,px;0,f,py;0,0,1,0]*(X;Y;Z;1) = P*X
