final exam fixed

Question 1

1. What is the objective of multiple view geometry?

Answer 1

To understand the 3D structure of a scene given multiple images taken from different perspectives.

Question 2

2. What is the difference between the 3D reconstruction and the Structure from Motion in multiple view geometry?

Answer 2

3D Reconstruction (Stereo Vision): Assumes known intrinsic (K) and extrinsic (R T) parameters to recover 3D scene using two cameras. Structure from Motion (SfM): Recovers 3D scene structure and camera poses simultaneously using multiple images/views (K might be given).

Question 3

3. In stereo vision with parallel cameras what is the meaning of the following equation? Z=bf/(u1−u2)

Answer 3

Depth (Z) = (Baseline (b) × Focal length (f)) / Disparity (u1−u2) where b is the distance between cameras f is the focal length and disparity is the difference in image x-coordinates of the same point between the two images.

Question 4

4. In stereo vision what is the potential issue of a small baseline?

Answer 4

A small baseline limits the depth resolution.

Question 5

5. What is the goal of triangulation?

Answer 5

To estimate the 3D coordinates of a point given its 2D projections in multiple images and the camera positions.

Question 6

6. What are the benefits of stereo rectification in feature matching?

Answer 6

Stereo rectification simplifies the process of finding feature correspondences by making the image planes coplanar.

Question 7

7. What is the epipolar constraint?

Answer 7

Corresponding points on one image must lie on the epipolar lines of the other image. The three vectors of p1 p2 and c1c2 are coplanar.

Question 8

8. Why can’t the scale ambiguity be avoided in multiple view geometry with monocular vision?

Answer 8

Both object distance from the camera and object size are needed to determine the scale which requires prior knowledge.

Question 9

9. What is the reprojection error in two-view geometry?

Answer 9

The distance between the original 2D point and the point obtained by triangulating its 3D position using the estimated (R T) and projecting it back onto the image plane using (R T) and (K1 K2).

Question 10

10. What are the possible causes for outliers in two-view geometry?

Answer 10

Changes in scale and perspective variations in illumination noise and blur and occlusions.

Question 11

11. What is the goal of RANSAC?

Answer 11

To estimate unknown pose when given measurements X which may contain outliers without considering the latent variable Z.

Question 12

12. Explain the procedures of RANSAC when applied to line fitting.

Answer 12

Randomly select a minimal subset to estimate the parameter. Calculate the number of inliers vs. outliers. Repeat k times and choose the parameter with the smallest number of outliers assuming enough inliers exist.

Question 13

13. What are the three main components needed to implement RANSAC?

Answer 13

random selection of data, model estimation and count of the inliers verifying this model

Question 14

14. In RANSAC why do we select the smallest number of data points required to determine the unknown parameter?

Answer 14

The probability of selecting a subset of points entirely of inliers is higher, creating a better estimation of the parameter.

Question 15

15. Describe the four steps required for the sequential structure from motion.

Answer 15

Feature detection -> Feature matching/tracking -> motion estimation -> Local Optimization (bundle adjustment)

Question 16

16. What is the difference between front-end and back-end of visual odometry?

Answer 16

Front-end: Handles feature detection matching and pose estimation between two frames. Back-end: Refines pose among multiple frames.

Question 17

17. Describe the goal the type of correspondence and the name of algorithm for bootstrapping.

Answer 17

2D-to-2D (8-point algorithm): Determines relative pose (up to scale) and 3D location of features from correspondence over two views. 3D-to-2D (Camera Calibration DLT and PnP): Determines absolute pose and intrinsic parameters between 3D feature locations and 2D pixel coordinates. 3D-to-3D (Point cloud registration): Determines relative pose using correspondence between 3D feature locations.

Question 18

18. Describe the goal the type of correspondence and the name of algorithm for localization.

Answer 18

Goal: Determine pose for each additional view using 3D-to-2D correspondence (DLT PnP).

Question 19

19. Why do we need the mapping step in visual odometry?

Answer 19

To extend the structure by selecting new keyframes and extracting new features as the number of features decreases quickly for additional views.

Question 20

20. Why do we need the bundle adjustment step in visual odometry?

Answer 20

needed in visual odometry to refine the 3D structure and camera motion estimates by minimizing the reprojection error across multiple frames

Question 21

21. How is visual SLAM different from visual odometry?

Answer 21

Visual SLAM addresses loop detection and closure to guarantee global consistency in addition to visual odometry’s goals of estimating incremental motion and guaranteeing local consistency.

Question 22

22. Describe the characteristics of the indirect method in visual SLAM.

Answer 22

Extracts features with RANSAC and minimizes reprojection error. Can handle large relative motion between frames but is slow due to RANSAC.

Question 23

23. Describe the characteristics of the direct method in visual SLAM.

Answer 23

Minimizes the photometric error of the image without extracting features using RANSAC. Uses all image information for greater robustness and accuracy. Fast because no RANSAC is used but sensitive to initial guess and cannot handle large relative motion between frames.

Question 24

24. What is the goal of tracking?

Answer 24

To locate a moving object in consecutive video frames.

Question 25

25. What are the pros and the cons of feature detection and matching compared with tracking?

Answer 25

Feature Detection and Mapping: Pros: Works even with large motion between two frames. Cons: Does not utilize additional information from small motion between frames. Tracking: Pros: Utilizes additional information from small motion between frames. Cons: May not work well with large motion between frames.

Question 26

26. Summary for Point Tracking

Answer 26

Block-based methods: Robust to large motions but computationally expensive. Differential methods: No search performed applied to small motions can be extended to large motions using multi-scale implementation and computationally efficient for optical flow.

Question 27

27. Summary for KLT Template Tracking

Answer 27

KLT (Kanade-Lucas-Tomasi) is a template tracking algorithm that estimates the motion of a template image patch between consecutive frames by minimizing the sum of squared intensity differences, assuming small motion and brightness constancy.

Question 28

28. Describe the image features that are not preserved under homography and the image feature that is preserved under homography.

Answer 28

Not preserved: Parallel lines distances lengths curvature. Preserved: Collinear points.

Question 29

29. What are the pros and the cons of vision compared with IMU?

Answer 29

Vision is more accurate for slow motion and provides richer information, but struggles with fast motion, challenging scenes, and has lower output rates. IMUs excel in fast motion scenarios with higher output rates, but are less accurate for slow motion and drift over time.

Question 30

30. What are the pros and the cons of IMU compared with vision?

Answer 30

IMU Pros: More accurate for motion with large accelerations and angular velocity higher output rate. IMU Cons: Inaccurate for motion with low acceleration measurement drifts over time.

Question 31

31. What are the differences between the loosely coupled approach and the tightly coupled approach in visual-inertial fusion?

Answer 31

In the loosely coupled approach, visual odometry (VO) and IMU estimate the pose independently, making it easier to implement but less accurate. The tightly coupled approach integrates IMU measurements directly with feature tracking and 3D reconstruction, resulting in higher accuracy but increased complexity.

Question 32

32. In the tightly coupled visual-inertial fusion compare the filtering and the optimization for speed and accuracy.

Answer 32

Filtering: Repeated procedure for prediction and correction. Faster but less accurate (sensitive to linearization). Optimization: Multiple iterations to minimize the objective function. Slower (can be improved with GTSAM) but more accurate.