Lecture 6 - 3D

Question 1

What are the primary types of 3D acquisition methods?

Answer 1

The primary types are passive methods (e.g., stereo, shape-from-texture, shape-from-shading) and active methods (e.g., structured light, time-of-flight, laser scanning).

Question 2

Define “triangulation” in the context of 3D stereo vision.

Answer 2

Triangulation is the process of determining the 3D position of a point by measuring angles from two different viewpoints, typically using two cameras.

Question 3

What is disparity in stereo vision?

Answer 3

Disparity is the difference in image location of an object seen by the left and right cameras. It is inversely proportional to the depth of the object.

Question 4

Explain the concept of “epipolar geometry”.

Answer 4

Epipolar geometry describes the geometric relationship between two views of the same scene. It is used to simplify the correspondence problem in stereo vision by reducing the search space for matching points to one-dimensional epipolar lines.

Question 5

What is the role of the fundamental matrix in stereo vision?

Answer 5

The fundamental matrix encapsulates the intrinsic and extrinsic parameters of two cameras, providing a relationship between corresponding points in stereo images. It is used to enforce the epipolar constraint.

Question 6

Describe the process of active triangulation using a laser.

Answer 6

Active triangulation involves projecting a laser beam onto an object and capturing the reflected light with a camera. The intersection of the laser ray and the viewing ray provides the 3D coordinates of the point on the object.

Question 7

What is structured light, and how is it used in 3D reconstruction?

Answer 7

Structured light involves projecting patterns (e.g., grids or stripes) onto a scene. The deformation of these patterns when viewed from a different angle is used to infer the 3D shape of the object.

Question 8

Define “time-of-flight” in the context of 3D imaging.

Answer 8

Time-of-flight measures the time a modulated light signal takes to travel to the object and back to calculate the distance, thereby determining the 3D structure of the scene.

Question 9

Explain the concept of “shape-from-shading”.

Answer 9

Shape-from-shading derives the 3D shape of an object based on the variations in shading (intensity) within an image, assuming known light source direction and surface reflectance properties.

Question 10

What is the purpose of photometric stereo?

Answer 10

Photometric stereo uses multiple images taken under different lighting conditions to estimate the surface normals and reconstruct the 3D shape of an object.

Question 11

Describe the process of shape-from-silhouettes.

Answer 11

Shape-from-silhouettes involves capturing images of an object from multiple viewpoints and extracting the object’s silhouette in each image. These silhouettes are then used to reconstruct the 3D shape of the object.

Question 12

What is the advantage of using a laser scanner for 3D acquisition?

Answer 12

Laser scanners provide high accuracy and resolution in 3D measurements, making them ideal for detailed surface reconstruction and precise modeling.

Question 13

Write the formula for calculating 3D coordinates from disparity in stereo vision.

Answer 13

Question 14

Provide the formula for the epipolar constraint in terms of the fundamental matrix.

Answer 14

Question 15

What is the formula for the projection of a point in 3D space onto an image plane?

Answer 15

Question 16

How does increasing the baseline
𝑏
b affect depth resolution in stereo vision?

Answer 16

Increasing the baseline
𝑏
b improves depth resolution by increasing the disparity between corresponding points, making it easier to detect small changes in depth.

Question 17

What are the challenges associated with finding correspondences in stereo vision?

Answer 17

Challenges include handling occlusions, textureless regions, repetitive patterns, and ensuring accurate matching of points between the two images.

Question 18

Explain how structured light can be used to measure 3D shapes.

Answer 18

Structured light projects known patterns onto a scene. The deformation of these patterns is captured by a camera and analyzed to infer the 3D shape of the object based on the distortions.

Question 19

What is the significance of the epipolar line in stereo matching?

Answer 19

The epipolar line constrains the search for corresponding points to a one-dimensional line, reducing the complexity of the matching process and improving accuracy.

Question 20

Describe the process of time-of-flight measurement for 3D reconstruction.

Answer 20

Time-of-flight measures the time taken for a modulated light signal to travel to the object and back to the sensor. This time is proportional to the distance, allowing calculation of the 3D coordinates of points on the object’s surface.

Question 21

How does photometric stereo estimate surface normals?

Answer 21

Photometric stereo captures images under different lighting directions. The variations in shading are used to estimate the surface normals, which describe the orientation of the surface at each point.

Question 22

What are the limitations of shape-from-shading?

Answer 22

Shape-from-shading requires accurate knowledge of the lighting conditions and surface reflectance properties. It also assumes smooth surfaces and can be sensitive to noise.

Question 23

How can the fundamental matrix be estimated from point correspondences?

Answer 23

The fundamental matrix can be estimated using eight or more point correspondences between the two images, typically through algorithms like the eight-point algorithm and RANSAC for robust estimation.

Question 24

What are the advantages of using a laser line scanner over a laser point scanner?

Answer 24

A laser line scanner can capture more data in a single scan, making it faster and more efficient for 3D surface reconstruction compared to a laser point scanner, which requires multiple scans to cover the same area.

Question 25

Explain the concept of an essential matrix and its relation to the fundamental matrix.

Answer 25

The essential matrix encapsulates the relative rotation and translation between two cameras. It is derived from the fundamental matrix and the intrinsic parameters of the cameras, used for calibrated stereo vision.

Question 26

How does active triangulation differ from passive stereo vision?

Answer 26

Active triangulation uses an additional light source, like a laser, to project known patterns onto the scene, simplifying the correspondence problem and improving accuracy, whereas passive stereo relies solely on ambient light.

Question 27

Describe an application of 3D acquisition in real-world scenarios.

Answer 27

One application is in autonomous vehicles, where 3D acquisition techniques like LiDAR and stereo vision are used to create accurate 3D maps of the environment for navigation and obstacle detection.