Homography and image alignment in Computer Vision - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a homography in computer vision?

A homography is a mathematical transformation that relates the positions of points between two images of the same planar surface or scene taken from different viewpoints. It is represented by a 3x3 matrix that maps points from one image to another.

beginner

Why do we need image alignment in computer vision tasks?

Image alignment helps to match two or more images by adjusting their positions, scales, or rotations so that corresponding points overlap. This is important for tasks like panorama stitching, object recognition, and 3D reconstruction.

intermediate

What are the main steps to compute a homography matrix between two images?

1. Detect key points in both images.<br>2. Extract descriptors for these points.<br>3. Match key points between images.<br>4. Use matched points to estimate the homography matrix, often with RANSAC to remove outliers.

intermediate

How does RANSAC help in homography estimation?

RANSAC (Random Sample Consensus) helps by repeatedly selecting random subsets of matched points to estimate the homography and then choosing the estimate that fits the most points (inliers). This reduces the effect of incorrect matches (outliers).

advanced

What is the difference between affine transformation and homography?

Affine transformation preserves parallel lines and includes translation, rotation, scaling, and shearing. Homography is more general and can represent perspective distortions, mapping any plane to another plane, including changes in viewpoint.

What does a homography matrix primarily represent?

A A color adjustment between images

B A noise filter for images

C A 3D rotation of an object

D A transformation between two planes in images

A homography matrix maps points from one plane in an image to another plane in a different image.

Which algorithm is commonly used to remove outliers when estimating homography?

A RANSAC

B K-Means

C PCA

D Gradient Descent

RANSAC is used to robustly estimate homography by ignoring outliers in matched points.

Image alignment is important for which of the following tasks?

A Panorama stitching

B Audio processing

C Text summarization

D Database indexing

Image alignment helps to stitch multiple images into a panorama by matching overlapping areas.

Which of these transformations can homography represent but affine transformation cannot?

A Rotation

B Perspective distortion

C Translation

D Scaling

Homography can represent perspective changes, which affine transformations cannot.

What is the minimum number of point correspondences needed to compute a homography matrix?

A 2

B 3

C 4

D 5

At least 4 point correspondences are needed to solve for the 8 degrees of freedom in a homography matrix.

Explain the process of estimating a homography matrix between two images.

Think about how you find matching points and then find the best transformation.

Describe why homography is useful for image alignment and give an example application.

Consider how images taken from different angles can be matched.