Homography and image alignment in Computer Vision - Model Metrics & Evaluation

Metrics & Evaluation - Homography and image alignment

Which metric matters for Homography and image alignment and WHY

For homography and image alignment, the key metric is the Reprojection Error. This measures how far the points from one image move when transformed to the other image using the estimated homography. A smaller reprojection error means the alignment is more accurate. This metric directly shows how well the model matches points between images, which is the goal of alignment.

Other useful metrics include Inlier Ratio from RANSAC, which tells us how many matched points fit the homography well, indicating robustness.

Confusion matrix or equivalent visualization

Homography estimation does not use a confusion matrix like classification. Instead, we visualize alignment quality with a point matching diagram or reprojection error histogram.

    Example reprojection error histogram:
    -------------------------------------
    | Error Range | Number of Points     |
    | 0-1 pixel   | 150 (inliers)        |
    | 1-3 pixels  | 30                   |
    | >3 pixels | 20 (outliers)         |
    -------------------------------------
    

This shows how many points align closely (inliers) versus poorly (outliers).

Precision vs Recall tradeoff with concrete examples

In homography, the tradeoff is between inlier precision and inlier recall during point matching:

• High precision: Most matched points are correct (few false matches). This leads to a more accurate homography but might miss some true matches.
• High recall: Most true matches are found, but some false matches may be included, risking a less accurate homography.

For example, if you set a strict threshold in RANSAC, you get high precision but lower recall. If you loosen it, recall improves but precision drops.

Choosing the right balance depends on the application. For stitching photos, high precision avoids visible misalignments. For augmented reality, high recall ensures enough points for stable tracking.

What "good" vs "bad" metric values look like for this use case

Good alignment:

• Reprojection error < 1 pixel on average
• Inlier ratio > 80%
• Visual check shows overlapping images aligned well without ghosting

Bad alignment:

• Reprojection error > 5 pixels on average
• Inlier ratio < 50%
• Images show visible misalignment or double edges

Metrics pitfalls

• Ignoring outliers: Including many wrong matches can lower homography quality but may not be obvious if only average error is reported.
• Overfitting to noise: A homography that fits noisy points too closely may have low error but poor generalization.
• Data leakage: Using the same points to estimate and evaluate homography inflates performance metrics.
• Ignoring scale and rotation: Metrics should consider geometric transformations, not just pixel distance.

Self-check question

Your homography model shows an average reprojection error of 0.8 pixels but only 40% inlier ratio. Is this good?

Answer: Not really. While the low reprojection error means the matched points fit well, the low inlier ratio means most points do not fit the homography. This suggests the model is only good for a small subset of points and may not align the images well overall. You should improve matching or outlier rejection.

Key Result

Reprojection error and inlier ratio are key metrics; low error with high inlier ratio indicates good homography alignment.

Practice

1. What is the main purpose of computing a homography matrix in image alignment?

easy

A. To increase the brightness of an image

B. To detect edges in an image

C. To segment objects in an image

D. To find a transformation that maps points from one image to another

Solution

1. Step 1: Understand homography concept

   Homography is a matrix that relates points between two images taken from different views.

2. Step 2: Identify its use in image alignment

   It helps to map points from one image to corresponding points in another to align them.

3. Final Answer:

   To find a transformation that maps points from one image to another -> Option D

4. Quick Check:

   Homography = Point mapping [OK]

Hint: Homography maps points between images [OK]

Common Mistakes:

• Confusing homography with edge detection
• Thinking homography changes image brightness
• Mixing homography with image segmentation

2. Which OpenCV function is used to compute the homography matrix from matched points?

easy

A. cv2.warpPerspective()

B. cv2.findHomography()

C. cv2.matchTemplate()

D. cv2.resize()

Solution

1. Step 1: Identify function for homography calculation

   cv2.findHomography() computes the homography matrix from matched point sets.

2. Step 2: Differentiate from other functions

   cv2.warpPerspective applies the homography, matchTemplate finds template matches, resize changes image size.

3. Final Answer:

   cv2.findHomography() -> Option B

4. Quick Check:

   Compute homography = findHomography [OK]

Hint: Find homography matrix with cv2.findHomography() [OK]

Common Mistakes:

• Using warpPerspective to compute homography
• Confusing template matching with homography calculation
• Trying to resize image to get homography

3. Given the following code snippet, what will be the shape of aligned_img after applying homography?

import cv2
import numpy as np
img1 = cv2.imread('img1.jpg')
img2 = cv2.imread('img2.jpg')
pts1 = np.array([[10,10],[100,10],[100,100],[10,100]])
pts2 = np.array([[12,14],[102,12],[98,110],[14,108]])
H, _ = cv2.findHomography(pts1, pts2)
aligned_img = cv2.warpPerspective(img1, H, (img2.shape[1], img2.shape[0]))

medium

A. Same height and width as img1

B. Shape is (4, 2) because of points

C. Same height and width as img2

D. Shape depends on H matrix size

Solution

1. Step 1: Understand warpPerspective parameters

   The third parameter in warpPerspective sets output image size as (width, height).

2. Step 2: Check given size argument

   It uses (img2.shape[1], img2.shape[0]) which is width and height of img2.

3. Final Answer:

   Same height and width as img2 -> Option C

4. Quick Check:

   Output size = img2.shape [OK]

Hint: warpPerspective size param sets output image shape [OK]

Common Mistakes:

• Assuming output shape matches img1
• Thinking homography matrix size affects output shape
• Confusing point arrays with image shape

4. You wrote this code to align two images but get a distorted output. What is the likely error?

H, status = cv2.findHomography(pts1, pts2)
aligned = cv2.warpPerspective(img1, pts1, (img2.shape[1], img2.shape[0]))

medium

A. Using pts1 instead of H in warpPerspective

B. Swapping pts1 and pts2 in findHomography

C. Not converting points to float32

D. Missing cv2.imshow to display image

Solution

1. Step 1: Check warpPerspective arguments

   warpPerspective expects the homography matrix as the second argument, not point arrays.

2. Step 2: Identify incorrect argument usage

   Code passes pts1 (points) instead of H (homography matrix), causing distortion.

3. Final Answer:

   Using pts1 instead of H in warpPerspective -> Option A

4. Quick Check:

   warpPerspective needs homography matrix [OK]

Hint: Pass homography matrix, not points, to warpPerspective [OK]

Common Mistakes:

• Passing points instead of homography matrix
• Swapping source and destination points in findHomography
• Ignoring data type requirements for points

5. You want to stitch two images taken from different angles into a panorama. Which sequence of steps correctly uses homography for alignment?

hard

A. Detect keypoints -> Match points -> Compute homography -> Warp one image -> Blend images

B. Resize images -> Compute homography -> Detect edges -> Warp images -> Blend images

C. Match points -> Resize images -> Compute homography -> Warp images -> Detect keypoints

D. Warp images -> Detect keypoints -> Compute homography -> Match points -> Blend images

Solution

1. Step 1: Detect and match keypoints

   First, find keypoints in both images and match them to get corresponding points.

2. Step 2: Compute homography and warp image

   Use matched points to compute homography, then warp one image to align with the other.

3. Step 3: Blend images to create panorama

   Finally, blend the aligned images smoothly to form a panorama.

4. Final Answer:

   Detect keypoints -> Match points -> Compute homography -> Warp one image -> Blend images -> Option A

5. Quick Check:

   Correct panorama steps = Detect keypoints -> Match points -> Compute homography -> Warp one image -> Blend images [OK]

Hint: Detect -> Match -> Compute -> Warp -> Blend for panorama [OK]

Common Mistakes:

• Resizing images before matching points
• Warping images before computing homography
• Detecting keypoints after warping images