SIFT Feature Matching, Error Metrics, and Lowe Ratio Filtering

Overview

A1. Visualizing SIFT Keypoints

• Every 10th keypoint from frame1.sift was plotted along with its gradient vector using quiver().
• Matching keypoints from slide1.sift were found using knnsearch() based on Euclidean distance in 128-D descriptor space.
• Collages for slide/frame pairs 1–3 were created:
  • Top: selected keypoints and gradients
  • Bottom: corresponding pairs linked by red lines
• The same code was reused for slide/frame 2 and 3.

A2. Measuring Error Between Features

• Compared three error measures:
  • Euclidean distance
  • Cosine similarity
  • Chi-square distance
• Used top 5% (P = 5%) best matches without skipping keypoints.
• Results:
  • Euclidean and cosine similarity gave identical matches.
  • Chi-square produced worse, likely due to sensitivity to noise or a faulty implementation.
• Chose Euclidean with P = 5% as the preferred measure due to performance and visual clarity.

A3. Pruning Keypoint Matches with Lowe Ratio

• Applied Lowe ratio filtering with a threshold of 92%:
  • Retained match only if the closest match was sufficiently better than the second-closest.
• Compared results to unfiltered matches from A2.
• Lowe ratio of 80% was too strict; 92% provided a balance between filtering and retaining matches.
• Observed that it successfully removed many-to-one mappings and inconsistent matches.

A4. Testing Error Metrics and Thresholds via Confusion Matrix

• Evaluated combinations of P and Lowe ratio using a nested loop.
• Generated confusion matrices to assess classification accuracy:
  • Best diagonal result: P = 73%, Lowe ratio = 0.65

    15  0   0
     0 13   0
     0  0 161
    

  • Best overall match count (without filtering): P = 44%, Lowe ratio = 1

    302 215  36
     52 233  22
     55  13 525
    

• Diagonal entries represent correct matches; off-diagonal entries indicate mismatches.
• Confusion matrix is a scalable tool for evaluating keypoint match accuracy and tuning hyperparameters.

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Conclusion

This assignment demonstrates robust SIFT feature matching through visualization, error metric comparison, and filtering using the Lowe ratio. The confusion matrix provides a quantitative basis for selecting optimal parameters and highlights the trade-off between strict filtering and total matches.