Given a feature in I 1, how to find the best match in I 2?

Transcription

1 Feature Matching 1

2 Feature matching Given a feature in I 1, how to find the best match in I 2? 1. Define distance function that compares two descriptors 2. Test all the features in I 2, find the one with min distance

3 Feature distance between f 1 and f 2 Simple approach is SSD(f 1, f 2 ) = Fails in ambiguous cases f 1 f 2 I 1 I 2

4 Feature distance between f 1 and f 2 Better approach is Ratio distance = SSD(f 1, f 2 ) / SSD(f 1, f 2 ) f 2 is best SSD match to f 1 in I 2 f 2 is 2 nd best SSD match to f 1 in I 2 f 1 f ' 2 f 2 I 1 I 2

5 Feature distance between f 1 and f 2 Better approach is Ratio distance = SSD(f 1, f 2 ) / SSD(f 1, f 2 ) The value is in the range [0, 1.0] f 1 f ' 2 f 2 I 1 I 2

6 Eliminating bad matches 0.2 true match false match feature distance Throw out features with distance > threshold How to choose the threshold?

7 True/false positives 0.2 true match false match feature distance Throw out features with distance > threshold The threshold affects performance True positives = # of detected matches that are correct Suppose we want to maximize these how to choose threshold? False positives = # of detected matches that are incorrect Suppose we want to minimize these how to choose threshold?

8 Evaluating the results Correct match We find a match True positive (TP) We did not find a match False negative (FN) Incorrect match False positive (FP) True negative (TN)

9 Evaluating the results Correct match We find a match True positive (TP) We did not find a match False negative (FN) Incorre ct match False positive (FP) True negative (TN) [ from wikipedia ]

10 Evaluating the results Correct match We find a match True positive (TP) We did not find a match False negative (FN) Incorre ct match False positive (FP) True negative (TN) TP TP + FN FP FP + TN [ from wikipedia ]

11 Evaluating the results TP TP + FN true positive rate false positive rate 1 FP FP + TN

12 Evaluating the results TP TP + FN true positive rate false positive rate 1 FP FP + TN With a loose threshold, where in the graph? (accept everything as a match)

13 Evaluating the results TP TP + FN true positive rate false positive rate 1 FP FP + TN With a tight threshold, where in the graph? (reject everything)

14 Evaluating the results TP TP + FN true positive rate false positive rate 1 FP FP + TN Where do you want the curve to go?

15 Evaluating the results ROC curve ( Receiver Operator Characteristic ) Different thresholds gives different points on this graph TP TP + FN true positive rate ROC Curves false positive rate 1 FP FP + TN Want to maximize area under the curve (AUC) Useful for comparing different feature matching methods For more info:

16 Evaluating the results Correct match We find a match True positive (TP) We did not find a match False negative (FN) Incorre ct match False positive (FP) True negative (TN) TP TP + FN FP FP + TN [ from wikipedia ]

17 Feature matching examples 17

18 SIFT Scale Invariance Results [slide by Neeraj Kumar]

19 SIFT Rotation Invariance Results [slide by Neeraj Kumar]

20 SIFT Lighting Invariance Results [slide by Neeraj Kumar]

21 SIFT Robustness to Clutter [slide by Neeraj Kumar]

22 SIFT for 3D Objects? [slide by Neeraj Kumar]

23 When does SIFT fail? Patches SIFT thought were the same but aren t:

24 SIFT References [Autopano] Software to make panaromas using SIFT. [Brown and Lowe, 2002] M. Brown and D. Lowe. Invariant Features from Interest Point Groups. BMVC, [Harris and Stephens, 1988] C. Harris and M. Stephens. A Combined Corner and Edge Detector. 4 th Alvey Vision Conference, [Lowe, 2004] D. Lowe. Distinctive Image Features from Scale-Invariant Keypoints. IJCV, [Lindeberg, 1994] T. Lindeberg. Scale-Space Theory: A Basic Tool for Analysing Structures at Different Scales. J. of Applied Statistics, [Matas et al., 2002] J. Matas, O. Chum, M. Urban, and T. Pajdla. Robust Wide Baseline Stereo from Maximally Stable Extremal Regions. BMVC, [Mikolajczyk, 2002] K. Mikolajczyk. Detection of Local Features Invariant to Affine Transformations. Ph.D. Thesis, [slide by Neeraj Kumar]

25 SIFT References [Mikolajczyk and Schmid, 2004] K. Mikolajczyk and C. Schmid. Scale and Affine Invariant Interest Point Detectors. IJCV, [Mikolajczyk and Schmid, 2005] K. Mikolajczyk and C. Schmid. A Performance Evaluation of Local Descriptors. PAMI, [SIFT] SIFT Binaries. [Witkin, 1983] A. Witkin. Scale-Space Filtering. IJCAI, [slide by Neeraj Kumar]