cvpr cvpr2013 cvpr2013-373 knowledge-graph by maker-knowledge-mining

373 cvpr-2013-SWIGS: A Swift Guided Sampling Method


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Author: Victor Fragoso, Matthew Turk

Abstract: We present SWIGS, a Swift and efficient Guided Sampling method for robust model estimation from image feature correspondences. Our method leverages the accuracy of our new confidence measure (MR-Rayleigh), which assigns a correctness-confidence to a putative correspondence in an online fashion. MR-Rayleigh is inspired by Meta-Recognition (MR), an algorithm that aims to predict when a classifier’s outcome is correct. We demonstrate that by using a Rayleigh distribution, the prediction accuracy of MR can be improved considerably. Our experiments show that MR-Rayleigh tends to predict better than the often-used Lowe ’s ratio, Brown’s ratio, and the standard MR under a range of imaging conditions. Furthermore, our homography estimation experiment demonstrates that SWIGS performs similarly or better than other guided sampling methods while requiring fewer iterations, leading to fast and accurate model estimates.

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Our method leverages the accuracy of our new confidence measure (MR-Rayleigh), which assigns a correctness-confidence to a putative correspondence in an online fashion. [sent-4, score-0.38]

2 Furthermore, our homography estimation experiment demonstrates that SWIGS performs similarly or better than other guided sampling methods while requiring fewer iterations, leading to fast and accurate model estimates. [sent-8, score-0.356]

3 Introduction Many computer vision tasks have to deal with incorrect image feature correspondences to estimate various types of models, such as homography, camera matrix, and others. [sent-10, score-0.247]

4 , geometrical and matching information) to compute a set of confidences that are used to select image feature correspondences for generating models. [sent-18, score-0.355]

5 In this work, we focus on exploiting the matching scores to compute these confidences. [sent-19, score-0.257]

6 Assigning a confidence on the fly can be important for applications where environmental conditions can drastically change the matching scores distributions for correct and incorrect image feature correspondences, or when real-time performance is desired. [sent-48, score-0.827]

7 Moreover, we show that MR-Rayleigh can be used to predict correct image feature correspondences more accurately than Lowe’s ratio [ 14], Brown’s ratio [3], and MetaRecognition [ 18] under a variety of different imaging conditions. [sent-49, score-0.571]

8 Predicting when an image feature correspondence is correct is used and can be extremely beneficial in image based localization [12, 13, 16], where the prediction is used to keep “good” matches, and other applications. [sent-50, score-0.33]

9 MR-Rayleigh: A confidence metric that allows more accurate predictions of correct matches and enables an 222777667088 efficient and quicker guided sampling, under the assumption that every correspondence has its own correct and incorrect matching scores distributions. [sent-53, score-1.425]

10 SWIGS: A fast and efficient guided sampling process for robust model estimation based on MR-Rayleigh confidences that only has a single parameter to tune and does not need an offline stage. [sent-55, score-0.386]

11 Previous work There exists a rich literature about computing weights or confidences to bias the selection of image feature correspondences to generate models in a robust model estimation process. [sent-57, score-0.246]

12 These approaches in general exploit prior information such as matching scores ([2, 11, 19]) or geometrical cues ([5, 17]) to compute these weights. [sent-58, score-0.257]

13 1 we show an overview of the main loop in a robust model estimation, where the confidences or weights are used to select feature correspondences and generate hypotheses. [sent-60, score-0.246]

14 In this section, we review the approaches that use match- ing scores as priors to compute a sampling strategy, as well as methods for predicting correct correspondences. [sent-62, score-0.476]

15 Prediction of correct matches Lowe’s ratio [14] has been one of the most efficient and widely used heuristics for predicting the correctness of a putative correspondence. [sent-66, score-0.771]

16 The ratio compares the first nearest neighbor matching score against the second nearest neighbor matching score. [sent-67, score-0.39]

17 This ratio exploits the fact that correct matching scores tend to be distant from the incorrect matching scores, consequently producing lower values (assuming a distance-based matching score). [sent-68, score-0.9]

18 [3] extend Lowe’s ratio by comparing the first nearest neighbor matching score against the average of the second nearest neighbor matching scores of multiple correspondences. [sent-71, score-0.538]

19 A more elaborate method for predicting correct matches was introduced by Cech et al. [sent-73, score-0.481]

20 We show that using the closest matching scores to the nearest-neighbor score can reveal useful information about the correctness of a putative correspondence, which boosts the prediction performance considerably. [sent-78, score-0.622]

21 Guided sampling using matching scores Tordoff and Murray [19] calculate the correctnessconfidence by considering the matching scores and the number ofcorrespondences to which a feature was matched. [sent-83, score-0.643]

22 Then, the probability that a match is correct, given all the matching scores of its potential matches, is calculated and used for biasing the selection of matches that are more likely to be valid. [sent-85, score-0.555]

23 The BEEM’s global search mechanism [11] estimates the correct and incorrect correspondence distributions for a given pair of images by considering Lowe’s ratio as the random variable. [sent-86, score-0.596]

24 Subsequently, BEEM estimates the mixing parameter between the computed distributions, and calculates the correctness confidences using the distributions and the mixing parameter. [sent-88, score-0.274]

25 BEEM then assumes that the statistics of the matching scores are fixed for the given pair of images. [sent-89, score-0.257]

26 An important feature of this method, which is similar to our approach, is that it computes the confidences on the fly as it only requires the similarity scores of every feature. [sent-91, score-0.376]

27 Hence, BLOGS considers that the statistics of the matching scores are defined per correspondence. [sent-92, score-0.288]

28 In contrast with most of the previous approaches, except BLOGS, SWIGS assumes that every correspondence has its own correct and incorrect matching scores distributions. [sent-93, score-0.704]

29 To compute the confidence for every match, we exploit information from the tail of the incorrect matching score distribution. [sent-94, score-0.627]

30 Swift guided sampling In this section we describe the cess used in SWIGS. [sent-97, score-0.244]

31 Given a query of reference descriptors {r}jn=1, a tohfe r e bfeesrte putative correspondence neighbor rule: keypoint matching prodescriptor qi and a pool feature matcher decides following the nearest- j? [sent-98, score-0.618]

32 In practice, the minimum matching score can belong to a correct or incorrect match due to several nuisances; e. [sent-105, score-0.557]

33 , a minimum matching score produced by an incorrect image − 222777667199 correspondence can be obtained when the scene contains repetitive structures. [sent-107, score-0.491]

34 We can consider the sequence of matching scores {si,1, . [sent-108, score-0.257]

35 , si,n} for a single query descriptor qi as a sequence composed by scores generated independently from a correct matching-scores distribution Fc and an incorrect matching-scores distribution F c¯. [sent-111, score-0.683]

36 The correct score (if any) can be the second, third, or other ranked score in the sequence, and hence we must consider overlapping distributions. [sent-113, score-0.329]

37 The objective of MR is to predict the correctness of a classifier; in our context we are interested in knowing whether a putative match is likely to be correct or incorrect. [sent-117, score-0.458]

38 To achieve this objective, MR considers a ranked sequence of scores for a given query and selects the best ranked k scores s1:k (the k lowest scores). [sent-118, score-0.482]

39 Meta-Recognition’s goal is to classify s1 as correct or incorrect, and a threshold α corresponding to the crossover of Fc and F c¯ suffices for the task. [sent-127, score-0.249]

40 Under the assumption that Fc is predominantly to the left of F c¯, MR-Weibull uses W (the CCDF of the tail model) for testing whether s1 is an outlier, in which case it is classified as a correct match (see Fig. [sent-131, score-0.361]

41 Nevertheless, the tail-fitting process in MR-Weibull can be affected by correct matching scores that are present in s2:k causing a bad model of the tail W and affecting the prediction. [sent-133, score-0.569]

42 Moreover, R decays gradually as soon as the matching score approaches the region of the tail of F c¯. [sent-148, score-0.344]

43 Hence, MR-Rayleigh assigns a higher confidence to those matching scores that fall to the left of F c¯ and a lower confidence to those that fall near F c¯, in contrast with MRWeibull, which assigns the confidence of one over the support of Fc (illustrated Fig. [sent-149, score-0.826]

44 Hence, MR-Weibull can assign a high confidence to scores corresponding to incorrect matches that fall near the distribution’s crossover, yielding false-alarms. [sent-151, score-0.712]

45 Guided Sampling using MR-Rayleigh The main idea of guided sampling for model fitting from feature correspondences is to use the computed confidences {cl}lN=1 ofbeing a correct match, where lindicates the index {ofc a putative correspondence. [sent-154, score-0.781]

46 (a) The lowest matching score is produced either by fc (the matching scores distribution of correct matches) or f c¯ (the matching scores distribution of incorrect matches). [sent-165, score-1.278]

47 (b) Meta-Recognition models the tail of f c¯ with a Weibull distribution w to then calculate a confidence using the CCDF and predict correctness (d). [sent-167, score-0.455]

48 MR-Rayleigh approximates the support of fc by computing a Rayleigh distribution r from data taken from the tail to calculate a confidence using the CCDF and predict correctness (d). [sent-168, score-0.557]

49 scores obtained from the query and reference images to calculate the required Lowe’s ratios. [sent-169, score-0.361]

50 (7) where cl is the confidence assigned to the l-th correspondence, ml is the best similarity score, and mlr and mlc are the two closest similarity scores obtained from a similarity matrix. [sent-178, score-0.468]

51 BLOGS assigns a higher confidence when the greatest similarity score is high and is distant from its closest scores, and the confidence is severely penalized when its closest scores are near the greatest similarity score. [sent-179, score-0.631]

52 We calculate the confidence of being a correct match using MR-Rayleigh (see Sec. [sent-180, score-0.406]

53 dence, and σˆ is calculated with its k−1 closest scores nScWe,I aGnSd σav iosci dasl any density ietsst kim−a1tio clno saensdts/ ocro an o(sffline stage; instead, it calculates a confidence on the fly. [sent-183, score-0.332]

54 Experiments To assess the performance of SWIGS, we present two experiments: correct matches prediction accuracy, and a guided sampling experiment for estimating homography from image feature correspondences. [sent-189, score-0.846]

55 We used OpenCV’s implementation of SIFT [14] and SURF [1] for describing the keypoints and we included (non-optimized) C++ code to calculate MR-Rayleigh, MR-Weibull, Brown’s ratio, and Lowe’s ratio into the brute-force feature matcher in OpenCV. [sent-199, score-0.265]

56 With these modifications, the matcher returns either a confidence (MR-Rayleigh or MR-Weibull) or a ratio (Lowe’s or Brown’s) for every putative correspondence. [sent-200, score-0.474]

57 We matched the reference keypoints (found in the reference image) against the query keypoints (detected per query image) for every sub-dataset. [sent-201, score-0.47]

58 We then identified the correct matches by evaluating the following statement ? [sent-202, score-0.432]

59 (9) where xq and xr are the query and reference keypoints, H is the homography transformation provided in the dataset that relates the reference and the query image, and ? [sent-205, score-0.436]

60 Those matches that did not comply were labeled as incorrect matches. [sent-207, score-0.392]

61 These identified correct correspondences were verified manually and used as our ground truth in our experiments. [sent-208, score-0.287]

62 Subsequently, we then identified the correct correspondences in a similar manner as described earlier but using the affine transformations instead of the homographies in Eq. [sent-213, score-0.287]

63 Correct match prediction experiment In this experiment we are interested in measuring the performance of MR-Rayleigh on detecting correct matches; and we use the labeled correct correspondences as our ground truth. [sent-217, score-0.649]

64 We considered a True-Positive when the predictor accurately detects a correct match, and a FalsePositive when the predictor inaccurately detected a positive match, i. [sent-218, score-0.277]

65 709 were good thresholds for SIFT and SURF matches respectively, while for Lowe’s ratio (LWR) we used the recommended threshold of τLWR = 0. [sent-230, score-0.379]

66 The top row corresponds to SIFT matches and the bottom row to SURF matches, and each column presents results for a different imaging condition; with the exception of the first column, which presents the results over all imaging conditions. [sent-234, score-0.351]

67 3 that MR-Rayleigh (MRR) outperformed MR-Weibull (MRW), Lowe’s ratio (LWR), and Brown’s ratio (BR) over all imaging conditions for SIFT and SURF matches. [sent-242, score-0.249]

68 Consequently, MR-Weibull can struggle in detecting correct matches when a low FalsePositive rate is required. [sent-249, score-0.513]

69 Lowe’s ratio in gen- eral performs competitively for SIFT and SURF matches, whereas, Brown’s ratio tends to perform competitively for SIFT matches but tends to fall short for SURF matches. [sent-251, score-0.568]

70 We also conducted an experiment on detecting correct matches per descriptor on the entire testing dataset using the thresholds found during our tuning stage. [sent-252, score-0.499]

71 From the results of this experiment we can conclude that Lowe’s ratio returned the lowest False-Positive rate (FPR) regardless of the descriptor. [sent-256, score-0.268]

72 MR-Weibull produced the highest True-Positive rate for SIFT matches but with the highest False-Positive rate, while MR-Rayleigh produced a high True-Positive rate and a low False-Positive rate. [sent-257, score-0.479]

73 For SURF matches MR-Rayleigh produced the highest TruePositive rate and a low False-Positive rate. [sent-258, score-0.364]

74 6081 False Positives rate False Positives rate False Positives rate False Positives rate False Positives rate False Positives rate LEUVEN WALL False Positives rate False Positives rate False Positives rate False Positives rate Figure 3. [sent-290, score-0.81]

75 ROC curves for evaluating correct matches predictions by using MR-Weibull (MRW), MR-Rayleigh (MRR), Lowe’s ratio (LRW), and Brown’s ratio (BR). [sent-291, score-0.63]

76 The top row presents the results for SIFT matches and bottom row for SURF matches. [sent-292, score-0.249]

77 Matlab was used to obtain the distributions required for the two Guided-Sampling [19] methods and to fit Weibull and Generalized Extreme Value distributions for correct and incorrect matches respectively (see Fig. [sent-298, score-0.673]

78 We implemented only the prior estimation stage of BEEM and BLOGS’ global search mechanism, as we aim at comparing the confidence mechanism used for data sampling in a robust estimation. [sent-300, score-0.27]

79 We used OpenCV’s findHomography function (without the RANSAC option) and the correct matches identified by each method to estimate the homography. [sent-301, score-0.432]

80 We executed the experiment 5000 times with a stopping criterion of 100% of correct matches found and a maximum of 1000 iterations, since we are interested in applications that have a limited budget of iterations; an iteration is a completion of the loop in Fig. [sent-302, score-0.468]

81 We report the median of the number of iterations a method took to find the best model within the required number of iterations and the median of the percentage of correct matches that the best model found considered as a correct match. [sent-304, score-0.781]

82 Fitted distributions for SIFT matches (left) and SURF matches (right) used in GEN. [sent-306, score-0.547]

83 The percentage of correct matches are presented in the first and third rows, while the iterations are in the second and fourth rows. [sent-312, score-0.523]

84 We can observe that SWIGS tends to require in general fewer iterations than the other methods (second and fourth rows) to find models that consider a comparable or higher percentage of correct matches within the allowed number of iterations (first and third row). [sent-315, score-0.622]

85 The GEN method struggles more to find models that consider a high percentage of correct matches in scenes with repetitive textures, e. [sent-317, score-0.475]

86 BLOGS and a random sampling (Uniform) method perform similarly in finding models that consider a high portion of the correct matches. [sent-325, score-0.279]

87 The experimental results presented in this section demonstrate that SWIGS can perform similarly or better in finding models that consider a good portion of correct matches in a dense matching scenario. [sent-326, score-0.541]

88 The experiments also show that SWIGS tends to require fewer iterations than the other guiding sampling methods without sacrificing the number of correct matches found. [sent-327, score-0.627]

89 Moreover, this confirms that MR-Rayleigh confidences tend to identify good matches, and these confidences yield an efficient and accurate sampling strategy. [sent-328, score-0.38]

90 6 we show two different sets of correct image feature correspondences found with SWIGS and MLESAC. [sent-330, score-0.287]

91 Conclusions and future directions We have introduced MR-Rayleigh, a confidence measure based on Meta-Recognition (MR) [18] for predicting correct image feature correspondences more accurately. [sent-332, score-0.477]

92 CorectSIFTmatchesfoundbetwentherf enc im- age (top-right) and query image (top-left) of the Graf dataset and correct SURF matches between reference image (bottom-right) and query image (bottom-left) of the Boat dataset using SWIGS and MLESAC. [sent-334, score-0.715]

93 222777777644 est matching scores produced by the matcher when comparing the query descriptor against the reference descriptors. [sent-335, score-0.565]

94 MR-Rayleigh assigns a higher confidence when the lowest matching score is closer to zero and gradually decays as it gets closer to the tail of the incorrect matching scores distribution. [sent-336, score-0.979]

95 Our experiments showed that MR-Rayleigh outperformed Lowe’s ratio, Brown’s ratio, and MR-Weibull in predicting correct matches across several image correspondences obtained in different imaging conditions. [sent-338, score-0.636]

96 This prediction is efficient to compute and can be useful in many applications such as image-based localization where only good matches are kept; in estimating the inlier-ratio, which can be used to estimate the maximum number of iterations in RANSAC, and others. [sent-339, score-0.361]

97 We also presented SWIGS, an efficient method to sample data in a guided manner for robust model fitting that exploits the confidence delivered by MR-Rayleigh. [sent-340, score-0.289]

98 , BEEM [11] and Guided-MLESAC [19]) that assume a correct or incorrect matching score distribution for a pair of images or for an entire dataset, SWIGS considers that every query feature has a correct and incorrect matching scores distributions. [sent-343, score-1.291]

99 SWIGS then computes the confidence of every correspondence on the fly and uses these confidences for sampling matches to estimate a model such as a homography. [sent-344, score-0.803]

100 Our homography estimation experiment suggests that SWIGS achieves competitive or better results than BEEM’s and BLOGS’s [2] guided sampling mechanisms, and Tordoff and Murray’s guided MLESAC [19]. [sent-345, score-0.504]


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