cvpr cvpr2013 cvpr2013-361 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Hsin-Yi Chen, Yen-Yu Lin, Bing-Yu Chen
Abstract: We present an algorithm that carries out alternate Hough transform and inverted Hough transform to establish feature correspondences, and enhances the quality of matching in both precision and recall. Inspired by the fact that nearby features on the same object share coherent homographies in matching, we cast the task of feature matching as a density estimation problem in the Hough space spanned by the hypotheses of homographies. Specifically, we project all the correspondences into the Hough space, and determine the correctness of the correspondences by their respective densities. In this way, mutual verification of relevant correspondences is activated, and the precision of matching is boosted. On the other hand, we infer the concerted homographies propagated from the locally grouped features, and enrich the correspondence candidates for each feature. The recall is hence increased. The two processes are tightly coupled. Through iterative optimization, plausible enrichments are gradually revealed while more correct correspondences are detected. Promising experimental results on three benchmark datasets manifest the effectiveness of the proposed approach.
Reference: text
sentIndex sentText sentNum sentScore
1 Inspired by the fact that nearby features on the same object share coherent homographies in matching, we cast the task of feature matching as a density estimation problem in the Hough space spanned by the hypotheses of homographies. [sent-2, score-0.418]
2 Specifically, we project all the correspondences into the Hough space, and determine the correctness of the correspondences by their respective densities. [sent-3, score-0.722]
3 In this way, mutual verification of relevant correspondences is activated, and the precision of matching is boosted. [sent-4, score-0.603]
4 On the other hand, we infer the concerted homographies propagated from the locally grouped features, and enrich the correspondence candidates for each feature. [sent-5, score-0.611]
5 Through iterative optimization, plausible enrichments are gradually revealed while more correct correspondences are detected. [sent-8, score-0.46]
6 Introduction Establishing correspondences among two or more images has attracted great attention in the field of computer vision. [sent-11, score-0.361]
7 Despite the great applicability, at least two difficulties hinder the advance in establishing correspondences of high quality. [sent-13, score-0.412]
8 (Top) We project correspondences into the transformation space, and distinguish correct (red) and wrong (black) correspondences by their densities. [sent-18, score-0.929]
9 (Bottom) Potential (green) correspondences are incrementally inferred by exploring density distributions of transformations grouped by BPLRs [17]. [sent-19, score-0.645]
10 They often work on a pre-selected, small subset of correspondence candidates, and result in low recall. [sent-22, score-0.147]
11 Our approach is developed upon the insight that nearby features on the same object typically share similar homographies if they are matched correctly. [sent-24, score-0.192]
12 It follows that their homographies tend to gather together in the transformation space. [sent-25, score-0.205]
13 Besides, each wrong matching is usually wrong in its own way. [sent-26, score-0.133]
14 It implies that the density of each correspondence in the transformation space can verify its correctness. [sent-27, score-0.304]
15 We leverage this property and cast the task of feature matching into a density estimation problem. [sent-28, score-0.225]
16 Specifically, we identify correct correspondences by comparing the densities among mutually exclusive correspon- dences, i. [sent-29, score-0.473]
17 On the other hand, it is allowed to dynamically recommend potential correspondences by exploring the density distributions of locally grouped features. [sent-32, score-0.619]
18 The proposed approach carries out Hough transform and inverted Hough transform alternately to establish robust feature correspondences. [sent-34, score-0.455]
19 First, every correspondence candidate is projected into the Hough space 222777666200 spanned by the transformations. [sent-36, score-0.172]
20 Only the correspondences associated to features within the same BPLR are considered in Hough voting. [sent-38, score-0.361]
21 In this way, mutual verification with relevant correspondences boosts the precision of matching. [sent-39, score-0.566]
22 Furthermore, it makes the complexity of geometric checking independent to the number of correspondences, and leads to one order speed-up in matching. [sent-40, score-0.072]
23 The inverted Hough transform recommends each feature additional transformations by investigating density distributions of nearby features covered by the same BPLR. [sent-42, score-0.631]
24 These transformations enable the dynamical construction of potential correspondences. [sent-43, score-0.111]
25 It allows relevant features to propagate their transformations to each other until consistency is reached. [sent-44, score-0.174]
26 Related Work The literature of feature correspondence is quite extensive. [sent-49, score-0.19]
27 Our review focuses on those that are relevant to the development of the proposed approach. [sent-50, score-0.057]
28 Point-to-point matching with local feature descriptors is a principal way for correspondence problems. [sent-52, score-0.257]
29 One way to address matching ambiguity with additional geometric checking is to cast feature correspondence as a graph matching problem. [sent-58, score-0.438]
30 By defining an objective function based on both photometric similarity and pairwise geometric compatibility between correspondences, promising results via graph matching have been demonstrated [11, 12, 18, 33]. [sent-59, score-0.096]
31 As mentioned in [20], graph matching is sensitive to corrupt cor- respondences and outliers. [sent-61, score-0.09]
32 Research efforts on clusteringbased mechanisms have been made to handle unconstrained matching cases. [sent-64, score-0.067]
33 Bottom-up clustering can integrate locally adaptive constraints to aggregates coherent bundles of matches. [sent-65, score-0.078]
34 [8] carry out object-based image matching via hierarchical agglomerative clustering. [sent-67, score-0.067]
35 RANSAC [14], a geometric verification model, can be incorporated with local descriptors to enhance the performance. [sent-75, score-0.116]
36 [32] treat each correspondence as a voter, and maintain an affinity matrix to encode how these correspondences vote each other according to their compatibilities. [sent-77, score-0.508]
37 Tolias and Avrithis [26] offer a variant of Hough transform for multi-object matching. [sent-79, score-0.096]
38 They rank the correspondences by adopting the mech- anism of pyramid match [15]. [sent-80, score-0.361]
39 Their method evenly quantizes the transformation space for fast matching. [sent-81, score-0.084]
40 However, the transformations of correct correspondences often distribute irregularly. [sent-82, score-0.513]
41 Our approach is a voting-based system, and can be distinguished by the advantage that the complexity of Hough voting for each feature is independent to the number of correspondences. [sent-84, score-0.153]
42 Furthermore, it dynamically enriches correspondences, and overcomes the low recall problem caused by working on a pre-selected, small subset of initial correspondences. [sent-85, score-0.065]
43 Most feature correspondence methods work with a small subset of pre-selected correspondences. [sent-87, score-0.19]
44 , [11, 13], propagate individual matches to nearby regions based on local appearance, but their performances heavily depend on the quality of initial matching. [sent-91, score-0.111]
45 [7] develop a region-growing algorithm to distinguish correct and incorrect correspondences. [sent-93, score-0.118]
46 [10] instead describe a progressive graph matching framework to enrich initial matching. [sent-95, score-0.139]
47 However, the yielded correspondences by their approach are biased to the density of features, and may be noisy due to diverse feature distributions in the two matched images. [sent-96, score-0.525]
48 In contrast, our method works on feature bundles guided by BPLRs, so the concerted transformations with high probability are transferred × × through mutually relevant features. [sent-97, score-0.424]
49 It turns out that the information can be propagated more efficiently and the resulting candidates of correspondences are much more targeted. [sent-98, score-0.447]
50 {Tvhe} region and the= =ce {nvter} }of feature vi ∈ VP ∪ VQ are denoted by Si and xi, respectively. [sent-101, score-0.102]
51 The appearance of vi is described by feature vector ui, and its orientation θi is estimated by a dominant orientation in the gradient histogram [23]. [sent-102, score-0.102]
52 O Vur goal is to find as many as possible correct correspondences in C. [sent-104, score-0.427]
53 Transformation space The local shape and the position of feature vi can be described by a 3 3 matrix T(vi), which specifies an affine strcarnibsefodrm by yo af vi ×w 3ith m regards (tov the normalized patch [23]: T(vi) =? [sent-107, score-0.161]
54 Given a feature pair viP ∈ VP and ∈ VQ, the relative transformation Hii? [sent-112, score-0.127]
55 can be considered as a point in the 6-dimensional transformation space. [sent-125, score-0.084]
56 projects xjP around For a pair of correspondences mii? [sent-152, score-0.361]
57 , they are considered compatible if the corresponding homographies are similar. [sent-154, score-0.146]
58 (5) Note that it is symmetric and is used to compute the dis- tances among correspondences in the transformation space. [sent-168, score-0.47]
59 deon ce C o r espondenc e H omography HHoough transform for homography verification transform for correspondence recommendation Figure 2. [sent-171, score-0.543]
60 The Proposed Approach Features with compatible geometric configurations are mutually dependent in matching. [sent-174, score-0.1]
61 We investigate feature dependence via BPLR detector [17], and cast feature matching as a density estimation problem. [sent-175, score-0.268]
62 The proposed approach carries out this idea by alternate Hough and inverted Hough voting. [sent-176, score-0.262]
63 While the former discovers the consistent homographies by projecting correspondences into the transformation space, the latter incrementally recommends potential correspondences driven by the concerted homographies. [sent-177, score-1.212]
64 Then the Hough and inverted Hough transforms for feature matching are introduced, respectively. [sent-180, score-0.279]
65 Initial correspondence candidates Our approach starts from the construction of initial correspondence candidates. [sent-183, score-0.372]
66 For each feature viP ∈ IP, we find {vQik}rk=1 × its r potential matchings in IQ according to their appearance similarity agnsd { vwit}h the constraint that none of the r matchings highly overlap. [sent-184, score-0.219]
67 c Wtioitnh d {iv iQikd}ekrd= b1y, the set of initial correspondences associated with viP is Mi = {miik = (vPi,vQik,Hiik)}kr=1, (6) viQk. [sent-191, score-0.394]
68 where Hiik is the relative transformation from viP to This process is repeated for each feature in IP. [sent-192, score-0.127]
69 Then the set of initial correspondences is constructed by N? [sent-193, score-0.394]
70 It contains many corrupted matchings zsien |cMe |th =ere r e ×xi Nsts at most one correct correspondence in each Mi. [sent-199, score-0.301]
71 In complex matching ctaosrkrse,c itt ciso usually dtehen case th eaact only a small subset of correct correspondences in C is included in M. [sent-200, score-0.519]
72 e Ethme precision woef correspondences decreases rapidly when r is larger than 5. [sent-202, score-0.417]
73 207 out of 222 correct correspondences in M are identified via Hough (contours) voting. [sent-207, score-0.427]
74 e (sb d) Henoouteg hth veo ctoinrgre acnt correspondences wdeitthec StIeFdT by 0b7ot hou approaches. [sent-209, score-0.361]
75 by only Hough voting and the nearest SIFT searching, respectively. [sent-210, score-0.11]
76 bcayn odnildyat Heso augndh vleoatdins gto a anddd thiteio nneaal 1e3st0 S (= T3 s3e7a − 207) eRcetd c aonrrde cyan leinncese are Mthe caorerr iedcetn correspondences (c) Inverted Hough voting. [sent-211, score-0.361]
77 It recommends rceosrpreecctti correspondences 147 (= 369 −222) correct (green lines) gd. [sent-212, score-0.52]
78 Hough transform for homography verification The goal at this stage is to detect the correct correspondences in M, which is either the initial correspondence sdeetn or sth ien e Mnri,ch wehdi shet by itthhee following stage. [sent-216, score-0.863]
79 s Wpoen idnevnecsetigate the property that the transformations of correct correspondences are concerted while those of incorrect correspondences are different in their own ways. [sent-217, score-1.044]
80 Hough voting for homography verification is employed since it can handle a high percentage of incorrect correspondences and detect correct correspondences via density estimation. [sent-218, score-1.159]
81 Specifically, the relative transformation of each correspondence is treated as a point in Hough space, and it is considered as a hypothesis about the underlying homography of interest. [sent-219, score-0.304]
82 Despite its robustness, Hough transform is developed upon the assumption that the hypotheses are a sum of independent votes, and thereby neglects the spatial dependence among features. [sent-220, score-0.096]
83 As pointed out in [3 1], choosing proper voters is critical in Hough transform, especially when voters are dependent. [sent-221, score-0.17]
84 We are inspired by the fact that nearby features on the same object are mutually dependent, and group relevant correspondences via BPLR detector [17], which re- spects object boundary and captures the local shape of an object. [sent-222, score-0.511]
85 It turns out that the performance of Hough voting is remarkably boosted. [sent-223, score-0.11]
86 Furthermore, only relevant, small-size correspondences are involved in density estimation, instead of the whole M. [sent-224, score-0.434]
87 We then cluster features relevant to viP by checking if they reside in at least one common BPLR, i. [sent-233, score-0.1]
88 (8) We assume that the grouped features with high probability undergo similar transformations in matching. [sent-236, score-0.134]
89 It follows that the correspondences relevant to viP in Hough voting can be collected by R(viP) = ? [sent-237, score-0.528]
90 (6), there exists at most one correct correspondence in Mi. [sent-241, score-0.213]
91 Hough voting as well as voters R(viP) are adopted eto in pick the most plausible correspondence associated with feature viP. [sent-242, score-0.418]
92 Specifically, it is accomplished by normalized kernel density estimation (KDE): mi∗i? [sent-243, score-0.102]
93 (10), zbautti oitn i tse required ivn comparing d aefnfescittie thse across feature points. [sent-249, score-0.068]
94 The procedure of correspondence selection is repeated for each feature in image IP. [sent-250, score-0.19]
95 It results in NP selected correspondences M∗ = We then sort them according oton dtheneicre ass Msocia=te {d mdens}ities in Eq. [sent-251, score-0.399]
96 (10), and return the top correspondences by a proper threshold. [sent-252, score-0.361]
97 An example of the verification results by Hough voting is shown in Figure 3b. [sent-254, score-0.197]
98 While Hough transform identifies correct correspondences M∗ M and boosts the precision in matching, tdheen goal Mof in⊆ve Mrted a Hough ttrsan thsefo rpmre ciiss oton e innri mcha Mchi so tthhaet gtohea lroe cfal inl can bde Hinocuregahs tedra. [sent-259, score-0.67]
99 sTfoherm locally eclnursitcehre Md fe saotures by BPLRs have consensus transformations and can assist each other in finding plausible correspondences. [sent-260, score-0.147]
100 We investigate this property and develop the inverted Hough transform, which allows grouped features to propagate their homographies to each other and recommends each feature ⊆ concerted correspondences by exploring the propagated homographies. [sent-261, score-1.077]
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