cvpr cvpr2013 cvpr2013-343 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Danfeng Qin, Christian Wengert, Luc Van_Gool
Abstract: Many recent object retrieval systems rely on local features for describing an image. The similarity between a pair of images is measured by aggregating the similarity between their corresponding local features. In this paper we present a probabilistic framework for modeling the feature to feature similarity measure. We then derive a query adaptive distance which is appropriate for global similarity evaluation. Furthermore, we propose a function to score the individual contributions into an image to image similarity within the probabilistic framework. Experimental results show that our method improves the retrieval accuracy significantly and consistently. Moreover, our result compares favorably to the state-of-the-art.
Reference: text
sentIndex sentText sentNum sentScore
1 ch } on , Abstract Many recent object retrieval systems rely on local features for describing an image. [sent-4, score-0.254]
2 The similarity between a pair of images is measured by aggregating the similarity between their corresponding local features. [sent-5, score-0.388]
3 In this paper we present a probabilistic framework for modeling the feature to feature similarity measure. [sent-6, score-0.359]
4 We then derive a query adaptive distance which is appropriate for global similarity evaluation. [sent-7, score-0.79]
5 Furthermore, we propose a function to score the individual contributions into an image to image similarity within the probabilistic framework. [sent-8, score-0.217]
6 Most of the recent state-of-the-art large scale image retrieval systems rely on local features, in particular the SIFT descriptor [14] and its variants. [sent-14, score-0.23]
7 We then derive a measure that is adaptive to the query feature. [sent-19, score-0.491]
8 We show - both on simulated and real data - that the Euclidean distance density distribution is highly query dependent and that our model adapts the original distance accordingly. [sent-20, score-0.678]
9 The expected distance to the non-corresponding features can be used to adapt the original distance and can be efficiently estimated by introducing a small set of random features as negative examples. [sent-22, score-0.402]
10 Furthermore, we derive a global similarity function that scores the feature to feature similarities. [sent-23, score-0.362]
11 Despite its simplicity, experimental results on standard benchmarks show that our method improves the retrieval accuracy consistently and significantly and compares favorably to the state-of-the-art. [sent-26, score-0.266]
12 Results in a large scale image retrieval system are presented in Section 5 and compared with the state-of-the-art. [sent-32, score-0.23]
13 Related Work Most of the recent works addressing the image similarity problem in image retrieval can be roughly grouped into three categories. [sent-34, score-0.407]
14 Feature-feature similarity The first group mainly works on establishing local feature correspondence. [sent-35, score-0.251]
15 In order to reduce quantization artifacts, [20] proposed to assign each feature to multiple visual words. [sent-39, score-0.199]
16 Additionally, product quantization [12] was used to esti111666001088 mate the pairwise Euclidean distance between features, and the top k nearest neighbors of a query feature is considered as matches. [sent-41, score-0.779]
17 Recently, several researchers have addressed the problem of the Euclidean distance not being the optimal similarity measure in most situations. [sent-42, score-0.299]
18 Intra-image similarity The second group focuses on effectively weighting the similarity of a feature pair considering its relationship to other matched pairs. [sent-45, score-0.459]
19 Inter-image similarity Finally, the third group addresses the problem of how to improve the retrieval performance by exploiting additional information contained in other images in the database, that depict the same object as the query image. [sent-54, score-0.748]
20 That is, after retrieving a set of spatially verified database images, this new set is used to query the system again to increase recall. [sent-56, score-0.369]
21 In [22], a set of relevant images is constructed using k-reciprocal nearest neighbors, and the similarity score is evaluated on how similar a database image is to this set. [sent-57, score-0.292]
22 By formulating the feature-feature matching problem in a probabilistic framework, we propose an adaptive similarity to each query feature, and a similarity function to approximate the quantitative result. [sent-59, score-0.848]
23 Although the idea of adapting similarity by dissimilarity has already been exploited in [11][17], we propose to measure dissimilarity by mean distance of the query to a set of random features, while theirs use k nearest neighbors (kNN). [sent-60, score-0.761]
24 Considering the large amount of data in a typical large scale image retrieval system, it is impractical to compute the pairwise distances between high-dimensional original feature vectors. [sent-64, score-0.35]
25 Our Approach In this section, we present a theoretical framework for modeling the visual similarity between a pair of features, given a pairwise measurement. [sent-68, score-0.257]
26 We then derive an analytical model for computing the accuracy of the similarity estimation in order to compare different similarity measures. [sent-69, score-0.4]
27 Since the distribution of the Euclidean distance varies enormously from one query feature to another, we propose to normalize the distance locally to obtain similar degree of measurement across queries. [sent-71, score-0.778]
28 Furthermore, using the adaptive measure, we quantitatively analyze the similarity function on the simulated data and propose a function to approximate the quantitative result. [sent-72, score-0.403]
29 A probabilistic view of similarity estimation We are interested in modeling the visual similarity between features based on a pairwise measurement. [sent-76, score-0.503]
30 Let us denote as xi the local feature vectors from a query image and as Y = {y1, . [sent-77, score-0.566]
31 F oufrt lohceramlo ferae-, let m(xi , yj) denote a pairwise measurement between xi and yj . [sent-84, score-0.771]
32 Instead of considering whether yj is similar to xi and how similar they look, we want to evaluate how likely yj belongs to T(xi) given a measure m. [sent-86, score-1.03]
33 This can be modeled as follows f(xi , yj) = p(yj ∈ T(xi) | m(xi, yj )) (1) For simplicity, we denote mj = m(xi , yj), Ti = T(xi), and Fi = F(xi). [sent-87, score-0.601]
34 T∈h Terefore, p(yj ∈ Ti) and p(yj ∈ Fi) only depend on the query feature xi. [sent-91, score-0.388]
35 In contrast, p(mj | yj ∈ Ti) and p(mj | yj ∈ Fi) are the probability density yfun∈cti oTns of the distr|ib yutio∈n Fof mj, for {yj | y ∈ Ti} and {yj | y ∈ Fi}. [sent-92, score-0.852]
36 Estimation accuracy Since the pairwise measurement between features is the only observation for our model, it is essential to estimate its reliability. [sent-100, score-0.224]
37 In other words, the better the measurement distinguishes the true correspondences from the false ones, the more accurately the feature similarity based on it can be estimated. [sent-102, score-0.407]
38 Query adaptive distance It has been observed that the Euclidean distance is not an appropriate measurement for similarity [21, 16, 11]. [sent-124, score-0.67]
39 As an example, Figure 2 depicts the distributions of the Euclidean distance of the corresponding and non corresponding features for the two different interest points shown in Figure 1. [sent-126, score-0.234]
40 It can be seen, that the Euclidean distance separates the matching from the non-matching features quite well in the local neighborhood of a given query feature xi. [sent-129, score-0.564]
41 Distribution of the Euclidean distance for two points from the simulated data. [sent-132, score-0.208]
42 Another property can also be observed in Figure 2: if a feature has a large distance to its correspondences, it also has a large distance to the non-matching features. [sent-136, score-0.337]
43 It is intractable to estimate the distance distribution between all feature and their correspondences, but it is simple to estimate the expected distance to non-corresponding features. [sent-138, score-0.343]
44 Since the non-corresponding features are independent from the query, a set of randomly sampled, thus unrelated features can be used to represent the set of noncorrespondent features to each query. [sent-139, score-0.202]
45 Moreover, if we assume the distance distribution of the non-corresponding set to follow a normal distribution N(μ, σ), then the estimattioo nfo error ao fn oirtsm mean rbiabsuetdio on a sμu,bσs)e,t hfoelnlow thse eansotimthearnormal distribution N(0, σ/N), with N the size of the subsneotr. [sent-140, score-0.221]
46 The probability that an unknown feature matches to the query one when observing their distance z can be modeled as, p(T|z)= {N1T+×N pTF(zN×|T p ×)( z p+ |(NzTF |) T}×−)1p(z|F) (14) with NT and NF the number of corresponding and noncorresponding pairs respectively. [sent-144, score-0.566]
47 Figure 3 illustrates how the adaptive distance recovers more correct matches compared to the Euclidean distance. [sent-147, score-0.253]
48 Similarity function In this section, we show how to derive a globally appropriate feature similarity in a quantitative manner. [sent-155, score-0.291]
49 After having established the distance distribution of the query adaptive distance in the previous section, the only unknown in Equation 5 remains As discussed in Sect∈ioTn 3. [sent-156, score-0.723]
50 The resulting curves follow an inverse sigmoid form such that the similarity is 1for dn → 0 and 0 if dn → 1. [sent-159, score-0.36]
51 For the reason of simplicity, we choose to approximate the similarity function as f(xi, yj) = exp(−α dn (xi, yj)4) (15) As can be seen in Figure 4, this curve is flatter and covers approximately the full range of possible values for c. [sent-166, score-0.27]
52 Overall method In this section we will integrate the query adaptive distance measurement and the similarity function presented 111666111311 0. [sent-171, score-0.868]
53 52 ftraluese c oorr erpeopnodnedenntt ppaairisrs ftraluese c oorr erpeopnodnedenntt ppaairisrs (a) Euclidean Distance (b) Query Adaptive Distance Figure 3. [sent-183, score-0.472]
54 The comparison of our adaptive distance to the Euclidean distance on dataset D. [sent-184, score-0.372]
55 Let the visual similarity between the query image q = {x1, . [sent-214, score-0.497]
56 1 with f(xi, yj) the pairwise feature similarity as in Equation 15. [sent-229, score-0.3]
57 For retrieval, we use a standard bag-of-words inverted file. [sent-231, score-0.238]
58 However, in order to have an estimation of the pairwise distance d(xi, yj) between query and database features, we add a product quantization scheme as in [12] and select the same parameters as the original author. [sent-232, score-0.665]
59 000 Voronoi cells according to a coarse quantization codebook Kc. [sent-234, score-0.198]
60 All features lcoocradtiendg i tno t ah ec same qVuoarnotnizoai cioenll are grouped into the same inverted list. [sent-235, score-0.295]
61 Each feature is further quantized with respect to its coarse quantization centroid. [sent-236, score-0.225]
62 That is, the residual between the feature and its closest centroid is equally split into m = 8 parts and each part is separately quantized according to a product quantization codebook Kp with Np = 256 centtoro aid psr. [sent-237, score-0.243]
63 Tdhucent, q euaacnhti fzeaattiuorne c cios deenbcooodked K using its related image identifier and a set of quantization codes, and is stored in its corresponding inverted list. [sent-238, score-0.414]
64 We select random features from Flickr and add 100 of them to each inverted list. [sent-239, score-0.345]
65 For performance reasons, we make sure that the random features are added to the inverted list before adding the database vectors. [sent-240, score-0.451]
66 At query time, all inverted lists whose related coarse quantization centers are in the k nearest neighborhood of the query vector are scanned. [sent-241, score-1.142]
67 Then, the query adaptive distance dn (xi, yj) to each database vector can directly be computed as in Equation 13. [sent-243, score-0.712]
68 In order to reduce unnecessary computation even more, a threshold β is used × to quickly drop features whose Euclidean distance is larger than β Nd(xi) . [sent-244, score-0.206]
69 Random feature dataset preparation Random images from Flickr (however different from the codebook training dataset) are used to generate the random feature dataset. [sent-274, score-0.236]
70 There are two parameters in our method: the number of random features in each inverted list, and the cut- × off threshold β for filtering out features whose contribution is negligible. [sent-278, score-0.402]
71 The influence of the number of the random features Table 1 shows the retrieval performance by varying the number of random features for each inverted list. [sent-279, score-0.699]
72 This supports the assumption, that the mean distance of a query feature to the dissimilar features can be robustly estimated even with a small number of random features. [sent-281, score-0.671]
73 We select 100 random features per inverted list throughout the rest of this paper. [sent-282, score-0.426]
74 The influence of the cut-off threshold β Table 2 shows that features with a distance larger than β Nd(xi) with Length50100500100010000 mAP0. [sent-283, score-0.226]
75 Influence of the size of the random feature set for inverted list on Oxford5k β0. [sent-289, score-0.413]
76 Effectiveness of our method Local adaptive distance In order to compare the adaptive distance function to the Euclidean distance, we use a threshold for separating matching and non-matching features. [sent-309, score-0.506]
77 4 shows the retrieval performance for a varying threshold both for the Euclidean distance as well as for the adaptive distance. [sent-311, score-0.45]
78 Overall, the best mAP using the adaptive distance is 3% better than the Euclidean distance. [sent-312, score-0.253]
79 Furthermore, the adaptive distance is less sensitive when selecting a non-optimal threshold. [sent-313, score-0.253]
80 Comparison of our adaptive distance with Euclidean distance on Oxford5k dataset Contributions of other steps In order to justify the contribution of other steps that are contained in our method, we evaluate the performance of our method by taking them out of the pipeline. [sent-316, score-0.433]
81 With multi-assignment only on the query side, mAP can increase from 0. [sent-321, score-0.317]
82 MA denotes the number of inverted lists that are traversed per query feature. [sent-325, score-0.611]
83 As expected, multi-assignment (scanning of several inverted lists) reduces the quantization artifacts and improves the performance consistently, however, in exchange for more computational load. [sent-329, score-0.366]
84 We choose to use reciprocal nearest neighbors (RNN) [22], for the reason that it can be easily integrated on top of a retrieval system independently from the image similarity function. [sent-331, score-0.472]
85 Considering that RNN tries to exploit additional information contained in other relevant database images, which are scarce in Holidays (in average only 2 to 3 relevant database images per query), it is difficult for query expansion methods to perform much better. [sent-334, score-0.448]
86 Retrieval Performance by using top k nearest neighbor as similar features [12] We first compare the performance of our method to [12] which relies on using the top k nearest neighbors of the Euclidean distance for selecting the similar features of a query. [sent-343, score-0.416]
87 In all of the previous experiments, each feature costs 12 bytes of memory. [sent-371, score-0.238]
88 Specifically, 4 bytes is used for the image identifier and 8 bytes for the quantization codes. [sent-372, score-0.51]
89 As [11] mainly show results using more bytes for feature encoding, we also compare our method to theirs with more bytes per feature. [sent-373, score-0.405]
90 As shown in Table 6, using more bytes further improves the retrieval results. [sent-374, score-0.364]
91 In all experiments, we compare favorably to the stateof-the-art by exploiting a simple similarity function without any parameter tuning for each dataset. [sent-376, score-0.252]
92 g for Oxford5k, we observe that our method is 30% faster than the original prod- uct quantization algorithm[12] while traversing the inverted lists, for the reason that our method requires no heap structure. [sent-386, score-0.366]
93 However, for a large scale experiment, we observe similar timing of our method to theirs as each inverted list contains a very long list of database features, and thus the computation of the Euclidean distance will dominate the computational time. [sent-387, score-0.582]
94 Conclusion In this paper, we present a probabilistic framework for the feature to feature similarity for high-dimensional local features such as SIFT. [sent-389, score-0.416]
95 We then propose a query adaptive feature to feature distance measurement and derive a global image to image similarity function. [sent-390, score-1.05]
96 Total recall: Automatic query expansion with a generative feature model for object retrieval. [sent-422, score-0.388]
97 Object retrieval with large vocabularies and fast spatial matching. [sent-509, score-0.24]
98 Lost in quantization: Improving particular object retrieval in large scale image databases. [sent-517, score-0.23]
99 Hello neighbor: Accurate object retrieval with k-reciprocal nearest neighbors. [sent-532, score-0.257]
100 Object retrieval and localization with spatially-constrained similarity measure and k-nn re-ranking. [sent-541, score-0.377]
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