nips nips2012 nips2012-202 knowledge-graph by maker-knowledge-mining

202 nips-2012-Locally Uniform Comparison Image Descriptor

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Author: Andrew Ziegler, Eric Christiansen, David Kriegman, Serge J. Belongie

Abstract: Keypoint matching between pairs of images using popular descriptors like SIFT or a faster variant called SURF is at the heart of many computer vision algorithms including recognition, mosaicing, and structure from motion. However, SIFT and SURF do not perform well for real-time or mobile applications. As an alternative very fast binary descriptors like BRIEF and related methods use pairwise comparisons of pixel intensities in an image patch. We present an analysis of BRIEF and related approaches revealing that they are hashing schemes on the ordinal correlation metric Kendall’s tau. Here, we introduce Locally Uniform Comparison Image Descriptor (LUCID), a simple description method based on linear time permutation distances between the ordering of RGB values of two image patches. LUCID is computable in linear time with respect to the number of pixels and does not require ﬂoating point computation. 1

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 edu Abstract Keypoint matching between pairs of images using popular descriptors like SIFT or a faster variant called SURF is at the heart of many computer vision algorithms including recognition, mosaicing, and structure from motion. [sent-4, score-0.197]

2 As an alternative very fast binary descriptors like BRIEF and related methods use pairwise comparisons of pixel intensities in an image patch. [sent-6, score-0.528]

3 Here, we introduce Locally Uniform Comparison Image Descriptor (LUCID), a simple description method based on linear time permutation distances between the ordering of RGB values of two image patches. [sent-8, score-0.423]

4 1 Introduction Local image descriptors have long been explored in the context of machine learning and computer vision. [sent-10, score-0.276]

5 One of the most widely used local feature descriptors is SIFT which uses automatic scale selection, orientation normalization, and histograms of oriented gradients to achieve partial afﬁne invariance [15]. [sent-12, score-0.161]

6 Ferns uses sparse binary intensity comparisons between pixels in an image patch for descriptive power. [sent-28, score-0.462]

7 presented a novel binary feature descriptor they named BRIEF [4]. [sent-32, score-0.227]

8 Rather than training off-line, BRIEF makes use of random pixel intensity comparisons to create a binary descriptor quickly. [sent-33, score-0.44]

9 These descriptors can be matched an order of magnitude faster than SIFT with the Hamming distance, even on mobile processors. [sent-34, score-0.187]

10 There is a fuzzy notion that pairwise intensity comparisons are an approximation to signed intensity gradients. [sent-37, score-0.227]

11 The study of distances between permutations began near the inception of group theory and has continued unabated since [5, 7, 8, 9, 11, 10, 16]. [sent-41, score-0.213]

12 A notable early use of permutation based methods in the realm of visual feature description was presented by Bhat and Nayar in [2]. [sent-42, score-0.239]

13 They investigated the use of rank permutations of pixel intensities for the purpose of dense stereo, the motivation being to ﬁnd a robust alternative to the 2 norm. [sent-43, score-0.34]

14 Permutations on pixel intensities offer a transformed representation of the data which is naturally less sensitive to noise and invariant to monotonic photometric transformations. [sent-44, score-0.247]

15 Their measure was designed to be robust to impulse noise, sometimes called salt and pepper noise, which can greatly corrupt a rank permutation. [sent-46, score-0.213]

16 Their improvement was in a similar vein to [20], based on a modiﬁcation to Kendall’s tau [11]. [sent-50, score-0.231]

17 The key observation made was that both Kendall’s tau metric and Bhat and Nayar’s metric are highly sensitive to Gaussian noise. [sent-51, score-0.265]

18 We choose to explore the Hamming and Cayley distances, in part because they are naturally robust to Gaussian noise, impulse noise is not a major issue for modern imaging devices, and they are computable in linear time as opposed to quadratic time. [sent-53, score-0.223]

19 In contrast to [2] and [20] the elements of the SIFT descriptor are sorted, rather than sorting pixel intensities themselves. [sent-56, score-0.372]

20 It follows from this that other descriptors based on binary intensity comparisons are dimensionality reduction schemes on Kendall’s tau. [sent-62, score-0.295]

21 We then explore alternative distances based on the observation that image patch matching can be viewed as a near duplicate recognition problem. [sent-63, score-0.427]

22 In the next section we describe LUCID, provide a background on permutation distances and discuss optimizations for an efﬁcient implementation. [sent-64, score-0.23]

23 Our descriptors implicitly encapsulate all possible intensity comparisons in a local area of an image. [sent-69, score-0.266]

24 1 Constructing a descriptor Let p1 and p2 be n × n image patches with c color channels. [sent-72, score-0.426]

25 We can compute descriptors for both patches and the Hamming distance between them in three lines of Matlab as shown in Figure 1. [sent-73, score-0.279]

26 2 [~, desc1] = sort(p1(:)); [~, desc2] = sort(p2(:)); distance = sum(desc1 ~= desc2); Permutation distances A more detailed discussion of the following is given in [16]. [sent-79, score-0.168]

27 Bottom: An position π1 π2 = π1 ◦π2 , the permutation that illustration of an image patch split into its RGB color results from ﬁrst applying π2 then π1 . [sent-88, score-0.407]

28 A convenient representation for a permutation π ∈ Sn is the n dimensional vector with the ith coordinate equal to π(i); this is the permutation vector. [sent-96, score-0.264]

29 The convex hull of the permutation vectors Sn ⊂ Rn is the permutation polytope of Sn . [sent-97, score-0.312]

30 There are at least two classes of distances that can be deﬁned between permutations [16]. [sent-103, score-0.213]

31 Spatial distances can be viewed as measuring the distance travelled along some path between two vertices of the permutation polytope. [sent-104, score-0.325]

32 Examples of spatial distances are Kendall’s tau which steps along the edges of the polytope, the Euclidean distance which takes the straight line path, and Spearman’s footrule which takes unit steps on the circumscribed sphere of the polytope. [sent-105, score-0.465]

33 A disorder distance measures the disorder between two permutations and ignores the spatial structure of the polytope. [sent-106, score-0.299]

34 We choose the generalized Hamming distance to relate our descriptors because it is much simpler than the Cayley distance to compute. [sent-108, score-0.266]

35 Disorder distances are not sensitive to Gaussian noise, but are highly sensitive to impulse noise. [sent-111, score-0.293]

36 In contrast, Kendall’s tau is confused by Gaussian noise, but is more resilient to impulse noise [2, 20, 18]. [sent-112, score-0.401]

37 Impulse noise can severely corrupt these permutations since it can cause pixels in a patch to become maximal or minimal elements changing each element in the permutation vector. [sent-113, score-0.464]

38 In the presence of moderate impulse noise the Cayley and Hamming distances will likely become maximal while Kendall’s tau would be at O(1/n) its maximal distance. [sent-114, score-0.499]

39 Generally, modern imaging devices do not suffer from severe impulse noise, but there are other sources of impulse noise such as occlusions and partial shadows. [sent-115, score-0.381]

40 LUCID is used with sparse interest points and only individual image patches would be affected by impulse noise. [sent-116, score-0.36]

41 Since impulse noise would cause the distance to become maximal these bad matches can be reliably identiﬁed via threshold. [sent-117, score-0.28]

42 Kendall’s tau is normally used in situations where multiple independent judges are ranking sets or subsets of objects, such as top-k lists, movie preferences or surveys. [sent-118, score-0.277]

43 In these scenarios multiple judges are asked to rank preferences and the permutation polytope can be used as a discrete analog to histograms to gain valuable insight into the distribution of the judges’ preferences. [sent-119, score-0.255]

44 In the context of sparse image patch matching, the imaging sensor ideally acts as a single consistent judge; thus a single image patch will correspond to one vertex on the permutation polytope. [sent-120, score-0.649]

45 Ideally, for a pair of corresponding patches in different images the permutations should be identical. [sent-121, score-0.223]

46 Thus in our scenario the image sensor can be viewed as one judge comparing nearly identical objects. [sent-122, score-0.173]

47 The structure of the permutation polytope becomes less important in this context. [sent-123, score-0.18]

48 Since the Cayley and Hamming distances are computed in linear time rather than quadratic time like Kendall’s tau, they may be better suited for fast image patch matching. [sent-124, score-0.343]

49 In section 3 we present a proof demonstrating that BRIEF is a locality sensitive hashing scheme on Kendall’s tau metric between vectors of pixel intensities. [sent-125, score-0.403]

50 3 An efﬁcient implementation Table 1: Time in milliseconds to construct 10,000 Our choice to use the Hamming distance descriptors and to exhaustively match 5000x5000 de- is inspired by the new Streaming SIMD Extensions (SSE) instructions. [sent-127, score-0.196]

51 One additional bit per descriptor element can be reserved allowing the use of binary addition and bit masks to produce a packed Hamming distance. [sent-132, score-0.275]

52 For descriptor lengths less than 215 , 16 bits per element are needed. [sent-133, score-0.163]

53 This strategy supports RGB image patches up to 105x105 pixels and yields 4x parallelism on 64-bit processors. [sent-134, score-0.314]

54 Since pixel intensities are represented with small positive integers they are ideal candidates for stable linear time sorting methods like counting and radix sort. [sent-138, score-0.209]

55 Therefore LUCID offers a modest improvement in terms of descriptor construction time as shown in Table 1. [sent-141, score-0.191]

56 4 We investigate three versions of LUCID since they are the ﬁrst three multiples of eight: LUCID-24RGB, LUCID-16-Gray, and LUCID-8-Gray which respectively are LUCID on image patches that are 24x24 in RGB color, 16x16 grayscale and 8x8 grayscale. [sent-142, score-0.264]

57 Before construction a 5x5 averaging blur is applied to the entire image to remove noise that may perturb the order permutation. [sent-143, score-0.294]

58 BRIEF uses 48x48 image patches and produces a descriptor with 256 dimensions which is equal to the dimension of LUCID-16-Gray. [sent-149, score-0.396]

59 Deﬁne a test τ τ (p; x, y) := 1, if p(x) < p(y) 0, otherwise (1) where p is a square image patch and p(x) is the smoothed value of the pixel with the local coordinates x = (u, v) . [sent-157, score-0.353]

60 To construct a BRIEF descriptor a set of pre-deﬁned pixel comparisons are performed. [sent-159, score-0.324]

61 This pattern is a set of nd pixel coordinate pairs (x, y) that should be compared in each image patch. [sent-160, score-0.282]

62 A descriptor is then deﬁned to be the nd dimensional bitstring fnd (p) := 1≤i≤nd 2i−1 τ (p; xi , yi ). [sent-161, score-0.163]

63 suggest that intuitively these pairwise intensity comparisons capture the signs of intensity gradients. [sent-163, score-0.227]

64 2 Then the Hamming distance between two of these BRIEF descriptors is equivalent to the Kendall’s tau distance between the pixel intensities of the vectorized image patches. [sent-167, score-0.87]

65 The original formulation of BRIEF is LSH on the normalized Kendall’s tau correlation metric. [sent-168, score-0.231]

66 Let p1 , p2 be m dimensional vectorized image patches. [sent-170, score-0.203]

67 For image patches containing m pixels, BRIEF chooses a pattern of pairs P ⊆ {(i, j)|1 ≤ i < j ≤ m}, and for two vectorized image patches p1 , p2 , it returns the score (i,j)∈P I(B1 (i, j) = B2 (i, j)). [sent-172, score-0.543]

68 i < p(j) where p is the m dimensional vectorized image patch and i = j. [sent-176, score-0.298]

69 The order in which the nodes are visited on this path is equivalent to the order permutation produced by a stable sort of the pixel intensities. [sent-178, score-0.316]

70 Since this path is unique the order permutation implicitly captures all O(m2 ) possible comparisons in O(m) space. [sent-179, score-0.21]

71 The FAST (FKD) and SURF (SKD) keypoint detectors are used to ﬁnd the top 500 of 1500 keypoints in the ﬁrst image for each pair. [sent-191, score-0.289]

72 The ratio of correct matches for each descriptor to the total number of ground truth matches is deﬁned to be the recognition rate. [sent-193, score-0.292]

73 For each image pair and keypoint detector the highest and second highest recognition rates are bolded with the second highest rate preﬁxed by an asterisk. [sent-194, score-0.27]

74 2 Our subset consists of the image pairs that do not undergo extreme afﬁne warping since neither BRIEF nor LUCID 2 The dataset is available for download at http://www. [sent-346, score-0.178]

75 uk/˜vgg/research/ affine/ 6 (a) bikes (b) light Figure 3: Recognition rates for LUCID-*-RGB on the bikes 1|4 and light 1|4 image pairs. [sent-350, score-0.568]

76 The rates are plotted as a function of the width of the descriptor patch and of the blur kernel applied. [sent-351, score-0.359]

77 The best 100 of 300 FAST keypoints were detected in the ﬁrst image of each pair. [sent-352, score-0.243]

78 These image pairs are denoted by name 1|k, where k represents the second image used in the pair, e. [sent-356, score-0.3]

79 bikes 1|k indicates the pair consisting of the ﬁrst image of the bikes set to the ﬁfth. [sent-358, score-0.515]

80 In each experiment we detect a large number of keypoints in the ﬁrst image of a set and select the top N keypoints sorted by response. [sent-359, score-0.336]

81 For each pair of images the keypoints are warped into the second image using a ground truth homography. [sent-360, score-0.296]

82 This makes sense since the order permutation is invariant to monotonic intensity transformations and unlike BRIEF captures all the comparative information. [sent-369, score-0.242]

83 1 Parameter selection LUCID has three parameters, blur kernel width, image patch size, and the option to use color or grayscale images. [sent-371, score-0.379]

84 Figure 3 gives plots of recognition rate as a function of blur kernel width and patch size for the medium difﬁculty warps of two different image sets. [sent-372, score-0.418]

85 2 Distance distributions Here we examine the discriminative capability of three distances, the Cayley distance, the generalized Hamming distance and Kendall’s tau on pixel intensities. [sent-376, score-0.409]

86 The Ham- Figure 2: ROC curves for descriptors on ming distance represents LUCID which approximates the image pair bikes 1|4 for 200 keypoints. [sent-377, score-0.541]

87 7 (a) Cayley (b) Hamming (c) Kendall’s tau Figure 4: Histograms of distances for correct matches and impostors for the bikes 1|4 image pair. [sent-378, score-0.717]

88 The plots show the Cayley, the Hamming distance on the order permutations, and Kendall’s tau on pixel intensities. [sent-379, score-0.409]

89 Kendall’s tau requires O(m2 ) time to compute while the Cayley and Hamming distances run in O(m) time making them efﬁcient alternatives. [sent-381, score-0.329]

90 In Figure 4 we plot the distance distributions for correct matches and impostors, focusing on the medium difﬁculty warp of the bikes images. [sent-384, score-0.338]

91 We chose this image set because bikes is a natural man-made scene and its distributions are representative for the other image sets. [sent-385, score-0.47]

92 BRIEF does particularly well on this image pair because the only transformation that occurs is blur. [sent-387, score-0.175]

93 It is important to note that Kendall’s tau is inefﬁcient to compute with quadratic running time contrasted with the linear running time of the Cayley and generalized Hamming distances. [sent-391, score-0.231]

94 We introduced a new simple and effective image descriptor that performs comparably to SURF and BRIEF. [sent-393, score-0.313]

95 For our comparison and simplicity we made use of every pixel in an image patch. [sent-394, score-0.258]

96 However, given BRIEF’s superior performance to Kendall’s tau we plan to explore sampling patterns of pixels and other dimensionality reduction techniques. [sent-395, score-0.279]

97 It would also be useful to ﬁnd a binary representation of LUCID to allow for a more compact descriptor and use of existing LSH schemes. [sent-400, score-0.192]

98 WTAHash produces an embedding for ordinal feature spaces such that transformed feature vectors are in binary form and the Hamming distance between them closely approximates the original metric. [sent-402, score-0.242]

99 Finally, we hope that this new understanding of BRIEF and other binary descriptors will allow for the creation of new efﬁcient visual feature descriptors. [sent-403, score-0.219]

100 I-BRIEF: A fast feature point descriptor with more robust features. [sent-479, score-0.224]

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