iccv iccv2013 iccv2013-288 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Jeffrey Byrne, Jianbo Shi
Abstract: In this paper, we propose a new family of binary local feature descriptors called nested shape descriptors. These descriptors are constructed by pooling oriented gradients over a large geometric structure called the Hawaiian earring, which is constructed with a nested correlation structure that enables a new robust local distance function called the nesting distance. This distance function is unique to the nested descriptor and provides robustness to outliers from order statistics. In this paper, we define the nested shape descriptor family and introduce a specific member called the seed-of-life descriptor. We perform a trade study to determine optimal descriptor parameters for the task of image matching. Finally, we evaluate performance compared to state-of-the-art local feature descriptors on the VGGAffine image matching benchmark, showing significant performance gains. Our descriptor is thefirst binary descriptor to outperform SIFT on this benchmark.
Reference: text
sentIndex sentText sentNum sentScore
1 edu Abstract In this paper, we propose a new family of binary local feature descriptors called nested shape descriptors. [sent-3, score-0.836]
2 These descriptors are constructed by pooling oriented gradients over a large geometric structure called the Hawaiian earring, which is constructed with a nested correlation structure that enables a new robust local distance function called the nesting distance. [sent-4, score-1.59]
3 This distance function is unique to the nested descriptor and provides robustness to outliers from order statistics. [sent-5, score-0.828]
4 In this paper, we define the nested shape descriptor family and introduce a specific member called the seed-of-life descriptor. [sent-6, score-0.908]
5 We perform a trade study to determine optimal descriptor parameters for the task of image matching. [sent-7, score-0.247]
6 Our descriptor is thefirst binary descriptor to outperform SIFT on this benchmark. [sent-9, score-0.407]
7 It is well known that for the task ofimage matching, descriptors constructed with larger support outperform descriptors with smaller support [20, 8, 3, 17, 15]. [sent-16, score-0.33]
8 (left) Hawaiian earrings with k-fold rotational symmetry define a member of the nested shape descriptor family called the seed-oflife descriptor (right) Two Hawaiian earrings substructures in the seed-of-life descriptor are highlighted in grey. [sent-18, score-1.576]
9 For example, there may be arbitrarily large outliers in the descriptor due to occlusions and geometric variation effects far from the descriptor center. [sent-20, score-0.417]
10 In this paper, we introduce nested shape descriptors to address this tradeoff. [sent-22, score-0.699]
11 A nested shape descriptor (NSD) is a family of binary local feature descriptors constructed by pooling oriented and scaled gradients over a large geometric structure called an Hawaiian earring. [sent-23, score-1.211]
12 An example of the nested shape descriptor is shown in figure 1. [sent-24, score-0.789]
13 Each descrip- tor has global support covering the entire image, and the structure of the descriptor exhibits fractal self-similarity in scale. [sent-25, score-0.252]
14 This correlated nested structure enables new a robust distance function called the nesting distance. [sent-26, score-1.25]
15 The nesting distance uses order statistics for robustness to outliers while maintaining a descriptor with global support. [sent-27, score-0.881]
16 1201 • • Binary: NSDs are binary, which enables for compact storage :a NndS Dalslo awres bthinea nesting hdi estnaanbclee st foo use a pfaacstt Hamming distance, without sacrificing matching performance. [sent-30, score-0.646]
17 Robust local distance function: The nesting distance iRs a quadratic dloisctaaln dcies tfaunnccet ifounn:cTt iohne tnheastt nisg r odibsutsant ctoe corruption of the descriptor due to occlusions, geometric variations or lighting. [sent-31, score-0.942]
18 In this paper, we provide sufficient conditions for construction of a nested shape descriptor using key concepts of cumulative nested pooling and log spiral normalization. [sent-32, score-1.538]
19 We perform a trade study to determine optimal descriptor parameters for the task of image matching. [sent-33, score-0.247]
20 Recent work has focused on introducing binary features from local comparison tests [3, 8, 17, 15] which enables fast distance metric based on Hamming distance and faster derivatives [13]. [sent-40, score-0.218]
21 A taxonomy for comparing and contrasting local feature descriptors can be described in terms of five criteria: preprocessing, support, pooling, normalization and descriptor distance. [sent-42, score-0.334]
22 Preprocessing refers to the filtering performed on the input image, support patterns are the geometric struc- ture used for constructing the descriptor and pooling is the aggregation of filter responses over the support structure. [sent-43, score-0.383]
23 Using this taxonomy, the nested shape descriptor is most closely related to DAISY, BRISK and FREAK. [sent-45, score-0.789]
24 In the taxonomy of [16], the nesting distance is per-exemplar (“where”), online (“when”) using order statistics (“how”) without requiring any offline training. [sent-51, score-0.719]
25 Nested Shape Descriptors In this section, we describe the construction of nested shape descriptors. [sent-53, score-0.615]
26 NSD are constructed by first defining the nested pooling structure (section 3. [sent-54, score-0.672]
27 We provide definitions for this construction and show how the nested shape descriptor is constructed from these pieces (section 3. [sent-56, score-0.816]
28 4), which uses the properties of the nested descriptor to provide robust distance function. [sent-59, score-0.801]
29 Finally, we define a specific member of the nested shape descriptor family called the seed-of-life descriptor (section 3. [sent-60, score-1.082]
30 The nested descriptor and nesting distance are compared to a generic grid descriptor (e. [sent-64, score-1.581]
31 The red X’s and green checkmarks show where a grid descriptor is corrupted due to the scene variation, which leads to poor matching performance. [sent-67, score-0.261]
32 For these cases, the NSD and nesting distance are able to select the best subset of supports during matching to provide robustness to these scene variations. [sent-68, score-0.789]
33 Given a pair of descriptors, the nesting distance computes a weighted sum of the best k coordinate matches. [sent-71, score-0.661]
34 The nesting distance relies on nesting, such that all supports are linked by exactly one point in the center of the descriptor. [sent-75, score-0.797]
35 Hawaiian Earrings and Nested Pooling Nested shape descriptors represent shape using cumulative pooling of oriented gradients within Hawaiian earrings. [sent-80, score-0.335]
36 Figure 1 (right) shows an example of the Hawaiian 1202 distance selects the best subset of supports in the nested descriptor that cover only the object (green checkmarks). [sent-81, score-0.9]
37 (middle) Viewpoint changes for long and thin foreground structures introduce errors in grid descriptor matching due to large changes in the background. [sent-82, score-0.219]
38 The nesting distance selects the subset of supports during matching that cover the foreground and are the correct scale to allow for background variation. [sent-83, score-0.789]
39 (right) Scale changes without scale invariant detectors introduce errors in grid descriptor matching due to changes in local support. [sent-84, score-0.235]
40 The nesting distance uses a subset of both large and small scale supports, ignoring intermediate scale supports with corruption. [sent-85, score-0.76]
41 earring substructure formed by a nested set of circles all intersecting at exactly one point at the center. [sent-86, score-0.703]
42 The Hawaiian earring is a nested structure analogous to Matryoshka or Russian nesting dolls, where each smaller doll fits neatly inside the next larger doll. [sent-87, score-1.258]
43 Hawaiian earrings may be combined into sets such that each earring is called a lobe. [sent-88, score-0.27]
44 Each lobe exhibits scale symmetry and all earrings intersect at exactly one point in the center. [sent-89, score-0.232]
45 For example, in figure 1(right), the two lobes highlighted in grey are Hawaiian earrings K6 (1) and K6 (4) and the two largest circles are referenced as supports K6 (1, 4) and K6 (4, 4). [sent-97, score-0.327]
46 Nested Shape Descriptors A nested shape descriptor D at interest point p is defined by nested pooling, logarithmic spiral normalization and binarization of oriented gradients B over a nested support Kn. [sent-100, score-2.2]
47 01 iofthdˆe(ir,wjis,ek) > 0 (3) Equation (1) is nested pooling. [sent-102, score-0.556]
48 The descriptor d(i, j,k) is the pooled response for orientation subband i, lobe j and lobe scale k. [sent-104, score-0.319]
49 Observe that the bandpass octave scale s is equal to the Hawaiian earring support radius k. [sent-105, score-0.253]
50 As the support radius increases, the pooling support contains the next smaller support, resulting in nested pooling within a lobe. [sent-107, score-0.865]
51 A nested support set Kn exhibits a logarithmic spiral when considering neighboring supports. [sent-113, score-0.791]
52 A nested shape descriptor can be binarized by computing the sign of (2). [sent-120, score-0.789]
53 This constructs a nested shape descriptor with binary entries. [sent-121, score-0.829]
54 (top) Logarithmic spiral property of the nested shape descriptor provides normalization and binarization. [sent-124, score-0.914]
55 (bottom) An NSD is formed at each interest point by (left) nested pooling of scaled and oriented gradients and (right) logspiral difference and binarization. [sent-126, score-0.71]
56 pooling is equivalent to pooling of fixed radius over scales × of a steerable pyramid [19], which is analogous to a “flattening” of a pyramid representation of scaled and oriented gradients. [sent-127, score-0.325]
57 The final nested shape descriptor D is a binary vector of length (R |K| |K|) for R orientation bands over |vKec| loorb oefs aenndg |hK (|R supports per floobre R. [sent-128, score-0.982]
58 The Seed-of-Life Descriptor The nested shape descriptors in section 3. [sent-132, score-0.699]
59 In this section, we define a specific member of this family called the seed-of-life nested shape descriptor or simply the seedof-life descriptor. [sent-135, score-0.908]
60 The seed-of-life descriptor is a nested shape descriptor such that the nested pooling Kn is defined using a rotationally symmetric geometric structure called the seed-oflife. [sent-136, score-1.661]
61 ber of the nested shape descriptor family since it exhibits rotational symmetry where Hawaiian earring lobes are spaced uniformly in angle. [sent-143, score-1.095]
62 Nesting Distance The nesting distance is a robust quadratic local distance function [16] unique to NSDs based on order statistics. [sent-147, score-0.748]
63 Given two nested descriptors p and q, the nesting distance d(p, q) uses order statistics to partition the supports of two nested descriptors into inliers and outliers by sorting the squared differences up to a given maximum order k. [sent-148, score-2.145]
64 Then, × the nesting distance is equivalent to computing the conditional Gaussian distribution of inliers given outliers. [sent-149, score-0.722]
65 Let p and q be two nested descriptors of length n. [sent-163, score-0.64]
66 dLifefet trhenisc partition )b e represented by selection − 1204 points between the reference image (middle) and the observed image using the nesting distance (left) and Euclidean distance (right). [sent-165, score-0.749]
67 The Euclidean distance is affected by occlusions at the image boundary (left ellipse) resulting in local misalignments, while the nested distance is more robust to these occlusion effects. [sent-166, score-0.736]
68 Then, the nesting distance d is d(p, q, Λ, k) = (p −q)T(I −S(k+1,n))ΛS(1,k)(p −q) (6) where Lambda is an optional quadratic weighting matrix. [sent-168, score-0.661]
69 Furthermore, if k = n and Λ = I then the nesting distance is equivalent to the Euclidean distance. [sent-170, score-0.68]
70 If the nesting distance is of the form (6), then it is equivalent to an unnormalizednegative log likelihood ofa conditional Gaussian distribution for inliers given outliers. [sent-173, score-0.722]
71 The nesting distance was designed specifically for the structure of the nested shape descriptor. [sent-182, score-1.276]
72 Therefore, this enables the use of order statistics to partition the supports into inliers and outliers, since all supports have one point in common. [sent-185, score-0.276]
73 The nesting distance cannot be used for descriptors with support constructed on a log-polar or Cartesian grid. [sent-186, score-0.822]
74 Figure 4 shows an example of the benefits of the nesting distance for image matching. [sent-191, score-0.661]
75 We extract interest points using an edge based detector, compute nested descriptors at each point, then perform greedy minimum distance assignment from the reference to the observation using either the nesting distance or Euclidean distance. [sent-192, score-1.372]
76 This example shows that the nested distance is more robust to occlusions at the image border than the Euclidean distance. [sent-193, score-0.649]
77 Finally, The nesting distance has two useful properties that are proven in the supplementary material. [sent-194, score-0.661]
78 First, the nesting distance is non-metric, since it does not satisfy identity or the triangle inequality properties. [sent-195, score-0.661]
79 Second, the nesting distance is robust up to corruption of n k coordinates. [sent-197, score-0.661]
80 Experimental Results In this section, we provide experimental results for the nested shape descriptor and nesting distance for the task of image matching. [sent-199, score-1.45]
81 First, we perform a trade study using the new experimental protocol of similarity stereo matching to determine an optimal set of descriptor parameters for the seed-of-life descriptor. [sent-200, score-0.343]
82 Next, we compare results for the seed-of-life and binary seed-of-life descriptor for the standard VGG-Affine benchmark [12] against SIFT [9] and BRISK [8]. [sent-201, score-0.214]
83 Finally, we show results on a challeng1205 Both SOL and BSOL outperform SIFT and BRISK, and Binary-SOL is the first binary descriptor to outperform SIFT on this benchmark. [sent-202, score-0.252]
84 VGG-Affine We show comparative performance for local feature descriptor matching on the VGG-Affine benchmark [12]. [sent-208, score-0.219]
85 We compare the performance of seed-of-life (SOL) and binary SOL descriptor (section 3. [sent-213, score-0.214]
86 Both SOL and Binary SOL use the Euclidean (and Hamming) distance, as we evaluate the effect of the nesting distance separately in section 4. [sent-217, score-0.661]
87 Furthermore, the binary SOL and SOL descriptor perform equally, which shows that the binarization provides a more compact descriptor without sacrificing performance. [sent-227, score-0.442]
88 VGG-Affine and Local Distance Functions Next, we performed a comparison of the nesting distance vs. [sent-230, score-0.661]
89 This evaluation was proposed to demonstrate the relative benefit of the nesting distance over the Euclidean distance baseline. [sent-232, score-0.732]
90 All distortion classes showed improved performance of the nesting distance over Euclidean. [sent-234, score-0.69]
91 This result summarizes the known tradeoff between descriptor support and matching performance as was discussed in section 1. [sent-264, score-0.253]
92 Automated Helicopter Landing In this section, we describe an application of the nested shape descriptors to the problem of visual landing of a ro- tary wing platform. [sent-274, score-0.789]
93 Seed-of-life descriptors are used to estimate the position and orientation of a candidate landing zone during approach and landing. [sent-275, score-0.276]
94 Visual pose estimation for landing is the problem of estimating the 6-DOF position and orientation of a moving landing zone relative to a vehicle with suitable accuracy for safe landing. [sent-276, score-0.282]
95 Application of the nested shape descriptors to visual landing zone pose estimation. [sent-280, score-0.858]
96 We com- pared the estimated landing zone position to differential GPS ground truth and results show that the nested shape descriptors achieve 2σ position errors in X, Y and Z of less than 1ft during the descent and landing. [sent-282, score-0.858]
97 Conclusions In this paper, we introduced the nested shape descriptor family and the associated nesting distance, and showed performance of the seed-of-life descriptor for the task of image matching. [sent-284, score-1.601]
98 Results show that this is the first binary descriptor to outperform SIFT on the standard VGG-Affine benchmark. [sent-285, score-0.233]
99 Furthermore, the NSD binary descriptor significantly outperforms BRISK, a state-of-the-art binary descriptor. [sent-286, score-0.254]
100 Evaluation of the nesting distance on VGG-Affine dataset. [sent-314, score-0.661]
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