iccv iccv2013 iccv2013-390 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Iasonas Kokkinos
Abstract: We present a method to identify and exploit structures that are shared across different object categories, by using sparse coding to learn a shared basis for the ‘part’ and ‘root’ templates of Deformable Part Models (DPMs). Our first contribution consists in using Shift-Invariant Sparse Coding (SISC) to learn mid-level elements that can translate during coding. This results in systematically better approximations than those attained using standard sparse coding. To emphasize that the learned mid-level structures are shiftable we call them shufflets. Our second contribution consists in using the resulting score to construct probabilistic upper bounds to the exact template scores, instead of taking them ‘at face value ’ as is common in current works. We integrate shufflets in DualTree Branch-and-Bound and cascade-DPMs and demonstrate that we can achieve a substantial acceleration, with practically no loss in performance.
Reference: text
sentIndex sentText sentNum sentScore
1 Shufflets: shared mid-level parts for fast object detection Iasonas Kokkinos Ecole Centrale de Paris INRIA Center for Visual Computing Galen Team, INRIA-Saclay iasonas. [sent-1, score-0.247]
2 fr ∗ Abstract We present a method to identify and exploit structures that are shared across different object categories, by using sparse coding to learn a shared basis for the ‘part’ and ‘root’ templates of Deformable Part Models (DPMs). [sent-3, score-0.585]
3 This results in systematically better approximations than those attained using standard sparse coding. [sent-5, score-0.175]
4 To emphasize that the learned mid-level structures are shiftable we call them shufflets. [sent-6, score-0.221]
5 Our second contribution consists in using the resulting score to construct probabilistic upper bounds to the exact template scores, instead of taking them ‘at face value ’ as is common in current works. [sent-7, score-0.465]
6 We integrate shufflets in DualTree Branch-and-Bound and cascade-DPMs and demonstrate that we can achieve a substantial acceleration, with practically no loss in performance. [sent-8, score-0.437]
7 In this work we use the models of [8] and focus on accelerating multiple-category detection by sharing computation. [sent-11, score-0.152]
8 Part score computation is the first, and most timeconsuming step in the pipeline of object detection with DPMs; at this stage Histogram-of-Gradient (HOG) features [3] are convolved with part filters to provide local part scores, which are then combined to deliver object scores. [sent-12, score-0.669]
9 and-Bound (DTBB) [16]; the real bottleneck is the frontend convolution with the part filters. [sent-15, score-0.185]
10 In this work exploit the redundancy that exists among the part filters of multiple categories to reduce the cost of computing part scores. [sent-16, score-0.435]
11 For this, we learn a common, ‘shared’, basis to reconstruct the part and root filters; this basis serves as a mid-level interface between parts and HOG features. [sent-17, score-0.689]
12 This approach was recently advocated in [29, 12], while [17, 33, 27] have pursued similar ideas, either by replacing the 32-dimensional inner products of HOG cells with lookup-based approximations [17, 33] or by building a common basis for multiple part filters [27]. [sent-18, score-0.568]
13 Along a complementary path, [6] developed a highly-optimized frequency domain acceleration technique for part score computation. [sent-19, score-0.295]
14 1393 Figure 2: A dictionary of 128 3 × 3 shufflets learned with Shift-Invariant Sparse Coding (SISC). [sent-20, score-0.423]
15 More recently [4] used hashing to efficiently retrieve the approximate top-K scoring templates at every candidate part position. [sent-21, score-0.144]
16 Our work presents advances with respect to these works in the following aspects: First, regarding quality of approximation, compared to [29] we obtain a better approximation for the same number of terms, by allowing the mid-level parts to translate. [sent-22, score-0.133]
17 Second, regarding detection accuracy, unlike [27, 33, 29] who take the midlevel-based approximation ‘at face value’, we only use it as a rough initial estimate of the part scores, which is then refined around a subset of locations shortlisted based on the approximation. [sent-23, score-0.4]
18 For this we use the probabilistic bounding technique of [17], and thereby attain virtually identical performance to the DPMs of [8]. [sent-24, score-0.197]
19 Third, unlike [6] who compute the part scores densely we have the option of computing part scores ‘on demand’, i. [sent-25, score-0.556]
20 Fourth, by virtue of being ‘shiftable’ our midlevel parts can be used as a common basis to reconstruct both the part and the root filters. [sent-28, score-0.483]
21 Finally, even though our method is linear in the number of categories -unlike the constant complexity of [4]- it has the advantage of coming with controllable accuracy, and we demonstrate that it yields virtually identical results as [8]. [sent-30, score-0.201]
22 In particular we combine the proposed shufflets with the Dual-Tree Branch-and-Bound technique [16, 17] which was originally developed to accelerate the stages following part computation. [sent-31, score-0.608]
23 We use shufflets to construct probabilistic upper bounds for the part scores, and use these bounds to drive branch-and-bound to a small set of candidate object locations. [sent-32, score-1.022]
24 Our algorithm eventually computes the exact values of the part scores and the correct object score, but only around the locations shortlisted by the preliminary bounding stage. [sent-33, score-0.565]
25 This spares us from computing the exact part scores at locations that do not merit it. [sent-34, score-0.466]
26 Previous Work The idea of using shared parts to detect multiple categories has its roots in the earliest days of recognition [7, 14, 37, 5], but its application to detection with statistical object models started later. [sent-38, score-0.295]
27 A ground-breaking work was [32] who proposed the sharing of weak learners for multi-view and multi-class object detection, using regionbased features as inputs to decision stumps. [sent-39, score-0.133]
28 These works have consistently demonstrated that the learned shared parts correspond to generic grouping rules at the lowest levels and more semantic configurations at the higher parts of the hierarchy. [sent-43, score-0.197]
29 The sparselets work of [29] introduced a sparse coding-based approach to express multiple part filters on a common basis and thereby accelerate detection with DPMs; in [12] this was shown to improve accuracy in large-scale category classification, if properly integrated during training. [sent-45, score-0.76]
30 In [27] the steerability of the part filters was enforced during training, and was shown to result in both better training and faster testing. [sent-46, score-0.28]
31 Even though shufflets could potentially be integrated in training, we have not explored this direction yet. [sent-47, score-0.379]
32 In that respect when it comes to part sharing for DPMS, the most relevant works are those covered in the introduction. [sent-48, score-0.237]
33 Shufflets: shiftable mid-level parts We start by describing the operation that we want to accelerate through our mid-level basis. [sent-50, score-0.355]
34 The score of a filter p at position y is expressed as the inner product of a weight vector wp and a HOG feature hy, sp(y) = hwp, hyi, with wp ∈ RD. [sent-51, score-0.409]
35 For a part filter of size v ·( yh) = = ( h6w w· 6) we hwaivthe D =∈ v · h. [sent-52, score-0.187]
36 = =So ( every part requires roughly a teho suizsean odf multiplications per candidate location. [sent-54, score-0.207]
37 Our goal is to recover a basis b of B vectors to approximate a large set of weight vectors wp, p = 1. [sent-55, score-0.206]
38 Coming now Lto finding a good basis, b, we consider first the basis that minimizes the ‘2 norm of the distortion, while using expansion vectors of bounded ‘0 norm. [sent-62, score-0.319]
39 This results in the following sparse coding problem: XP (P1) s. [sent-63, score-0.141]
40 3 penalizes the distortion of the basis elements, the constraint in Eq. [sent-76, score-0.206]
41 4 enforces the sparsity of the expansion vector and the constraint in Eq. [sent-77, score-0.113]
42 5 ensures that the basis elements will have unit ‘2 norm. [sent-78, score-0.275]
43 This standard sparse coding formulation was used for sparselets [29]. [sent-80, score-0.204]
44 We propose instead to use Shift-Invariant Sparse coding, which intuitively amounts to having ‘shiftable’ basis elements. [sent-81, score-0.206]
45 Namely, instead of using a basis with arbitrary vectors of dimension v · h · d, we first consider a kernel k for our basis edlimemeennstiso on a s·md,al wleer f dirosmt caoinns oidfe rsi aze k ev0r n· hl 0k k· od. [sent-83, score-0.412]
46 l Wlowes t htehen displaced kernel to be fully contained in the original basis domain. [sent-85, score-0.284]
47 hkb0,0, 1395 This illustrates the merit of this scheme: during the approximation of wp we are free to use any of the replicas kν,η of k; but at test time we only need to convolve with a single replica k0,0, and then use appropriately displaced convolution scores. [sent-91, score-0.471]
48 B (10) (11) kvbb,hb where the last constraint indicates that the replica of kernel kb is used to form the b-th basis element. [sent-109, score-0.31]
49 For known basis elements, the expansion coefficients are obtained through OMP, as in P1. [sent-111, score-0.319]
50 However the estimation of the basis elements is more challenging, since we no longer optimize over an arbitrary basis b, but rather constrain the basis to be ‘shiftable’, through the set of constraints in Eq. [sent-112, score-0.687]
51 11becomes decoupled in the different frequencies; we refer to [13] for further details, since we rely entirely on their approach for basis learning. [sent-116, score-0.206]
52 Our main difference with the method of [13] is that we use the ‘0 instead of ‘1 sparsity penalty on the expansion vectors. [sent-117, score-0.113]
53 We demonstrate in Table 1 the decrease in reconstruction error attained by our method, when compared to the simpler sparse coding technique employed in [29]. [sent-119, score-0.199]
54 Actually we used the sparse coding results of [29] as initialization for our optimization procedure, which practically ensures a better approximation quality. [sent-120, score-0.283]
55 Furthermore, the approximation of the root scores can be effortlessly achieved by our method; qualitative results are provided in Fig. [sent-122, score-0.302]
56 From approximate scores to score bounds We now describe how shufflets can be used to provide not only an estimate of the part score, but also a probabilistic upper bound to it. [sent-125, score-1.125]
57 This allows us to avoid a pitfall of Root filters for components 1and 3 of class ‘aeroplane’ Reconstructions using shufflets (SISC). [sent-126, score-0.478]
58 most of the existing works on fast approximate part score computation, which take the approximated score ‘at face value’, which incurs performance degradation as faster -and cruder- approximations are used. [sent-129, score-0.443]
59 Instead, as in [17], we consider that we should be using the shufflet-based scores only as proxies to the exact part scores; these proxies serve to reduce the set of locations that are considered for a subsequent, more refined estimation of the exact part score. [sent-130, score-0.724]
60 For this, we efficiently compute upper bounds to the part scores, and use them in bounding-based detection with DPMs. [sent-131, score-0.451]
61 This guarantees accuracy, and allows us to get the best of both worlds, namely a fast ‘bottom-up’ detection of objects with quickly computable scores, which is then complemented by an exact, ‘top-down’ score refinement around promising locations [17, 18]. [sent-132, score-0.251]
62 Turning to how this can be achieved, we construct bounds on the approximation error: ? [sent-133, score-0.254]
63 = s −ˆ s = hw, hi − h wˆ, hi (12) between the exact score s obtained by convolving with the 1396 and expansion length, L. [sent-134, score-0.289]
64 as a random variable, and construct probabilistic bounds that are valid with controllable accuracy. [sent-140, score-0.258]
65 which provides upper and lower bouns for s in terms What remains is to express the second moment of ? [sent-150, score-0.166]
66 c = X(w[c,d] − wˆ [c,d])h[c,d] (16) dX= X1 with c ranging over the C HOG cells comprising a part filter, and d ranges over the 32 HOG cell dimensions. [sent-156, score-0.189]
67 Namely, for every cell c we are taking the inner product between then part score approximation error w [c, ·] − wˆ [c, ·] and tthhee nas psaortci astceodr eH aOppGr ocxeilml, hti o[cn, n· ]e . [sent-157, score-0.427]
68 What we gain in this way is that instead of computing a 32-dimensional inner product per HOG cell, we only need to multiply the two quantities on the right of Eq. [sent-167, score-0.102]
69 14 to construct the upper and lower bounds to the score. [sent-174, score-0.248]
70 The quantities involved in this bounding scheme are illustrated in Fig. [sent-175, score-0.104]
71 1 Figure 4: Part score approximation and bounding: our goal is to rapidly bound the value ofthe part score s shown on the top right. [sent-179, score-0.506]
72 14 is formed from two quantities, a shufflet-based approximation in (d) and an estimate of the approximation error’s second moment, shown in (c). [sent-181, score-0.168]
73 The values of the lower and upper bounds for pe = 0. [sent-183, score-0.328]
74 Integration with DPM detection We now describe how we integrate the bound obtained above with the Dual-Tree Branch-and-Bound (DTBB) method [16, 17]; for lack of space, we refer to [16, 17] for details, and intend to provide a thorough presentation in a forthcoming technical report. [sent-187, score-0.139]
75 In [16] Branch-and-Bound is used to bypass Generalized Distance Transforms (GDTs); this can result in substantial speedups for the part combination phase. [sent-188, score-0.144]
76 However in [16] we consider the part scores to be computed in advance of DTBB, while this is actually the main bottleneck in detection with DPMs. [sent-189, score-0.337]
77 Instead, following [17], we now integrate into DTBB our efficient upper bound of the part scores. [sent-190, score-0.302]
78 (21) |∈X{z} {Sz The |com{pzutati}on of the bounds relevant to the geometric term, B[x0, x] exploits the fact that Xs , Xd are rectangular, and is detailed in [16]. [sent-194, score-0.17]
79 Coming to bounding the unary terms, the approach of [16] has been to compute the exact part scores at every location s[x] and then obtain S,S. [sent-195, score-0.412]
80 Instead we propose to accelerate the computation of S,S by initially sidestepping the computation of s[x] upsing the probabilistic bound pof Eq. [sent-197, score-0.294]
81 14 apre with probability 1 − pe lpower and upper bounds of s[x] respectively. [sent-199, score-0.328]
82 lBitays1e d − on thpese we can upper and lower bound S as follows: S = maxx0∈Xs0 s[x0] ≤ maxx0∈Xs0 s[x0] and S = minx0∈Xs0 s[x0] ≥ minx0∈Xs0 ≤s[x m0],a xand thereby use s, s as surrogates for ]s[ ≥x] imn iDnTBB. [sent-200, score-0.272]
83 As soon as Branch-and-Bound converges to singleton intervals, we evaluate the exact part scores, s[x]; as we show in the experimental section, this boosts performance when compared to using only the midlevel-based approximation. [sent-202, score-0.221]
84 This more elaborate computation however is performed around a drastically reduced set of points, namely around those image locations that survive the first, quick bounding phase. [sent-203, score-0.232]
85 Our method thereby combines the speed of shared part filter computation with the accuracy of DPMs. [sent-204, score-0.381]
86 The remedy used in [8] is to use separate conservative thresholds for the PCA-based part scores, and estimate them from the training data. [sent-210, score-0.202]
87 l oEcavteino though we nheaevde Lthe o option osf, using our bounding-based scheme to compute upper bounds throughout, we can now avoid it altogether, since the empirically computed thresholds for cascades can take into account the distortion due to the shufflet approximation. [sent-213, score-0.438]
88 We report Average Precision scores on all classes in Table 2. [sent-217, score-0.134]
89 5 we provide precision-recall curves for bicycle detection when using (a) the ‘golden standard’ Truncated Distance Transform (TDT) detector of [11] and (b) the raw shufflet score for different combinations of basis size, B, and expansion size, L (we use 2L terms for the larger root filters). [sent-219, score-0.751]
90 As expected, increasing the size of the basis and the expansion improves performance, but there still remains a gap in performance. [sent-220, score-0.319]
91 Moreover we observe that the exact value of the probability of error pe is not that important, and the performace is robust even for relatively large values of pe. [sent-222, score-0.157]
92 The first row indicates the time spent to compute part scores by the different methods, and the following rows indicate detection times. [sent-224, score-0.337]
93 For more conservative threshold values the part score is fully evaluated at more points and the merits of having a quick first fast pass get eliminated. [sent-225, score-0.339]
94 o0s itt as fnass to;u bt tuht our es hTDufTfl-ebt-absaesded im approximation atunr nbse out to be faster than both DTBB and TDT for moderate values of the threshold θ. [sent-228, score-0.121]
95 We note that these timings are (i) for a single-threaded implementation and (ii) do not include steps that are shared (a) Shufflet parameter variation (b) Raw vs bounding-based score Figure 5: Precision-recall curves for bicycles on PASCAL VOC 2007. [sent-233, score-0.281]
96 The left plot shows the performance of the raw, shufflet-based score for different shufflet parameter combinations, ans the right plot shows the performance of the bounding-based scheme. [sent-235, score-0.289]
97 by all classes, namely HOG pyramid construction, and shufflet convolutions. [sent-258, score-0.233]
98 Conclusion In this work we have introduced shufflets, a shiftable basis for mid-level part representation, demonstrated its usefulness for part sharing in DPMs, and introduced probabilis1399 Ou[r8w]orka0 irp. [sent-264, score-0.808]
99 tic bounds to accommodate the effects of distortions due to approximations on this basis, thereby enabligh fast and accurate detection with DPMs. [sent-285, score-0.344]
100 In future work we intend to explore how this basis can be exploited during training [2, 12, 27], incorporated in hierarchical models [18, 34] and used for scalable object detection [4], while also exploring connections with convolutional models [35, 20, 15, 19]. [sent-286, score-0.422]
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