cvpr cvpr2013 cvpr2013-280 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Liang Li, Wei Feng, Liang Wan, Jiawan Zhang
Abstract: This paper addresses a challenging problem of regularizing arbitrary superpixels into an optimal grid structure, which may significantly extend current low-level vision algorithms by allowing them to use superpixels (SPs) conveniently as using pixels. For this purpose, we aim at constructing maximum cohesive SP-grid, which is composed of real nodes, i.e. SPs, and dummy nodes that are meaningless in the image with only position-taking function in the grid. For a given formation of image SPs and proper number of dummy nodes, we first dynamically align them into a grid based on the centroid localities of SPs. We then define the SP-grid coherence as the sum of edge weights, with SP locality and appearance encoded, along all direct paths connecting any two nearest neighboring real nodes in the grid. We finally maximize the SP-grid coherence via cascade dynamic programming. Our approach can take the regional objectness as an optional constraint to produce more semantically reliable SP-grids. Experiments on object localization show that our approach outperforms state-of-the-art methods in terms of both detection accuracy and speed. We also find that with the same searching strategy and features, object localization at SP-level is about 100-500 times faster than pixel-level, with usually better detection accuracy.
Reference: text
sentIndex sentText sentNum sentScore
1 For this purpose, we aim at constructing maximum cohesive SP-grid, which is composed of real nodes, i. [sent-2, score-0.42]
2 SPs, and dummy nodes that are meaningless in the image with only position-taking function in the grid. [sent-4, score-0.422]
3 For a given formation of image SPs and proper number of dummy nodes, we first dynamically align them into a grid based on the centroid localities of SPs. [sent-5, score-0.522]
4 We then define the SP-grid coherence as the sum of edge weights, with SP locality and appearance encoded, along all direct paths connecting any two nearest neighboring real nodes in the grid. [sent-6, score-0.428]
5 We finally maximize the SP-grid coherence via cascade dynamic programming. [sent-7, score-0.209]
6 Our approach can take the regional objectness as an optional constraint to produce more semantically reliable SP-grids. [sent-8, score-0.268]
7 Experiments on object localization show that our approach outperforms state-of-the-art methods in terms of both detection accuracy and speed. [sent-9, score-0.088]
8 We also find that with the same searching strategy and features, object localization at SP-level is about 100-500 times faster than pixel-level, with usually better detection accuracy. [sent-10, score-0.162]
9 From the angle of MRF [8], superpixels (SPs), generated by grouping similar pixels into perceptually meaningful atomic regions [ 18], can dramatically reduce the number of variables to be optimized, thus leading to significant speed-up and allowing the analysis of long-range correlations. [sent-13, score-0.106]
10 (e)-(g) Object detection results of TurboPixel [14], SuperLattice [ 17] and pixel-level RC with finer searching step [23]. [sent-41, score-0.099]
11 Due to the apparent scale variation in query and target images, pixel-level RC needs finer step to search the foregroundbox, which may become very slow. [sent-42, score-0.066]
12 (h) and (i) are the results of our approach by regularizing SLIC SPs (c) without/with the guidance of SP objectness (d), respectively. [sent-43, score-0.224]
13 At the very beginning, superpixels were simply treated as fast over-segmentations to the image [ 15]. [sent-48, score-0.106]
14 1(c), image over-segmentations usually tend to generate SPs with variant sizes, shapes and irregular spatial dis333 111777224 tributions. [sent-50, score-0.067]
15 As the increasing usage of SPs in image parsing [22], segmentation [ 18, 24], co-segmentation [ 10, 20], and object localization [ 13], people start to realize the importance of structural regularities in SPs [ 1, 16, 21, 25]. [sent-51, score-0.13]
16 seeking proper tradeoff between the structural regularity and the boundary accuracy of superpixels. [sent-57, score-0.134]
17 Thus, compared to particular regular SP algorithms, it is more desirable to find a way rectifying arbitrary segmentations into a regular structure. [sent-62, score-0.131]
18 Besides, anothernotable weakness ofcurrent regular SP methods is that their performance may highly depend on the pre-computed edge map [ 16, 21]. [sent-63, score-0.083]
19 This paper, to the best of our knowl- edge, for the first time proposes a generic approach to optimally regularizing arbitrary SPs into a regular grid. [sent-64, score-0.135]
20 By this, we can both fully take advantage of the strength of various image segmentation/SP methods [ 1, 6, 5, 8], and enjoy the desirable properties of grid at the same time. [sent-65, score-0.081]
21 To this end, we define cohesive SP-grid, which is composed of (1) real nodes, i. [sent-66, score-0.367]
22 real SPs generated by any appropriate superpixel or segmentation algorithms, and (2) dummy nodes that are meaningless in the image with only position-taking function in the grid. [sent-68, score-0.531]
23 We aim at constructing maximum cohesive SP-grid that regularizes all pairwise SP connections into a lattice, while preserving the most important image structures. [sent-69, score-0.34]
24 First, we unevenly assign all real nodes into a grid by minimizing the overall locality discrepancy cost. [sent-71, score-0.383]
25 The initial cohesive SP-grid is obtained by appending proper number of dummy nodes at the end of each grid column. [sent-72, score-0.809]
26 We then iteratively refine the cohesive SP-grid by optimizing each grid column within its contemporary context configurations. [sent-73, score-0.418]
27 As an optional compensation, the regional objectness score [ 2] can also be used as an extra constraint to refine the SP coherence measurement, thus leading to a more semantically feasible SP-grid. [sent-75, score-0.417]
28 Experiments on object localization show that our approach outperforms state-of-the-art ones in terms of both detection accuracy and speed. [sent-76, score-0.088]
29 With the same strategy and features [23], object localization via our SP-grid is 100-500 times faster (including grid regularization and matching time) than pixel-level matching, and usually produces better detection accuracy. [sent-77, score-0.191]
30 The concept of superpixels stems from the homogeneous subregions generated by a fast oversegmentation to the image, e. [sent-80, score-0.106]
31 This kind of SPs usually form an irregular graph, with SP boundaries well-aligned to image edges. [sent-83, score-0.067]
32 Recently, people start to realize the advantages of regular structured SPs. [sent-85, score-0.075]
33 In contrast to the near-grid property of SLIC and TurboPixel, SuperLattice and LatticeCut are able to produce exact grid structured SPs. [sent-88, score-0.081]
34 For instance, based on a pre-computed reliable edge map, SuperLattice adopts a greedy strategy to generate the optimal paths of SP-grid by following the input edge map and satisfying the grid structural constraints [ 17]. [sent-89, score-0.186]
35 Recent useful object localization routines includes Region Covariance (RC) [23] and Efficient Subwindow Search (ESS) [ 12]. [sent-91, score-0.063]
36 In [23], the RC descriptor encoding color, gradient and locality features has been proposed for robust object detection in differen- t images. [sent-92, score-0.078]
37 Note that, integralimage acceleration cannot be directly applied to irregular graphs with arbitrary structures. [sent-96, score-0.09]
38 However, there is no general way to apply DP to any kind of irregular graphs of SPs. [sent-100, score-0.067]
39 With the proposed approach, most successful algorithms for both object localization and DP-based applications can be directly applied to SP-level, via any suitable type of SPs. [sent-101, score-0.063]
40 Overview To regularize arbitrary SPs with any kind of irregular structure, we consider optimally allocating SPs within a virtual grid. [sent-103, score-0.146]
41 Since the SP pair coherence defined as their centroid locality and regional appearance closeness in Eq. [sent-108, score-0.274]
42 Thus, we need also to incorporate position-taking dummy nodes. [sent-111, score-0.289]
43 1 Note that, condition (2) and (3) in the Definition 1 ensure the only positive-taking function of dummy nodes. [sent-115, score-0.289]
44 Hence, for a given set of real nodes P and dummy nodes D, our objective onf s generic aSlP n grid regularization can o bdee formally expressed as constructing an optimal cohesive SP-grid G = ? [sent-116, score-0.956]
45 Maximum Cohesive Grid of Superpixels For a given set of superpixels P, seeking global maximum cro ahe gsivivene SP-grid uisp generally Pin,t sreaecktaibnlge, g e. [sent-122, score-0.16]
46 alelt m r ×x c mum cohesive SP-grid i 1Direct path from p to q is the sequence of edges connecting them and passing only dummy nodes in the same row/column of p and q. [sent-124, score-0.703]
47 2 Moreover, recalling condition (3) in Definit(i|oPn| 1 + ,t 1he) state of a grid position, i. [sent-146, score-0.081]
48 either some real node or the dummy node, highly correlates to its nearest neighboring positions, if they together form a direction path. [sent-148, score-0.45]
49 2, this paper proposes a two-step nearotimum approach to (1) cohesive SP-grid initialization, and (2) cohesive SP-grid maximization by cascade DP. [sent-151, score-0.642]
50 Locality-based SP-grid initialization For a good cohesive SP-grid, the relative localities ofSPs in the image should be respected. [sent-154, score-0.394]
51 fN Pote in tthoa ct, oinl utmhisn paper, d binotght oof th our initialization and maximization are conducted in columns only, which is empirically proven to be comparable with optimizing in rows or in both rows and columns for object localization by our experiments. [sent-156, score-0.196]
52 c PThe c columns can be determined by c − 1 column-cuts, with all 2This assumes an SP can be assigned to more than one grid positions. [sent-158, score-0.118]
53 Then, we measure its goodness by t ahned following locality discrepancy score, and seek an optimal Bˆ = arg minB Loc(B) : ? [sent-163, score-0.137]
54 1 where Loc(B) is the sum of discrepancy values of all c cwohleumren Ls. [sent-167, score-0.084]
55 3, intrai is the intra-column discrepancy measured by the average centroid L2-distance ofall consecutive SP pairs in the #i column; interi is the inter-column discrepancy measured by the x-coordinates difference between two neighboring SPs of the #i column-cut; constant ? [sent-172, score-0.225]
56 > 0 avoids dividing by zero; Li = bi+1 − bi + 1is the length of the #i column and L¯ = is the average column length. [sent-173, score-0.12]
57 ωsep and ωlen are the weights of column separability and size regularity in Eq. [sent-176, score-0.102]
58 (4) (5) (6) #N real node Figure 4: Maximizing cohesive SP-grid using cascade DP. [sent-179, score-0.454]
59 The blue solid-lined region is the correlated subgraph used to calculate coh(p, k, n); the orange solid-lined region is the correlated subgraph of S(k − 1, p − 1); while the red tdhaesh c-olrinreedla region gisr atpheh c oofrr Se(lkat−e d subgraph corresponding to S(k, n). [sent-180, score-0.279]
60 The red arrow-lines starting from the #p position in column ρ denote the direct path connecting two nearest neighboring left and right real nodes of #p. [sent-181, score-0.269]
61 Then, we can efficiently obtain Bˆ with minimum discrepancy using Algorithm 1 under theB following boundary croepndain-tions: 2 ≤ k ≤ c, 1 ≤ n ≤ |P|, C(1, n) = loc(1, n) and tBioLn n(s1:, n2) ≤= k1. [sent-184, score-0.084]
62 ≤Ba cs,e 1d on nBˆ, we Pco|n,s Ctr(1uc,tn th)e = =ini ltoica(l 1c,onhe)s aivned DP-grid G(0) by simply padding proper nthuem ibneitri aolf c dummy nDoPd-egsr iadt Gthe end of each column (see Fig. [sent-185, score-0.386]
63 Dynamic maximization of cohesive SP-grid Starting from G(0) , our near-optimal maximum cohesive SP-Sgtaridrt nGg∗ firso m pro Ggressively refined by optimizing its every cSoPl-ugmridn uGnder current configurations of other columns. [sent-189, score-0.628]
64 Since we in turn repeatedly update every column of G ∗ via iDncPe e to w me ainxi tumrinze r ethpeea otevdelryal ul SdPat-ger eidve cryoh ceorelunmcen, we name the method cascade DP. [sent-190, score-0.088]
65 (8) Note that, S(k, n) is the maximum overall coherence of the correlated subgraph, asserting the maximum increments caused by allocating k dummy nodes in the first n real nodes of the current column ρ. [sent-193, score-0.889]
66 The correlated subgraph corresponding to such change is composed of all the nodes in the first n + k rows of G∗ whose states (i. [sent-194, score-0.228]
67 either some partthiceul fairrs tr nea+l nko rdoew or othf eG dummy node) jointly contribute to increasing Coh(G∗ ). [sent-196, score-0.31]
68 If p = n + 1, this dummy node will be assigned right after the #n real node. [sent-200, score-0.418]
69 BS (k, n) is the back-retrieval table recording the best position of #k dummy node that forms the best configuration of adding k dummy nodes in the first n real nodes of ρ. [sent-201, score-0.917]
70 Note, to meet condition (3) of Definition 1, calculating coh(p, k, n) needs to find the nearest horizontal real node neighbors for a particular position p (see Fig. [sent-202, score-0.129]
71 4 We repeat the above process column by column till convergence. [sent-204, score-0.1]
72 For a particular column ρ, the whole SP-grid can be divided into two correlated subgraphs, as shown in Fig. [sent-205, score-0.101]
73 The overall coherence of these two correlated subgraphs is S(k − 1, p − 1) aenncde ec oohft( hp,e ske, ntw),o respectively. [sent-207, score-0.245]
74 bItg risa chlsea irs t Sh(akt maximizing the coherence of the first (n + k) rows of G ∗ is equivalent to mtheax ciomhiezrienngc etheo sum ofirfscto (hne+renkc)e r oowfs the of ft wGo correlated subgraphs, i. [sent-208, score-0.236]
75 i=p (9) where il and ir is the left-first real node and right-first real node for #i real node of column ρ, kl and kr is the left-first real node and right-first real node for #k dummy node of column ρ. [sent-214, score-1.103]
76 Superpixel coherence metric We calculate the coherence of two SPs according to both their localities and appearances. [sent-219, score-0.397]
77 For the #p SP of P, we their localities and app 4As we only update columns of G∗ , the overall coherence along vertical direcAtiosnw eo fo any cpodalutme cno lisu mfunslly o fd Getermined by G(0) and is invariant to any configurations olfum thnat sco fluumllyn. [sent-220, score-0.286]
78 d eStoe,r we can btrye Gat the vertical coherence component of coh(p, k, n) for the #i column as a constant Vi, which can be pre-computed using G(0). [sent-221, score-0.199]
79 Then, we define the coherence of any two SPs p and q as Coh(p,q) = exp? [sent-224, score-0.149]
80 , (10) where op and oq are the normalized centroids of superpixel p and q, while Hp and Hq are the quantized color histograms of p and q, respectively. [sent-228, score-0.07]
81 1, the accuracy of our cohesive SP-grid for object detection may be further refined by incorporating the SP-level objectness that is defined as the mean objectness of all inclusive pixels. [sent-238, score-0.63]
82 We compute the objectness of each pixel by averaging the objectness scores of a number of randomly-sampled subwindows in the image using the method of [2]. [sent-239, score-0.318]
83 We impose the guidance ofthresholded SP objectness in the following way: for any two neighboring SPs p and q in the image, if they both survive the objectness thresholding, we amplify their original coherence Coh(p, q) by a constant factor F > 1. [sent-240, score-0.53]
84 Since our cohesive SPgrid initialization and maximization strictly satisfy Definition 1, the resultant G∗ is certainly a cohesive SP-grid. [sent-242, score-0.633]
85 Be- stiiodnes 1, ,t thhee c raesscualdtaen Dt GP guarantees strictly increasing coherence of G∗ in each iteration. [sent-243, score-0.17]
86 The complexity of SP-grid einnictieal oifzat Gion is O(|P| 2c), where |P| is the number of input superpixels na insd O c |isP |thec c,o wluhmerne n |Pum| ibse thr oef n target SP-grid. [sent-244, score-0.106]
87 Due to the computation of correlated subgraphs, the complexity of maximizing column ρ is O( |ρ| 3m), where |ρ| is tphlee nituym obfer m aofx irmeailz inngod ceos aumndn m i ss Oth(e| ρn|ummb)e,r w ohfe dummy nodes to be added in the column. [sent-245, score-0.531]
88 SuperLattice [17] and TurboPixel [ 14], by the task of object localization on benchmark datasets. [sent-249, score-0.063]
89 Note, for TurboPixel, we simply assign the grid coordinates for each SP as the grid coordinates of its corresponding seed [ 14]. [sent-250, score-0.162]
90 5 same integral-image based searching strategy and RC fea- 5The source code of our approach will be released soon. [sent-274, score-0.074]
91 333 111777779 For any object localization result R, in this paper, we measure its accuracy rate compared to ground truth GT as the cardinality ratio of their intersection and union sets Acc(R) = | RR∩∪GGTT||. [sent-275, score-0.063]
92 We can clearly see that for all methods, exact query constantly leads to higher accuracy than query by bounding box. [sent-279, score-0.088]
93 For pixel-level RC, searching by finer steps may lead to better results than using large steps, but with the cost ofrapidly increased running time. [sent-280, score-0.074]
94 The grid regularity of TurboPixel and SuperLattice help to quickly produce the detection results, with comparable (or better) accuracy to pixel-level methods. [sent-281, score-0.158]
95 Note that, except for MS, SP-grid based object localization is 100-500 times faster (including SP generation, SP-grid regularization and matching time) than pixel-level matching, while producing more than 15% accuracy improvements. [sent-283, score-0.063]
96 All results of our approach reported in Table 1were generated without objectness guidance. [sent-284, score-0.159]
97 We can see that compared to SuperLattice and TurboPixel, our approach tends to produce more accurate detection results better aligned to the real object boundaries. [sent-287, score-0.085]
98 5, our approach used objectness guidance to refine the SP pair coherence matrix using F = 10. [sent-290, score-0.339]
99 Conclusion We have proposed an efficient approach to regularize arbitrary superpixels into a regular grid by adding dummy n- Figure 6: The robustness of our approach to rotation and scale variances in object localization. [sent-304, score-0.553]
100 We also show how to incorporate regional objectness as an extra (optional) constraint to produce semantically more feasible SP-grids. [sent-307, score-0.227]
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