cvpr cvpr2013 cvpr2013-418 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Zhuolin Jiang, Larry S. Davis
Abstract: The problem of salient region detection is formulated as the well-studied facility location problem from operations research. High-level priors are combined with low-level features to detect salient regions. Salient region detection is achieved by maximizing a submodular objective function, which maximizes the total similarities (i.e., total profits) between the hypothesized salient region centers (i.e., facility locations) and their region elements (i.e., clients), and penalizes the number of potential salient regions (i.e., the number of open facilities). The similarities are efficiently computedbyfinding a closed-form harmonic solution on the constructed graph for an input image. The saliency of a selected region is modeled in terms of appearance and spatial location. By exploiting the submodularity properties of the objectivefunction, a highly efficient greedy-based optimization algorithm can be employed. This algorithm is guaranteed to be at least a (e − 1)/e ≈ 0.632-approximation to t heeed optimum. lEeaxpster aim (een −tal 1 r)e/seult ≈s d 0e.m63o2n-satrpaptero txhimata our approach outperforms several recently proposed saliency detection approaches.
Reference: text
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1 edu Abstract The problem of salient region detection is formulated as the well-studied facility location problem from operations research. [sent-4, score-1.027]
2 High-level priors are combined with low-level features to detect salient regions. [sent-5, score-0.323]
3 Salient region detection is achieved by maximizing a submodular objective function, which maximizes the total similarities (i. [sent-6, score-0.231]
4 , total profits) between the hypothesized salient region centers (i. [sent-8, score-0.519]
5 , clients), and penalizes the number of potential salient regions (i. [sent-12, score-0.384]
6 The saliency of a selected region is modeled in terms of appearance and spatial location. [sent-16, score-0.511]
7 m63o2n-satrpaptero txhimata our approach outperforms several recently proposed saliency detection approaches. [sent-21, score-0.311]
8 Introduction Visual saliency modeling is relevant to a variety of computer vision problems including object detection and recognition [29, 26], image editing [13, 4, 6] and image segmentation [16]. [sent-23, score-0.311]
9 Most saliency models [2, 20, 4, 6, 8] are based on a contrast prior between salient objects and backgrounds. [sent-24, score-0.648]
10 Saliency models map natural images into saliency maps, in which each image element (pixel, superpixel, region) is assigned a saliency strength or probability. [sent-25, score-0.7]
11 For example, Figure 1 illustrates saliency detection results using four state-of-art algorithms [2, 6, 4, 26]. [sent-30, score-0.311]
12 However, given the ground truth salient regions in Figure 1(b), even for the first simple example, these approaches either fail to separate the object from the background, as in Figures 1(c) and 1(e), or mostly outline the object but miss the interior as in Figure 1(d). [sent-32, score-0.317]
13 (a) Input images; (b) Ground truth salient regions; (c)∼(e): Saliency maps using ;[ (2,b )6 ,G r4o] wnidth t cuothnt sraalsiet priors; (f) Saliency map using [26] with a low-rank prior. [sent-35, score-0.337]
14 [26, 28] represent an image as a low-rank matrix plus sparse noise, where the background is modeled by the low-rank matrix and the salient regions are indicated by the sparse noise (i. [sent-39, score-0.457]
15 For example, the poor saliency detection results in Figure 1(f) using the low-rank prior are due to the cluttered background. [sent-43, score-0.391]
16 We present a submodular objective function for effi- ciently creating saliency maps from natural images; these maps can then be used to detect multiple salient regions within a single image. [sent-44, score-0.767]
17 The diminishing return property of submodularity has been successfully applied in various applications including sensor placement [18], facility location [24] and image segmentations [15]. [sent-45, score-0.716]
18 Our objective function consists oftwo terms: a similarity term (between the selected centers of salient regions and image elements (superpixels) assigned to that center), and the ‘facility’ costs for the selected region centers. [sent-46, score-0.717]
19 The first term encourages the selected centers to represent the region elements well. [sent-47, score-0.351]
20 Hence it favors the extraction of high-quality potential salient regions. [sent-48, score-0.353]
21 The second term penalizes the number of selected potential salient region centers, so it avoids oversegmentation of salient regions. [sent-49, score-0.757]
22 It reduces the redundancy among selected salient region centers because the small gain obtained by splitting a region through the introduction of an extrane222000444311 ous region center is offset by the facility cost. [sent-50, score-1.538]
23 This high level prior is integrated with low level feature information into a unified objective function to identify salient regions. [sent-51, score-0.441]
24 This is in contrast to previous approaches based on low level features [2, 4] or high level information only [29, 5], or heuristic integration approaches [13, 6] based on weighted averages on the saliency maps from low level features and high level priors. [sent-52, score-0.504]
25 In contrast to some approaches [28, 27] which use uniform image patches to represent an image, our representation is based on super-pixels, which are less likely to cross object boundaries and lead to more accurately segmented salient regions. [sent-53, score-0.257]
26 Unlike approaches that identify only one salient region in an image [7], our approach identifies multiple salient regions simultaneously without any strong assumptions about the statistics of the backgrounds [28]. [sent-54, score-0.773]
27 The main contributions of our paper are: • Salient region selection is modeled as the facility locSaalti oenn tp rreogbiloenm, s ewlehcictioh nis sso mlvoedde e bleyd dm aasx tihmeiz faincgil a ysu lbo-modular objective function. [sent-55, score-0.749]
28 This provides a new perspective using submodularity for salient region detection, and it achieves state-of-art performance on two public saliency detection benchmarks. [sent-56, score-0.788]
29 • The similarities between hypothesized region centers aTnhde sthimeiril region eeltewmeeennts h are tfhoersmizueldate redg as a elanbteelr-s ing problem on the vertices of a graph. [sent-57, score-0.428]
30 • We naturally integrate high-level priors with low-level saliency rianltlyo a nutneigfireadte f hraigmh-elwevoerlk fporiro srasl iwenitth region dvee-l tection. [sent-60, score-0.514]
31 Related Work Existing salient region detection approaches can be roughly divided into two categories: bottom-up and topdown approaches. [sent-63, score-0.423]
32 Recently, [26, 28] decompose an image into a low-rank matrix representing the background (low-rank prior) and a sparse noise matrix indicating the salient regions by low-rank matrix recovery. [sent-68, score-0.428]
33 [27] proposes to use the boundary prior, which assumes the image boundary is mostly background for saliency detection. [sent-69, score-0.353]
34 Top-down approaches make use of high level knowledge about ‘interesting’ objects to identify salient regions [29, 5, 14]. [sent-70, score-0.382]
35 [29] learns interesting region features by dictionary learning and then generates the saliency map by modeling spatial consistency via a CRF model. [sent-71, score-0.491]
36 [5] proposes a topdown saliency algorithm by selecting discriminant features from a pre-defined filter bank. [sent-72, score-0.34]
37 In addition, some approaches integrate multiple saliency maps generated from different features or priors to detect salient regions. [sent-73, score-0.671]
38 The saliency maps are combined by weighted averaging, where the weights are predefined [6, 8], learned by a SVM [13] or estimated by a CRF [20]. [sent-74, score-0.348]
39 Unlike previous approaches that are purely top-down or bottom-up, we integrate high level priors with low level information into a unified framework, which is graph-based and is optimized in a submodular framework. [sent-75, score-0.234]
40 Preliminaries Facility Location: [17, 22] We solve a facility location problem to generate candidate regions for saliency-based segmentation. [sent-77, score-0.693]
41 fj is the cost of opening a facility at location j and cij denotes the profit made by satisfying the demand of client iby facility j. [sent-89, score-1.943]
42 y˜j = 1 if facility j is open and y˜j = 0 otherwise; ˜x ij = 1 if the demand of client iis satisfied from facility j and ˜x ij = 0 otherwise. [sent-91, score-1.414]
43 h client to an open facility to maximize the overall profit. [sent-100, score-0.71]
44 Submodular Saliency There are three main steps in our approach: First, a set of potential region centers are extracted from an image. [sent-161, score-0.329]
45 They serve as a set of potential facility locations (denoted by J). [sent-162, score-0.697]
46 Second, given that set of potential region centers, we identify the final region centers and cluster superpixels into regions by solving the facility location problem. [sent-163, score-1.285]
47 Finally, the saliencies ofthe potential salient regions and their constituent superpixels are computed from color and spatial location information. [sent-166, score-0.554]
48 Identifying A Set of Potential Region Centers It is computationally too expensive to use the whole set V as the set, J, of potential region centers to identify the final region centers, denoted by A. [sent-183, score-0.492]
49 chosen as a region center, the region extracted is more or less the same. [sent-185, score-0.274]
50 Extraction of Potential Salient Regions We model the problem of identifying high quality potential salient regions as selecting a subset, A, of J as the final region centers. [sent-192, score-0.521]
51 A is regarded as the set of locations for opening facilities, and the similarities between elements of A and superpixels eventually assigned to elements of A as the profits made by satisfying the demand of clients by facilities from A. [sent-193, score-0.654]
52 As discussed previously, this problem can be modeled as the facility location problem [22]. [sent-194, score-0.657]
53 With the constraint NA = |A| ≤ K, the combinatorial formulation of the facility lo=ca |tAio|n ≤ problem cino m[2b2i]n can biael applied ttioo our problem: mAaxH(A) =i? [sent-196, score-0.588]
54 A ⊆ J ⊆ V, NA ≤ K (3) where cij denotes the similarity between a vertex vi (considered as clients) and its potential region center vj (considered as facilities), and the cost fj of facility opening is fixed to The overall profit H : 2J → R on the graph G is a tsoub λm. [sent-200, score-1.549]
55 2 The first term encourages the similarity between vi and its assigned region center to have the greatest value. [sent-202, score-0.31]
56 The optimization favors region centers that are visually similar to their ‘clients’ . [sent-203, score-0.291]
57 It mitigates against fragmentation of visually homogenous regions, since the small gain in visual similarity to marginally ‘productive’ region centers is more than offset by the cost of opening such a facility. [sent-205, score-0.404]
58 K is the maximum number of salient regions that the algorithm might identify, and is a parameter specified by the user. [sent-211, score-0.317]
59 Generally, fewer than K locations are chosen because the marginal gain does not outweigh the facility cost. [sent-212, score-0.8]
60 1 Computation of cij cij serves as the profit made by satisfying the demand of client ifrom a facility at location j ∈ J. [sent-215, score-1.577]
61 Iitt sish an input cvoamri-able for the facility location problem. [sent-217, score-0.633]
62 Since not all nodes in G should be assigned to any j, we add a background node vg to G with label 0 so vi ∈ U can also be assigned to background. [sent-222, score-0.326]
63 Examples of facility location and facility assignment results (clustering) on two synthetic datasets. [sent-273, score-1.269]
64 The selected region centers (facility locations) are marked as circles. [sent-274, score-0.301]
65 (b)∼(e): a1, a2, a3 are yse l oecctatedio nb as)se adre on athrkeierd marginal gains ri na H(A c∪h {a}) H(A) ainp t uhrreese hiteer asttriuoncstu. [sent-277, score-0.255]
66 (f) Facility assignment d re osnul t hs by using ahal grmaionnsic in so Hl(utAio∪n {toa compute cij . [sent-281, score-0.409]
67 e (g) Facility assignment − results by simply using naive weight wij as cij . [sent-284, score-0.425]
68 (a) Input image; (b) Center prior map; (c) Face prior map; (d) Color prior map; (e) Final combined and smoothed prior map. [sent-287, score-0.32]
69 Hence the possibility of a potential region center close to A being selected increases during the subsequent iteration of the optimization. [sent-290, score-0.278]
70 cij can be computed by finding the harmonic function on the graph G with the labeled nodes L set to nodej with label 1 and the background node with label 0, while the other nodes in G are the unlabeled nodes U. [sent-291, score-0.737]
71 cij is the probability that a random walker starting from vi, will reach j before reaching the background node [9, 32]. [sent-293, score-0.416]
72 With cgj = 0 and cjj = 1, we can also obtain cij = hU ∈ Ru×1 for ∀i ∈ U. [sent-295, score-0.414]
73 cij is fixed during the subsequent optimization o anf (d3∀). [sent-298, score-0.328]
74 Here, the detected face regions Λ are assigned higher probabilities to generate the face prior map pf (x) = σ1 , for x ∈ Λ; otherwise pf (x) = 0. [sent-304, score-0.288]
75 We introduce an ‘assignment cost’ 1− PH for each superpixel tarnodd incorporate int minentot tchoes computation of cij as follows. [sent-327, score-0.375]
76 Given a labeled set L (comprised of a region center node vj and the background node vg), we augment the graph G to include a set of labeled nodes, by attaching a labeled node vqi to each unlabeled node vi (i ∈ U) as its prior. [sent-328, score-0.713]
77 l data points having high gains are aggregated in the area with high prior values; (i) Final selected facility locations with prior. [sent-343, score-0.772]
78 uth |A s|a =lien 5t region; (l) Saliency map without prior; (m) Saliency map with prior; (n) Salient region mask based on the saliency map in (m). [sent-346, score-0.577]
79 We can compute cij = hU ∈ Ru×1while cjj = 1 and cgj = 0. [sent-368, score-0.414]
80 The region center with the largest marginal gain is the location with the lowest assignment cost. [sent-371, score-0.435]
81 Hence this computation of cij encourages the selected facility locations to be close to low cost areas (i. [sent-373, score-1.022]
82 Figures 3(e) and 3(h) show the marginal gain for each point in J in the first iteration of the facility location optimization without and with the high level prior. [sent-378, score-0.842]
83 After highlevel prior integration, the points with large marginal gains are more concentrated in the perceptually important areas (indicated by high-level prior map) such as the flower and the flower leaf. [sent-379, score-0.27]
84 Compared to the selected region centers A without the prior in Figure 3(f), our approach with priors will select most of the potential region centers for A from the high prior areas as shown in Figure 3(i). [sent-380, score-0.856]
85 3 Potential Salient Region Extraction Given a set of selected facility locations A, let the current maximal profit from vi be ρicur = maxj∈A cij, and the facility assignment for vi be xicur = arg maxj∈A cij . [sent-383, score-1.99]
86 Hence, we ccolursrteesrp tohned image eeplesm 1e0nt −s t 1ha4t nsh Aarelg tohrei same facility elo, cwaetion as the most profitable to obtain potential salient regions {ri}i=1. [sent-389, score-0.972]
87 Figure 2 show two examples of facility location and facility assignment results (i. [sent-393, score-1.269]
88 The results in Figure 2(f) using a harmonic function to compute cij are better than the results in Figure 2(g) that simply uses the edge weight wij as cij . [sent-396, score-0.799]
89 The reason is that harmonic solution for cij enforces that nearby points have similar harmonic function values; this better models the geometry of the data induced by the graph structure (edges and weights W). [sent-397, score-0.549]
90 Figures 3(g) and 3(j) show the region extraction results for the two sets of selected region centers A shown in Figure 3(f) and Figure 3(i), respectively. [sent-402, score-0.438]
91 |A| , we next compute the saliency o efx ri icnt tnegrm {sr of} its color and spatial information. [sent-422, score-0.434]
92 The color saliency of ri is defined as: fc(ri) = ? [sent-425, score-0.434]
93 A region which has a wider spatial distribution is typically less salient than regions which have small spatial spread [20, 8]. [sent-430, score-0.454]
94 The spatial saliency of ri is computed as fs(ri) = 1 −maxVi (Vri) (ri). [sent-431, score-0.409]
95 ances of superpixels from ri to the spatial mean μk of region rk . [sent-434, score-0.374]
96 After fc and fs are maximum normalized to [0, 1], the saliency of ri is computed as: f(ri) = fc(ri)fs (ri). [sent-436, score-0.468]
97 We generate the final saliency map S by weighted averaging over superpixels, nwahle sarlei etnhec weights are computed by pair-wise feature distances between superpixels using a Gaussian kernel to enforce that similar superpixels should have similar visual saliency. [sent-437, score-0.554]
98 Figures 3(l) and 3(m) present the saliency maps using our approach without and with high-level priors, respectively. [sent-438, score-0.348]
99 Compared to the ground truth region in Figure 3(k), the saliency maps with priors are better than the result without priors. [sent-439, score-0.551]
100 (a) Input images; (b) Ground truth salient regions; (c) High-level prior map; (d) Saliency map without high level prior; (e) Saliency map with high level prior; (f) Salient Region extraction based on (e) by simple thresholding. [sent-443, score-0.501]
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