iccv iccv2013 iccv2013-186 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Meng Tang, Lena Gorelick, Olga Veksler, Yuri Boykov
Abstract: Among image segmentation algorithms there are two major groups: (a) methods assuming known appearance models and (b) methods estimating appearance models jointly with segmentation. Typically, the first group optimizes appearance log-likelihoods in combination with some spacial regularization. This problem is relatively simple and many methods guarantee globally optimal results. The second group treats model parameters as additional variables transforming simple segmentation energies into highorder NP-hard functionals (Zhu-Yuille, Chan-Vese, GrabCut, etc). It is known that such methods indirectly minimize the appearance overlap between the segments. We propose a new energy term explicitly measuring L1 distance between the object and background appearance models that can be globally maximized in one graph cut. We show that in many applications our simple term makes NP-hard segmentation functionals unnecessary. Our one cut algorithm effectively replaces approximate iterative optimization techniques based on block coordinate descent.
Reference: text
sentIndex sentText sentNum sentScore
1 GrabCut in One Cut Meng Tang Lena Gorelick Olga Veksler University of Western Ontario Canada Yuri Boykov Abstract Among image segmentation algorithms there are two major groups: (a) methods assuming known appearance models and (b) methods estimating appearance models jointly with segmentation. [sent-1, score-0.496]
2 The second group treats model parameters as additional variables transforming simple segmentation energies into highorder NP-hard functionals (Zhu-Yuille, Chan-Vese, GrabCut, etc). [sent-4, score-0.296]
3 It is known that such methods indirectly minimize the appearance overlap between the segments. [sent-5, score-0.428]
4 We propose a new energy term explicitly measuring L1 distance between the object and background appearance models that can be globally maximized in one graph cut. [sent-6, score-0.615]
5 We show that in many applications our simple term makes NP-hard segmentation functionals unnecessary. [sent-7, score-0.36]
6 The most basic object segmentation energy [3, 20] combines boundary regularization with loglikelihood ratios for fixed foreground and background appearance models, e. [sent-11, score-0.663]
7 {p,q}∈N ωpq |sp − sq | where sp ∈ {0, 1} are binary indic? [sent-18, score-0.201]
8 n tO Sne ⊂ important practical advantage o off tnheisig hbbasoicri energy is that there are efficient methods for their global minimization using graph cuts [4] or continuous relaxations [5, 18]. [sent-20, score-0.221]
9 Some well-known approaches to segmentation [25, 19, 6] consider model parameters as extra optimization variables in their segmentation energies. [sent-22, score-0.372]
10 p∈Ω which is known to be NP-hard [22], is used for interactive segmentation in GrabCut [ 19] where initial appearance models θ1, θ0 are computed from a given bounding box. [sent-27, score-0.493]
11 using a graph cut algorithm for energy (1) as in [3]. [sent-31, score-0.351]
12 Second, they fix segmentation S and then optimize over model parameters θ1 and θ0. [sent-32, score-0.226]
13 Two wellknown alternatives, dual decomposition [22] and branchand-mincut [14], can find a global minimum of energy (2), but these methods are too slow in practice. [sent-33, score-0.29]
14 We observe that when appearance models θ1, θ0 are represented by (non-parametric) color histograms, minimization of (2) is equivalent to minimization of energy · H(θS¯) + |∂S| on S only. [sent-34, score-0.389]
15 HT(h·i)s sfo trhme of energy (2) can be obtained by replacing the sum over pixels in (2) by the sum over color bins. [sent-36, score-0.337]
16 Interestingly, the global minimum|θ of) segmentation energy (3) does not depend on the initial color models provided by the user. [sent-40, score-0.42]
17 The entropy terms of this energy prefer segments with more peaked color distributions. [sent-43, score-0.378]
18 In general, the color separation bias in energy (3) is shown by equivalently rewriting its two entropy terms as hΩ(S) −? [sent-49, score-0.518]
19 Energy (3): volum−eh balancing (a) and −Jen|Ssen−-Shan|non color separation terms (b). [sent-85, score-0.349]
20 plicitly bias image segmentation to two parts of equal size, see Fig. [sent-87, score-0.251]
21 The remaining terms in (4) show bias to color separation between the segments, see Fig. [sent-89, score-0.299]
22 Note that a similar analysis in [22] is used to motivate their convexconcave approximation algorithm for energy (2). [sent-91, score-0.237]
23 Volume balancing hΩ (S) is the only term in (4) and (2) that is not submodular and makes optimization difficult. [sent-92, score-0.247]
24 Our observation is that in many applications this volume balancing term is simply unnecessary, see Sections 3. [sent-93, score-0.207]
25 Moreover, while it is known that JS color separation term −hΩi (Si) is submodular1 and can be optimized by graph c−uhts [11, 12, 22], we propose to replace it with a more basic L1 separation term in Fig. [sent-99, score-0.744]
26 We show that it corresponds to a simpler construction with much fewer auxiliary nodes leading to higher efficiency. [sent-101, score-0.338]
27 Interestingly, it also gives better color separation effect, see Section 3. [sent-102, score-0.231]
28 We also observe one practical limitation of blockcoordinate approach to (2), as in GrabCut [ 19], could be due to deteriorating sensitivity to local minima when the number of color bins for models θS and is increased, see Table 2 and Fig. [sent-105, score-0.415]
29 In practice, however, finer bins better capture the information contained in the full dynamic range of color images (8-bit per channel or more). [sent-107, score-0.35]
30 This applies to JS, χ2, Bhattacharyya, and our L1 color separation terms in Figs. [sent-109, score-0.266]
31 The corresponding ROC curves show that the color separation between the object and background increases for finer bins. [sent-113, score-0.305]
32 curves show that even a difficult camouflage image in Figure 2 has a good separation of intensities between the object and background if larger number of bins is used. [sent-114, score-0.485]
33 With bins, however, the overlap between the “fish” and the background is too strong making it hard to segment. [sent-115, score-0.347]
34 Our contributions are summarized below: 163 • • • We propose a simple energy term penalizing L1 measure orfo appearance overlap ybe tetwrmee pne segments. [sent-118, score-0.701]
35 Unlike NP-hard multi-label problems discussed in [ 11, 12], we focus on binary segmentation where such high-order constraints can be globally minimized. [sent-121, score-0.293]
36 Moreover, we show that our L1 term works better for separating colors than other concave separators (including JS, Bhattacharyya, and χ2). [sent-122, score-0.204]
37 We are first to demonstrate fast globally optimal binary segmentation technique explicitly minimizing overlap between object/background color distributions. [sent-123, score-0.651]
38 In one graph cut we get similar or better results at faster running times w. [sent-124, score-0.248]
39 We show general usefulness of the proposed appearance overlap penalty by showing dthifefe prreonpto practical applications: binary segmentation, shape matching, etc. [sent-130, score-0.619]
40 Minimizing appearance overlap in One-Cut Let S ⊂ Ω be a segment and denote by θS and the Luentno Srm ⊂aliz Ωed b eco alor s histograms f dore thoete foreground and background appearance respectively. [sent-132, score-0.827]
41 vnkcor- responding to the pixels in bin k are connected to the auxiliary node Ak using undirected links. [sent-135, score-0.434]
42 The capacity of these links is the weight of appearance overlap term β > 0. [sent-136, score-0.659]
43 of pixels in the image the belong to bin k and let nkS and be the according number of the foreground and background pixels in bin k. [sent-137, score-0.566]
44 Our appearance overlap term penalizes the intersection between the foreground and background bin counts by incorporating the simple yet effective high-order L1 term into the energy function: nSk¯ EL1(θS, θS¯) = −? [sent-138, score-1.107]
45 (5) Below we explain how to incorporate and optimize the term EL1 (θS, θS¯) using one graph cut. [sent-141, score-0.236]
46 The details of the graph construction for the above term are shown in Fig. [sent-145, score-0.289]
47 , AK into the graph and connect kth auxiliary node to all the pixels that belong to the kth bin. [sent-150, score-0.364]
48 Assume that bin k is split into foreground and background, resulting in nkS and nSk¯ pixels accordingly. [sent-153, score-0.279]
49 Then any cut separating the foreground and background pixels must either cut nkS or nSk¯ number of links that connect the pixels in bin k to the auxiliary node Ak. [sent-154, score-0.971]
50 A similar graph construction with auxiliary nodes is proposed in [11, 12] to minimize higher order pseudo-boolean functions of the following form: f(Xc) = min{θ0+? [sent-156, score-0.443]
51 The construction in [11, 12] can be used to minimize EL1 as follows: consider each color bin as a clique and set parameters wi0 = 1, wi1 = Figure4. [sent-166, score-0.357]
52 1, θ0 = 0, θ1 = 0 and θmax = nk/2, where nk is the number of pixels in bin k. [sent-168, score-0.247]
53 e Oedn one auxiliary fn ooudre g froarp hea ccohn bsitrnu icncontrast to two auxiliary nodes in [11, 12]. [sent-171, score-0.468]
54 To see how it works we consider four possible label assignments for the auxiliary nodes Ak1 and Ak0. [sent-174, score-0.245]
55 ments to the binary auxiliary nodes Ak1 and Ak0 . [sent-177, score-0.311]
56 Applications In this section we apply our appearance overlap penalty term in a number of different practical applications including interactive binary segmentation in Sec. [sent-189, score-0.941]
57 Interactive segmentation First, we discuss interactive segmentation with several standard user interfaces: bounding box [ 19] in Section 3. [sent-198, score-0.608]
58 We compare different color separation terms in Section 3. [sent-203, score-0.266]
59 1 Binary segmentation with bounding box First, we use appearance overlap penalty in a binary segmentation experiment a la GrabCut [19]. [sent-234, score-1.144]
60 A user provides a bounding box around an object of interest and the goal is to perform binary image segmentation within the box. [sent-235, score-0.424]
61 The pixels outside the bounding box are assigned to the background using hard constraints. [sent-236, score-0.317]
62 e bounding Ωbo dxe,n oStGeT t ⊆e Ωibe the ground truth segmentation and S ⊆ Ω be a segment. [sent-238, score-0.274]
63 The segmentation energy }fu tnhceti cohna rEac(tSer) istsi given by E(S) = |S¯ ∩ R| − β? [sent-241, score-0.335]
64 L1 + λ|∂S|, (9) where the first term is a standard ballooning inside the bounding box R, the second term is the appearance overlap penalty as in (5), and the last term is a contrast-sensitive smoothness term. [sent-243, score-1.11]
65 It is common to tune the relative weight of each energy term for a given dataset [22]. [sent-251, score-0.337]
66 We use the measure of appearance overlap between the box R and its background R¯ to automatically find image specific relative weight β of the appearance overlap term w. [sent-253, score-1.138]
67 The error rate is defined as the number of misclassified pixels within the bounding box R divided by the size of the box |R| . [sent-270, score-0.494]
68 We test with different number of color boifn sth aend b provide quantitative comparison with the grab-cut method [ 19] (our implementation, modified to work with histograms as in [22]) and the dual decomposition method [22] (results reported by the authors). [sent-271, score-0.231]
69 As we increase the number of color bins, the error rate for the GrabCut method increases, while the error rate of One-Cut decreases. [sent-277, score-0.285]
70 When using 1283 bins One-Cut runs twice as fast, while obtaining much lower error rate. [sent-278, score-0.31]
71 This is because with more bins, more auxiliary nodes are used, but each auxiliary node is connected to less pixels. [sent-279, score-0.466]
72 Finally, Figures 6-7 show examples of input bounding boxes and segmentation results with the GrabCut [ 19], Dual Decomposition [22] and our One-Cut method. [sent-283, score-0.274]
73 2 Comparison of Appearance Overlap Terms Below we discus additional variants for appearance overlap penalty term. [sent-286, score-0.501]
74 4 and compare their performance in the task of binary segmentation applied to the GrabCut dataset [19]. [sent-288, score-0.252]
75 We consider four appearance overlap terms based on the L1 norm, χ2 distance, Bhattacharyya coefficient and Jensen-Shannon divergence 3There are 50 images in the dataset, but we exclude the cross image for the sake of comparison with [22]. [sent-289, score-0.463]
76 All four terms above are concave functions of nks attaining maximum at nk/2. [sent-313, score-0.407]
77 These truncated components can be incorporated into our graph using the construction shown in Fig. [sent-319, score-0.234]
78 All three appearance overlap terms above can be optimized with one graph cut. [sent-322, score-0.535]
79 We wish to find out which term and what level of approximation accuracy are optimal for the task of binary segmentation. [sent-323, score-0.246]
80 In the first experiment, we use an adaptive image specific weight βImg for the appearance overlap term as in (10) and set β? [sent-331, score-0.552]
81 In the second experiment, we choose the optimal βImg separately for each appearance overlap term by replacing the denominator of (10) with either Dχ2 (θR, θR¯), θR¯) θR¯) DBha(θR, or DJS(θR, according to the appearance overlap term used. [sent-336, score-1.154]
82 Comparison of appearance overlap terms: (top-left) shows the functions plotted for one bin k, (top-right) shows segmentation error rates using the same βImg as in (10) for all overlap terms and (bottom-left) shows segmentation results when using a term-specific βImg . [sent-343, score-1.369]
83 10 reports the error (θR, θR¯) rates of the segmentation as a function of the parameter t. [sent-355, score-0.272]
84 This further proves the benefit of our proposed DL1 appearance overlap term. [sent-357, score-0.428]
85 3 Interactive Segmentation with Seeds Unlike interactive segmentation with abounding box, using seeds a la Boykov-Jolly [3] makes volumetric balancing unnecessary due to hard constraints enforced by the user. [sent-371, score-0.432]
86 Therefore, the segmentation energy is quite simple: Eseeds(S) = −β? [sent-372, score-0.335]
87 Template Shape Matching Below we discuss how appearance overlap penalty term can be used for template shape matching. [sent-378, score-0.784]
88 Several prior methods rely on graph-cut based segmentation with shape prior [2 1, 8, 14, 23]. [sent-379, score-0.238]
89 Most commonly, these methods use a binary template mask M and combine the shape matching cue a contrast sensitive smoothness term via energy E1(S) = mρ∈iΦnEShape(S,Mρ) + λ|∂S|. [sent-380, score-0.539]
90 We further incorporate the appearance overlap into the energy: E2(S) = E1(S) − β? [sent-384, score-0.428]
91 Without the appearance overlap term shape matching yields erroneous segmentation due to the clutter edges in the background. [sent-389, score-0.831]
92 We down-scaled all images to 320 240 and used 1283 color bins per image. [sent-392, score-0.35]
93 For the template matching, we scan the image in a sliding-window fashion and compute maxflow/mincut with dynamic graph cut [13]. [sent-394, score-0.309]
94 Template shape matching examples: ages, (b) Contrast sensitive edge weights, (c-d) with and without the appearance overlap penalty. [sent-400, score-0.521]
95 Table 3 provides quantitative comparison of the results obtained with and without incorporating the appearance overlap term, namely using E2 (S) and E1(S). [sent-404, score-0.428]
96 The results are reported with respect to manually outlined ground truth segmentations and clearly point to the benefit of incorporating the overlap term EL1 into the segmentation energy. [sent-405, score-0.583]
97 Template shape matching: comparing E1(S) and E2 (S) in terms of TP, FP, misclassified pixels, and mean running time. [sent-418, score-0.2]
98 Salient object segmentation Salient region detection and segmentation is an important preprocessing step for object recognition and adaptive compression. [sent-423, score-0.372]
99 Salient objects usually have an appearance that is distinct from the background [1, 7, 17]. [sent-424, score-0.229]
100 Below we show how our appearance overlap penalty term can be used for the task of salient object segmentation. [sent-425, score-0.67]
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