iccv iccv2013 iccv2013-259 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Hongteng Xu, Hongyuan Zha
Abstract: Data sparsity has been a thorny issuefor manifold-based image synthesis, and in this paper we address this critical problem by leveraging ideas from transfer learning. Specifically, we propose methods based on generating auxiliary data in the form of synthetic samples using transformations of the original sparse samples. To incorporate the auxiliary data, we propose a weighted data synthesis method, which adaptively selects from the generated samples for inclusion during the manifold learning process via a weighted iterative algorithm. To demonstrate the feasibility of the proposed method, we apply it to the problem of face image synthesis from sparse samples. Compared with existing methods, the proposed method shows encouraging results with good performance improvements.
Reference: text
sentIndex sentText sentNum sentScore
1 Specifically, we propose methods based on generating auxiliary data in the form of synthetic samples using transformations of the original sparse samples. [sent-3, score-0.894]
2 To incorporate the auxiliary data, we propose a weighted data synthesis method, which adaptively selects from the generated samples for inclusion during the manifold learning process via a weighted iterative algorithm. [sent-4, score-1.449]
3 To demonstrate the feasibility of the proposed method, we apply it to the problem of face image synthesis from sparse samples. [sent-5, score-0.491]
4 This learning problem can be viewed as estimating a nonlinear function mapping from a learned parameter space to the sample space (e. [sent-11, score-0.234]
5 Many nonlinear synthesis algorithms have been proposed to solve this problem. [sent-15, score-0.435]
6 Particularly, because of their strong capability of extracting low-dimensional structural information from high-dimensional data, manifold based methods are widely applied for synthesis and learning probHongyuan Zha College of Computing, Georgia Tech Atlanta, GA 30332 zha @ cc . [sent-16, score-0.877]
7 In [5], Locally-Smooth-ManifoldLearning (LSML) is proposed to learn a warping function from a point on an manifold to its neighbors. [sent-26, score-0.478]
8 However, a common issue for all the methods above is that because the manifold is fitted locally by linear models, they can produce good results only if the number of samples are relatively large. [sent-34, score-0.609]
9 In the case of sparse samples, the underlying manifold will be poorly captured because enough neighbors of sample can2208 not be found so that a good linear fit will not be feasible. [sent-35, score-0.622]
10 In this paper, we prove that it is possible to synthesize some special images based on sparse samples by leveraging the methodology of transfer learning in manifold-based image synthesis. [sent-36, score-0.448]
11 Specifically, we use the idea of leveraging auxiliary data to enhance the learning for the target domain [18, 15, 17, 4, 16, 12]. [sent-37, score-0.522]
12 For example, for the image clas- sification problem in [12], for those classes with very few training samples, new training samples are borrowed from transformed samples generated from other classes. [sent-38, score-0.457]
13 Such an auxiliary data based strategy can also be applied in image synthesis. [sent-40, score-0.371]
14 Given sparse samples, most regions of the manifold are not adequately covered. [sent-41, score-0.492]
15 Fortunately, with the help of certain transformations, we can generate auxiliary data and then obtain a more comprehensive albeit noisier coverage of the manifold. [sent-42, score-0.371]
16 The key difference between the proposed method and the works mentioned above is that we do not have external data set transformations are applied to the original data points in order to generate the auxiliary data. [sent-43, score-0.602]
17 To incorporate the noisy auxiliary data, we develop a new de-noising scheme into the manifold based synthesis methods. [sent-44, score-1.126]
18 Section 2 gives a brief review of manifold learning and data synthesize from dense samples. [sent-49, score-0.61]
19 Section 3 presents the strategy for designing transformations for sparse samples and the proposed learning algorithm. [sent-50, score-0.441]
20 The transformations applied to head pose images and the synthesis results are discussed in section 4. [sent-51, score-0.561]
21 Manifold Learning and Data Synthesis from Dense Samples The basic assumption of manifold learning is that the high-dimensional data can be viewed as a manifold embedded in the sample space. [sent-54, score-1.028]
22 , a bijection function) between samples and their coordinates in the low-dimensional latent space. [sent-57, score-0.264]
23 In [5], these two problems can bMe addressed simultaneously by learning a warping function that maps a point on the manifold to its neighbors. [sent-68, score-0.533]
24 e Wbeetw heaevne Wthe( samples i Mn the latent space. [sent-76, score-0.23]
25 So, the manifold learning becomes a problem about learning parameter Θ and ? [sent-84, score-0.546]
26 lTohsse function of manifold learning can be written− as follows, minΘ,yi ? [sent-90, score-0.491]
27 (1) measures the error between 2209 the point xi on the manifold and its local linear estimate. [sent-102, score-0.554]
28 Given optimal Θ and yi, the new data corresponding to ynew can be synthesized as xnew = ? [sent-108, score-0.235]
29 In the case of dense samples, the manifold can be recovered with high accuracy. [sent-113, score-0.436]
30 Our main idea to overcome this is to introduce auxiliary data points into the data set resulting in noisy dense samples. [sent-115, score-0.406]
31 Create Auxiliary Data via Transformations We propose to create auxiliary data by applying certain class of transformations to the original sparse samples. [sent-119, score-0.677]
32 In other words, although transformed samples are no longer on the target manifold in general, they may not be very far from the target manifold, which can be viewed as “noisy” samples for the recovery of the target manifold. [sent-146, score-1.069]
33 For example, xi and xj are tw ino t original samples. [sent-148, score-0.299]
34 It requires that the two synthetic manifolds have some overlaps, so that the path is composed of Xi and Xj . [sent-151, score-0.25]
35 Condition 2: To arbitrary xi ∈ X, we apply transCfoormndatitiioonn nT 2 t:o Tcore aatreb new samples XX,i ,w weh aopsepl yele tmranenstsfaotrmisfaiteiso nco Tnd tioti ocnre 1a . [sent-153, score-0.291]
36 s W thhaitle M Mthe condition 2 en• sures that the samples in Mi are connected with other syntshuerteisc mhaatn tihfeol sdasm, so sth iant Mthe global structure of the target manifold can be captured. [sent-156, score-0.793]
37 As a result, the samples of Mi can ibfeo bldor craonw ebde fcoarp learning tsh ae rsetrsuucltt,ur the eo fs aMmp alresou onfd M xi. [sent-157, score-0.228]
38 Tthhee barlgueet a mnda green curves are synthetic manifolds created by two transformations. [sent-162, score-0.296]
39 For some samples, their neighbors are close to the other manifold (condition 2), which is labeled by orange circles. [sent-165, score-0.598]
40 The samples are blue “◦”s, whose neighbors can only be found in the set created by th bleu corresponding teraignhsbfoorrmsa ctainon o. [sent-167, score-0.314]
41 All of the synthetic manifolds and the target manifold we want to recover are fused together in the same latent space. [sent-169, score-0.812]
42 The auxiliary data we created is the samples of synthetic manifolds meeting condition 1and 2. [sent-170, score-1.022]
43 By borrowing auxiliary data from synthetic manifolds, the partial structural information of synthetic manifolds is shared by the unknown target manifold. [sent-171, score-0.824]
44 As a result, we can fit the target manifold with synthetic manifolds, rather than a linear hyperplane. [sent-172, score-0.603]
45 The principle of this method is based on transfer learning, which is inspired by the work in [12] where the feature space of different classes are shared and their samples can be borrowed by each other. [sent-173, score-0.288]
46 Here, all the manifolds are in the same latent space and parts of their samples can be shared with each other. [sent-174, score-0.382]
47 The difference is that the proposed method is not dependent on external data set we apply transformations on the original data set to generate the auxiliary data. [sent-175, score-0.602]
48 Another nonlinear manifold learning work appears in [8], which fits manifold with piecewise polynomial regression, but it still requires dense samples to estimate the model — 2210 parameters. [sent-176, score-1.181]
49 For sparse images of the horizontal rotation of head, we use shifting, flipping and rotation, to create auxiliary data. [sent-180, score-0.592]
50 We observe that the auxiliary data indeed can help to recover the original manifold. [sent-184, score-0.41]
51 Modifications of the Loss Function + + Given auxiliary data {xi , i = 1 N, . [sent-193, score-0.371]
52 we get a new daatetad set, wsevheerrae lth trea nfirsfsto rNm samples are the original samples while the rest L ones are auxiliary data. [sent-198, score-0.721]
53 The parameters of transformations and number of neighbors will be given in Section 4. [sent-201, score-0.252]
54 analysis above, only the samples in the auxiliary data satisfying condition 1and 2 can be used. [sent-202, score-0.659]
55 The scheme is described in Algorithm 1which removes samples not meeting condition 2 from the data set. [sent-205, score-0.39]
56 eat1,dN+L For samples meeting condition 2, their neighbors are also selected adaptively. [sent-208, score-0.45]
57 Weighting neighbors of samples and error × terms ensures that the influence of the samples far from the target manifold will be suppressed, so that the condition 1 will be satisfied. [sent-221, score-1.061]
58 , wN+L]T is the weight vector denoting the auxiliary data meeting condition 2. [sent-242, score-0.585]
59 According to the evaluation about various manifold learning algorithms shown in [20], Local-Tangent-Space-Alignment (LTSA) algorithm [24] performs the best. [sent-258, score-0.491]
60 Experimental Results To demonstrate the feasibility, we apply the proposed method on the synthesis of face images2 [7]. [sent-332, score-0.403]
61 We resize images to 100 90 and create auxiliary data by following ti mhreaeg steps. [sent-336, score-0.425]
62 From the 2nd to the 5th column are synthesis results gotten by LSML [5] with sparse samples, LLE based method [21], LGGA [9], LSML with dense samples and proposed method. [sent-345, score-0.63]
63 According to [9], the manifold of the image shifting sequence × is a curve. [sent-349, score-0.557]
64 3 that a part of the curve can be viewed as a good local fitting for the manifold of rotated head image. [sent-351, score-0.517]
65 After learning manifold, the location of the new image on the manifold is decided by its coordinates in the tangent space. [sent-368, score-0.594]
66 2213 Given original sparse samples and corresponding auxiliary data, we compare the proposed method with other competitors, including the LLE based method [21], LGGA [9] and the state of the art method, LSML [5]. [sent-373, score-0.604]
67 Specifically, for showing the influence of auxiliary data on the result of synthesis, LSML are applied in two cases — purely using original sparse samples and combining sparse samples with auxiliary data. [sent-374, score-1.204]
68 On the other hand, when samples are sparse, the number of sample is too small to avoid over-fitting phenomenon of parameters in the learning phase. [sent-380, score-0.263]
69 As a result, LSML leads to obvious “ghost effect” the synthesis result is similar to that of traditional linear interpolation. [sent-381, score-0.354]
70 Even if applying LSML with the help of auxiliary data, without adaptive strategies for sample and neighbor selection, the performance are also inferior to the proposed method. [sent-382, score-0.415]
71 4, we can find that some LSML results in the situation having auxiliary data still have “ghost effect”. [sent-384, score-0.371]
72 The reason for this problem is that the outliers in the auxiliary data are not removed in the learning phase. [sent-385, score-0.511]
73 So, in the synthesis phase, it is possible that the neighbors we find include outliers. [sent-386, score-0.449]
74 In such a situation, synthesis results will be corrupted by outliers. [sent-387, score-0.354]
75 The image labeled by green frame is the synthesis result of LSML. [sent-392, score-0.381]
76 Another problem may happen in the result ofLSML with auxiliary data is “missing rotation”. [sent-394, score-0.371]
77 4, the synthesis results of LSML looks like the repeat of original image. [sent-396, score-0.393]
78 Because the outliers disobeying condition 2 are not removed, the synthetic manifolds are isolated to each other. [sent-400, score-0.489]
79 As a result, the global structure of the target manifold cannot be learned by LSML. [sent-401, score-0.505]
80 The proposed method, on the other hand, makes samples sufficient by transformations and removes outliers during the iterations of learning algorithm. [sent-404, score-0.429]
81 4 and 5, the synthesis results of the proposed method avoid serious “ghost effect”. [sent-406, score-0.354]
82 At the same time, the subtle change of image is learned by the proposed method while the synthesis result of LSML is almost the same with original image. [sent-407, score-0.393]
83 images are original samples and red curve shows the target manifold. [sent-408, score-0.281]
84 The orange “+”s and corresponding images are synthetic results based on wrong samples (green “+”s). [sent-410, score-0.311]
85 The “ghost effect” is caused by choosing the outliers disobeying condition 1 as samples. [sent-411, score-0.239]
86 The outliers disobeying condition 2 are not removed, which causes that structure of target manifold is not captured. [sent-413, score-0.744]
87 We now discuss a limitation of the proposed method sometimes the samples cannot be created or borrowed correctly. [sent-414, score-0.281]
88 This is because the samples are created by flipping are not on the original manifold perfectly. [sent-417, score-0.759]
89 After learning the manifold and getting the coordinates of all the images in the latent space, we remove one original image and auxiliary data created from it. [sent-421, score-1.074]
90 The average mean-square-error (MSE) of the synthesis results of 15 people are measured for various methods. [sent-423, score-0.354]
91 According to Table 1, the performances of LLE based method and LGGA is not satisfying because of the failed synthesis results like Fig. [sent-424, score-0.354]
92 Conclusion and Future Work In this paper, a manifold-based face synthesis method is proposed for the case of sparse samples. [sent-430, score-0.459]
93 By combining transfer learning strategy with manifold learning algorithm, the samples are supplied by their transformed results, which provide additional structural information for manifold recovery. [sent-431, score-1.257]
94 Additionally, the auxiliary data is weighted for outlier detection during the learning phase, which improves learning and final synthesis results. [sent-432, score-0.865]
95 To the data set having certain special properties that can be used to design transformations, the proposed method has potential to improve the learning result when the number of samples is insufficient. [sent-433, score-0.263]
96 Learning mappings for face synthesis from near infrared to visual light images. [sent-469, score-0.441]
97 Simultaneous learning of nonlinear manifold and dynamical models for highdimensional time series. [sent-517, score-0.629]
98 Dynamic textures synthesis as nonlinear manifold learning and traversing. [sent-534, score-0.926]
99 Face synthesis and recognition from a single image under arbitrary unknown lighting using a spherical harmonic basis morphable model. [sent-595, score-0.39]
100 Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. [sent-607, score-0.298]
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