iccv iccv2013 iccv2013-302 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Georgios Tzimiropoulos, Maja Pantic
Abstract: We describe a very simple framework for deriving the most-well known optimization problems in Active Appearance Models (AAMs), and most importantly for providing efficient solutions. Our formulation results in two optimization problems for fast and exact AAM fitting, and one new algorithm which has the important advantage of being applicable to 3D. We show that the dominant cost for both forward and inverse algorithms is a few times mN which is the cost of projecting an image onto the appearance subspace. This makes both algorithms not only computationally realizable but also very attractive speed-wise for most current systems. Because exact AAM fitting is no longer computationally prohibitive, we trained AAMs in-the-wild with the goal of investigating whether AAMs benefit from such a training process. Our results show that although we did not use sophisticated shape priors, robust features or robust norms for improving performance, AAMs perform notably well and in some cases comparably with current state-ofthe-art methods. We provide Matlab source code for training, fitting and reproducing the results presented in this paper at ht tp ://ibug. . doc . i . a c . uk/resources. c
Reference: text
sentIndex sentText sentNum sentScore
1 Optimization problems for fast AAM fitting in-the-wild Georgios Tzimiropoulos 1. [sent-1, score-0.275]
2 We show that the dominant cost for both forward and inverse algorithms is a few times mN which is the cost of projecting an image onto the appearance subspace. [sent-11, score-0.545]
3 Because exact AAM fitting is no longer computationally prohibitive, we trained AAMs in-the-wild with the goal of investigating whether AAMs benefit from such a training process. [sent-13, score-0.341]
4 Our results show that although we did not use sophisticated shape priors, robust features or robust norms for improving performance, AAMs perform notably well and in some cases comparably with current state-ofthe-art methods. [sent-14, score-0.248]
5 We provide Matlab source code for training, fitting and reproducing the results presented in this paper at ht tp ://ibug. [sent-15, score-0.301]
6 They are statistical models of shape and appearance that can generate instances of a specific object class (e. [sent-23, score-0.161]
7 faces) given a small number of model parameters which control shape and appearance variation. [sent-25, score-0.161]
8 Recovering the shape parameters is important because it implies that the location of a set of landmarks (or fiducial points) has been detected in the Maja Pantic 1. [sent-27, score-0.128]
9 The appearance model of the AAM was built using raw un-normalized pixel intensities as features. [sent-36, score-0.142]
10 Neither sophisticated shape priors or robust norms were used during fitting nor robust image features were employed to build the AAM. [sent-37, score-0.476]
11 Even without such sophisticated enhancements, AAM fitting produced satisfactory accuracy in landmark localization. [sent-38, score-0.367]
12 To obtain these results, we simply trained the AAM in-the-wild (on the same database) and additionally for fitting and we used Fast-Forward algorithm, an exact but fast simultaneous algorithm. [sent-39, score-0.352]
13 Hence, fitting AAMs robustly to new images has been the focus of extensive research over the past years. [sent-42, score-0.275]
14 AAM fitting is an iterative process at each iteration of which an update of the current model parameters is esti- mated. [sent-43, score-0.337]
15 For example in [5], the relationship between the error image and the update is assumed lin593 ear and independent of the current model parameters. [sent-48, score-0.091]
16 Other discriminative methods for fitting AAMs have been proposed in [11, 22, 20]. [sent-50, score-0.275]
17 The second line of research for fitting AAMs is through non-linear least-squares [16]. [sent-51, score-0.275]
18 AAM fitting is formulated as a Lukas-Kanade (LK) problem which can be solved iteratively using Gauss-Newton optimization. [sent-52, score-0.275]
19 One of the major contributions of [16] is the so-called project-out inverse compositional algorithm (POIC). [sent-55, score-0.185]
20 This combination results in an algorithm which is as efficient as regression-based approaches and is now considered the standard choice for fitting personspecific AAMs (i. [sent-57, score-0.275]
21 AAMs trained for fitting face images of a specific subject which is known in advanced). [sent-59, score-0.331]
22 AAMs trained for fitting face images of various subjects not known in advance). [sent-62, score-0.331]
23 In contrast to POIC, the simultaneous inverse compositional (SIC) algorithm, proposed in [1], has been shown to perform robustly for the case of generic fitting [7]. [sent-63, score-0.532]
24 However, the computational cost of the algorithm is almost prohibitive for most applications. [sent-64, score-0.103]
25 Let n and m denote the number of the shape and appearance parameters of the AAM. [sent-65, score-0.161]
26 Then, the dominant cost per iteration of SIC is on the order of (n + m)2N, where N is the number of pixels in the reference frame. [sent-66, score-0.126]
27 We show that the cost for solving the exact AAM non-linear least squares problem with no approximations for both forward and inverse is significantly less than O((n + m)2N). [sent-76, score-0.308]
28 (1) As we show later on, using (1) reduces the dominant cost for both forward and inverse algorithms to nmN. [sent-79, score-0.34]
29 n, which is the case for generic face alignment, tfoher mcos ? [sent-81, score-0.093]
30 is n r,e wduhcicehd itso a ef cewas etifm oers g emnNer wc fhaicceh ailsi gthnecost of projecting an image onto the appearance subspace. [sent-83, score-0.128]
31 Hence, our derivations shed further light on the different optimization problems that POIC and SIC solve. [sent-87, score-0.089]
32 Additionally, the authors of [18] investigated only the inverse case. [sent-88, score-0.113]
33 As it is well known, the inverse compositional approach cannot be applied to 3D AAMs [23]. [sent-89, score-0.185]
34 One of our main contributions is to show that (1) can be used to derive a forward additive update scheme and hence can be readily applied to 3D. [sent-90, score-0.245]
35 Our second main contribution is to train AAMs in-thewild using the well-known LFPW database [3] and then fit using the proposed fast forward and inverse simultaneous algorithms, with the goal of investigating whether AAMs benefit from such a training process. [sent-92, score-0.248]
36 These results are notable given that no shape prior was used, the employed appearance model was built using raw pixel intensities and no attempt to use more sophisticated image features (like Gabor filter responses as in [14] or SIFT features [12] as in [3]) was made. [sent-95, score-0.299]
37 AAMs An AAM is defined by the shape, appearance and motion models. [sent-97, score-0.093]
38 Learning the shape model requires consistently annotating a set of u landmarks [x1, y1, . [sent-98, score-0.128]
39 Finally, PCA is applied on these shapes to obtain a 594 shape model defined by the mean shape and n shape eigenvectors {s0, S ∈ R{2u,n} }. [sent-106, score-0.243]
40 (2) Finally, in this work, to model similarity transforms the shape matrix S is appended with 4 similarity eigenvectors [16], all eigenvectors are re-orthonormalized, and then (2) is applied. [sent-110, score-0.146]
41 Learning the appearance model requires removing shape variation from the texture. [sent-111, score-0.161]
42 Finally, PCA is applied on the shape-free textures, to obtain the appearance model defined by the mean appearance and m appearance eigenvectors {A0, A ∈ R{N,m} }. [sent-113, score-0.318]
43 The model captures appearance rvasr {iaAtio,nA Afor ∈ example d}u. [sent-114, score-0.093]
44 (3) Iˆ We used piecewise affine warps W(x; p) as the motion model in this work. [sent-117, score-0.145]
45 Briefly, to define a piecewise affine warp, one first needs to triangulate the set of vertices of the given shapes. [sent-118, score-0.108]
46 The collection of all affine warps defines a piecewise affine warp which is parameterized with respect to p. [sent-120, score-0.264]
47 Finally, a model instance is synthesized to represent a test object by warping from the mean shape s0 to using the piecewise affine warp define by s0 and Please see [16, 5] for a detailed coverage of AAMs. [sent-121, score-0.24]
48 Fitting AAMs Our approach to fitting AAMs is based on non-linear least-squares [16]. [sent-124, score-0.275]
49 (4) Because (4) is a non-linear function of p, the standard approach to proceed is to linearize with respect to the shape parameters p and then optimize iteratively in a GaussNewton fashion. [sent-128, score-0.106]
50 In theforward case, the test image I linearized around the current estimate p, is a solution for a Δp is sought using least-squares, and p is × + updated in an additive fashion p ← p Δp. [sent-130, score-0.161]
51 In the inverse case, the model {A0, A} is linearized around p = 0, a solutciaosne f,o thr a mΔopd eisl sought using least-squares, adndp p =i s0 updated in a compositional fashion p ← p ◦ Δp−1, where ◦ denotes tihne a composition aolf f atwshoio warps. [sent-131, score-0.284]
52 pN◦otΔe pthat, applying tehneo iten-s verse compositional approach for piecewise affine warps is by no means straightforward. [sent-132, score-0.217]
53 Please see [16] for a principled way of applying the inverse composition to AAMs. [sent-133, score-0.113]
54 Following the seminal work of [16], inverse algorithms have gained increased popularity. [sent-134, score-0.138]
55 The two most popular inverse algorithms are SIC and POIC. [sent-135, score-0.138]
56 ∂W∂(xpk;p) x and y gradients of Ai for the k−th pixel and ∈ R2×n is the Jacobian of the piecewise affine warp. [sent-139, score-0.108]
57 SIC is slow because the cost for calculating Hsic is O((n + m)2N) [1]. [sent-146, score-0.194]
58 POIC reduces this cost dramatically by decoupling shape and appearance by solving (6) in the subspace orthogonal to A. [sent-147, score-0.261]
59 Fast algorithms for fitting AAMs Solving the exact problem in a simultaneous fashion as described above is not the only way for fitting AAMs. [sent-153, score-0.694]
60 The solution of the inverse problem was originally proposed in [18]. [sent-155, score-0.113]
61 Hence, our derivations shed further light on the different optimization problems that POIC and SIC solve. [sent-157, score-0.089]
62 Fast-SIC first linearizes (the appearance model), and then projects out. [sent-167, score-0.131]
63 This has the effect that the appearance terms Ac and AΔc immediately vanish. [sent-169, score-0.093]
64 To readily see this notice that to calculate JI the cost is nN, and hence the cost for calculating PJI is nmN. [sent-199, score-0.342]
65 Alternatively, one could avoid calculating PJI directly because JfTsic(I − A0) = JITP(I − A0), and P(I − A0) has a cost of mN(I. [sent-200, score-0.17]
66 −H Aowever, theP c(oIs t− f oAr calculating ATJI= AT[Ix Iy]∂∂Wp (18) is nmN (Ix and Iy are the gradients of I evaluated at ∂∂Wp) and calculating ATJI is necessary if we wish to efficiently calculate Hffw from Hffw = JITJI − (ATJI)T(ATJI). [sent-201, score-0.186]
67 (19) 596 Note that the cost for calculating Hffw as above is n2N and comes from the first term (this is because ATJI ∈ Rm×n). [sent-202, score-0.17]
68 An additional cost for the forward additive form∈u Rlation is that is evaluated at p and not at p = 0, but the cost for doing this can be negligible. [sent-203, score-0.267]
69 An interesting observation following the above analysis is that, for both forward and inverse algorithms, the dominant computational cost comes from projecting out the ap- ∂∂Wp pearance subspace when calculating the Hessian. [sent-204, score-0.466]
70 Fitting AAMs in-the-wild Simultaneous AAM fitting algorithms are known to perform well but their performance has not been previously assessed on recently collected in-the-wild data sets. [sent-209, score-0.3]
71 In particular, we show that AAMs perform almost comparably to some state-of-the-art face alignment algorithms, even without using any priors (the fitting algorithms described above are used as is) and using raw pixel intensities as features. [sent-211, score-0.531]
72 n, which is the case for generic face alignmciaelnlyt. [sent-213, score-0.093]
73 This cost can be easily handled by current systems possibly allowing a close to real-time implementation. [sent-216, score-0.102]
74 Another reason for ruling out AAMs from unconstrained face alignment experiments is the fact that AAMs are not considered robust. [sent-217, score-0.128]
75 The problem with feature extraction is that it might slow down the speed of the fitting algorithm significantly especially when the dimensionality of the featured-based appearance model is large. [sent-222, score-0.392]
76 The problem with robust norms is that scale parameters must be estimated (or percentage of outlier pixels must be predefined) and this task is not trivial. [sent-223, score-0.089]
77 We propose a third orthogonal direction for fitting AAMs in unconstrained conditions which is via training AAMs inthe-wild. [sent-224, score-0.307]
78 Landmarks were detected by fitting the AAM using the Fast-SIC algorithm. [sent-229, score-0.275]
79 (b) Reconstruction of the image from the appearance subspace. [sent-230, score-0.093]
80 The appearance subspace is powerful because the AAM was built in the wild. [sent-231, score-0.116]
81 This image was not seen during training, but similar images of unconstrained nature were used to train the shape and appearance model of an AAM. [sent-236, score-0.193]
82 2 (b) shows the reconstruction of the image from the appearance subspace. [sent-238, score-0.093]
83 As we may see the appearance model is powerful enough to reconstruct the texture almost perfectly. [sent-239, score-0.093]
84 Fitting with a robust algorithm (Fast-SIC in this case) gives the fitting result of Fig. [sent-240, score-0.275]
85 Results The main target of our experiments was not to prove that AAM fitting is state-of-the-art in face alignment but to show that robust fitting plus training in-the-wild improves AAM fitting performance dramatically. [sent-244, score-0.945]
86 For this reason, we did not attempt to use sophisticated shape priors for regularization, nor we employed robust features/appearance models or robust norms for improving performance. [sent-245, score-0.201]
87 To facilitate fitting, we used a multi-resolution fitting approach with m = 50, n = 3 at the lowest level and m = 200, n = 10 at the highest. [sent-249, score-0.275]
88 (a) mean point-to-point error (Euclidean) normalized by the face size vs percentage of test images. [sent-255, score-0.117]
89 For our experiments, we used the training set of LFPW to train the shape and appearance model of the AAM. [sent-259, score-0.161]
90 In all cases, fitting was initialized by the face detector recently proposed in [24]. [sent-264, score-0.331]
91 The first error measure that we used is the pointto-point error normalized by the face size as proposed in [24]. [sent-265, score-0.114]
92 Similarly to [24], for this error measure, we produced the cumulative curve corresponding to the percentage of test images for which the error was less than a specific value. [sent-266, score-0.09]
93 uk / re s ource s c for more details on our experimental setting (we provide source Matlab code for training, fitting and reproducing the results presented in this paper). [sent-272, score-0.301]
94 Although both databases are inthe-wild, the faces of Helen seem to be much more natural, with more shape and appearance variation, and hence are more challenging to fit. [sent-285, score-0.232]
95 Conclusions We described a very simple framework based on (1) for deriving the optimization problems and solutions for fast AAM fitting in both inverse (Fast-SIC) and forward (Fast-Forward) coordinate frames. [sent-291, score-0.537]
96 Based on the proposed framework, exact AAM fitting is no longer computationally prohibitive. [sent-292, score-0.317]
97 Then, we proposed a new direction for employing AAMs in unconstrained conditions by means of 598 599 training AAMs in-the-wild, and fitting using the proposed fast and exact algorithms. [sent-293, score-0.349]
98 Our results show that although we did not use sophisticated shape priors, robust features or robust norms for improving performance, AAMs perform almost comparably with current state-of-the-art methods. [sent-294, score-0.248]
99 Efficient image inner products applied to active appearance models. [sent-410, score-0.144]
100 Adaptive and constrained algorithms for inverse compositional active appearance model fitting. [sent-415, score-0.354]
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