iccv iccv2013 iccv2013-243 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Lazaros Zafeiriou, Mihalis A. Nicolaou, Stefanos Zafeiriou, Symeon Nikitidis, Maja Pantic
Abstract: A recently introduced latent feature learning technique for time varying dynamic phenomena analysis is the socalled Slow Feature Analysis (SFA). SFA is a deterministic component analysis technique for multi-dimensional sequences that by minimizing the variance of the first order time derivative approximation of the input signal finds uncorrelated projections that extract slowly-varying features ordered by their temporal consistency and constancy. In this paper, we propose a number of extensions in both the deterministic and the probabilistic SFA optimization frameworks. In particular, we derive a novel deterministic SFA algorithm that is able to identify linear projections that extract the common slowest varying features of two or more sequences. In addition, we propose an Expectation Maximization (EM) algorithm to perform inference in a probabilistic formulation of SFA and similarly extend it in order to handle two and more time varying data sequences. Moreover, we demonstrate that the probabilistic SFA (EMSFA) algorithm that discovers the common slowest varying latent space of multiple sequences can be combined with dynamic time warping techniques for robust sequence timealignment. The proposed SFA algorithms were applied for facial behavior analysis demonstrating their usefulness and appropriateness for this task.
Reference: text
sentIndex sentText sentNum sentScore
1 z afe i s riou , Abstract A recently introduced latent feature learning technique for time varying dynamic phenomena analysis is the socalled Slow Feature Analysis (SFA). [sent-4, score-0.413]
2 In this paper, we propose a number of extensions in both the deterministic and the probabilistic SFA optimization frameworks. [sent-6, score-0.236]
3 In particular, we derive a novel deterministic SFA algorithm that is able to identify linear projections that extract the common slowest varying features of two or more sequences. [sent-7, score-0.448]
4 In addition, we propose an Expectation Maximization (EM) algorithm to perform inference in a probabilistic formulation of SFA and similarly extend it in order to handle two and more time varying data sequences. [sent-8, score-0.194]
5 Moreover, we demonstrate that the probabilistic SFA (EMSFA) algorithm that discovers the common slowest varying latent space of multiple sequences can be combined with dynamic time warping techniques for robust sequence timealignment. [sent-9, score-0.587]
6 The proposed SFA algorithms were applied for facial behavior analysis demonstrating their usefulness and appropriateness for this task. [sent-10, score-0.091]
7 Introduction Slow Feature Analysis (SFA) was first proposed in [25] as an unsupervised methodology for finding slowly varying (invariant) features from rapidly temporal varying signals. [sent-12, score-0.422]
8 The exploited slowness learning principle in [25] was motivated by the empirical observation that higher order meanings of sensory data, such as objects and their attributes, are often more persistent (i. [sent-13, score-0.242]
9 , change smoothly) than the independent activation of any single sensory receptor. [sent-15, score-0.111]
10 For instance, the position and the identity of an object are visible for extended periods of time and change with time in a continuous fashion. [sent-16, score-0.054]
11 uk c} any primary sensory signal (like the responses of individual retinal receptors or the gray-scale values of a single pixel in a video camera), thus being more robust to subtle changes in the environment. [sent-21, score-0.176]
12 The proposed in [25] optimization problem aims to minimize the magnitude of the approximated first order time derivative of the extracted slowly varying features under the constraints that these are centered (i. [sent-23, score-0.246]
13 Thus, the slowest varying features are identified by solving a generalized eigenvalue problem for the joint diagonalization of the data covariance matrix and the covariance matrix of the first order forward data differences. [sent-26, score-0.533]
14 Intuitively, SFA imitates the functionality of the receptive fields of the visual cortex [2], thus being appropriate for describing the evolution of time varying visual phenomena. [sent-27, score-0.167]
15 Recently, SFA and its discriminant extensions have been successfully applied for human action recognition in [26], while hierarchical segmentation of video sequences using SFA was investigated in [15]. [sent-29, score-0.113]
16 In [8] SFA was applied for object and object-pose recognition on a homogeneous background, while in [14] SFA for vectorvalued functions was studied for blind source separation. [sent-30, score-0.033]
17 In [4], the equivalence between linear SFA and the second-order ICA algorithm, in the case of one time delay, is demonstrated. [sent-33, score-0.027]
18 In [20], the relation between we 1Continuous time SFA has been proposed in [24] but since in this paper assume discrete time signals, such works are out of our scope. [sent-34, score-0.054]
19 2840 f1 f7 f10 f23 f33 f38 f42 frames Figure 1: The latent space obtained by EM-SFA, accurately capturing the transition between temporal phases of action units. [sent-35, score-0.384]
20 LE and SFA was studied and exhibited that SFA is a special case of kernel Locality Preserving Projections (LPP) [9] acquired by defining the data neighborhood structure using their temporal variations. [sent-37, score-0.089]
21 In [21], it was shown that the projection bases provided by SFA are similar to those yielded by the Maximum Likelihood (ML) solution of a probabilistic generative model in the limit case that the noise vari- ance tends to zero. [sent-38, score-0.136]
22 The probabilistic generative model comprises a linear model for the generation of observations and imposes a Gaussian linear dynamical system with diagonal covariances over the latent space. [sent-39, score-0.289]
23 In this paper, we study the application of SFA for unsupervised facial behaviour analysis. [sent-40, score-0.161]
24 1, we can see the resulting latent space obtained by EM-SFA, applied on a video sequence where the subject is activating Action Unit (AU) 22 (Lip Funneler). [sent-45, score-0.179]
25 In general, when activating an AU, the following temporal phases are recorded: Neutral, when the face is relaxed, Onset, when the action initiates, Apex, when the muscles reach the peak intensity and Offset when the muscles begin to relax. [sent-46, score-0.475]
26 It can be clearly observed in the figure, that the latent space obtained by EM-SFA accurately captures the transitions between the temporal phases of the AU, providing an unsupervised method for detecting the temporal phases of AUs. [sent-48, score-0.586]
27 Summarising the contributions of our paper, we propose the following theoretical novelties: • We propose the first Expectation Maximization (EM) algorithm for learning the model parameters of a probabilistic SFA (EM-SFA). [sent-49, score-0.076]
28 In contrast to existing ML approaches ([21]), our approach allows for full probabilistic modelling of the latent distributions instead of mapping the variances to zero, as in ML. [sent-50, score-0.194]
29 • We extend both deterministic and probabilistic SFA to enable us to find the common slowest varying features of two or more time varying data sequences, thus allowing the simultaneous analysis of multiple data streams. [sent-51, score-0.603]
30 The novelties of our paper in terms of application can be summarized as follows: • • We apply the proposed EM-SFA to facial behaviour dynamics analysis and in particular for facial Action Units (AUs) analysis. [sent-52, score-0.271]
31 More precisely, we demonstrate that it is possible to discover the dynamics of AUs in an unsupervised manner using EM-SFA. [sent-53, score-0.075]
32 To the best of our knowledge, this is the first unsupervised approach which detects the temporal phases of AUs (other unsupervised approaches such as [29] focus on detecting global structures (i. [sent-54, score-0.3]
33 We combine the common latent space derived by EM-SFA with Dynamic Time Warping techniques [18] for the temporal alignment of dynamic facial behaviour. [sent-57, score-0.294]
34 We claim that by using the slowest varying features for sequence alignment is well motivated by the principle of slowness as described above (i. [sent-58, score-0.377]
35 , slowly varying features correspond to meaningful changes rather than rapidly varying ones, which most likely correspond to noise [25]). [sent-60, score-0.289]
36 × The rest of the paper is organised as follows. [sent-61, score-0.03]
37 2, we describe the deterministic SFA model, while in Sec. [sent-63, score-0.136]
38 2), while the latter method is incremented with warpings in Sec. [sent-70, score-0.063]
39 Deterministic Slow Feature Analysis In order to identify the slowest varying features deterministic SFA considers the following optimization problem. [sent-80, score-0.409]
40 Given an M-dimensional time-varying input sequence X = [xt, t ∈ [1, T]], where t denotes time and xt ∈ ? [sent-81, score-0.087]
41 termine appropriate projection bases stored in the columns of matrix V = [v1, v2, . [sent-83, score-0.054]
42 imize the variance of the approximated first order time derivative of the latent variables Y = [y1, y2, . [sent-88, score-0.197]
43 N×T subject to zero mean, unit covariance and decorre]l∈a ti ? [sent-92, score-0.081]
44 ] is the matrix trace operator, 1is a T (1) 1vector × wwihtehr aell t ri[ts. [sent-96, score-0.126]
45 ]e ilse tmheen mts equal atoc eT1 o, Ip eirsa a oNr, ×1 N is identity m veactrtioxr and matrix Y˙ approximates the first order time derivative of Y, evaluated using the forward latent variable differences as follows: Y˙ = [y2 − y1, y3 − y2, . [sent-97, score-0.388]
46 (3) where B is the input data covariance matrix and A is an M M covariance matrix evaluated using the forward temporal Mdiff ceorveanrcieasn coef mthaet input adluaatate, cdo unstianigne tdhe ei fno mrwaatrridx tXe˙m A =1X˙X˙T,B =T1XXT. [sent-104, score-0.389]
47 (4) The solution of (3) can be found from the Generalized Eigenvalue Problem (GEP) [25]: AV = BVL (5) where the columns of the projection matrix V are the generalized eigenvectors associated with the N-lower general- ized eigenvalues contained sorted in the diagonal matrix L. [sent-105, score-0.11]
48 A Probabilistic Interpretation of SFA In this section, we discuss a probabilistic approach to SFA latent variable extraction. [sent-107, score-0.194]
49 Let us assume the following linear generative model that relates the latent variable yt with the observed samples xt as: xt = V−Tyt + et, et ∼ N(0, σx2I) (6) where ei is the noise which is assumed to be an isotropic Gaussian model. [sent-108, score-0.437]
50 Let us also assume the lin|Vea,ry yGauss)ia =n dynamical system priors over the latent space Y are: ? [sent-110, score-0.156]
51 m=o =h Σ = [δi,jσ2n] and Σ1 = [δi,jσ2n,1] the prior over the latent space can be evaluated as: P(Y|θy)=+(Z21 yσ1n2e xy? [sent-119, score-0.118]
52 In [21], it was shown that the ML solution of the above model in the deterministic case (i. [sent-128, score-0.136]
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Abstract: In this paper, we formulate saliency detection via absorbing Markov chain on an image graph model. We jointly consider the appearance divergence and spatial distribution of salient objects and the background. The virtual boundary nodes are chosen as the absorbing nodes in a Markov chain and the absorbed time from each transient node to boundary absorbing nodes is computed. The absorbed time of transient node measures its global similarity with all absorbing nodes, and thus salient objects can be consistently separated from the background when the absorbed time is used as a metric. Since the time from transient node to absorbing nodes relies on the weights on the path and their spatial distance, the background region on the center of image may be salient. We further exploit the equilibrium distribution in an ergodic Markov chain to reduce the absorbed time in the long-range smooth background regions. Extensive experiments on four benchmark datasets demonstrate robustness and efficiency of the proposed method against the state-of-the-art methods.
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Author: Zhengxiang Wang, Rujie Liu
Abstract: This paper introduces to use semi-supervised learning for large scale image cosegmentation. Different from traditional unsupervised cosegmentation that does not use any segmentation groundtruth, semi-supervised cosegmentation exploits the similarity from both the very limited training image foregrounds, as well as the common object shared between the large number of unsegmented images. This would be a much practical way to effectively cosegment a large number of related images simultaneously, where previous unsupervised cosegmentation work poorly due to the large variances in appearance between different images and the lack ofsegmentation groundtruthfor guidance in cosegmentation. For semi-supervised cosegmentation in large scale, we propose an effective method by minimizing an energy function, which consists of the inter-image distance, the intraimage distance and the balance term. We also propose an iterative updating algorithm to efficiently solve this energy function, which decomposes the original energy minimization problem into sub-problems, and updates each image alternatively to reduce the number of variables in each subproblem for computation efficiency. Experiment results on iCoseg and Pascal VOC datasets show that the proposed cosegmentation method can effectively cosegment hundreds of images in less than one minute. And our semi-supervised cosegmentation is able to outperform both unsupervised cosegmentation as well asfully supervised single image segmentation, especially when the training data is limited.
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Author: Zhuwen Li, Jiaming Guo, Loong-Fah Cheong, Steven Zhiying Zhou
Abstract: This paper addresses real-world challenges in the motion segmentation problem, including perspective effects, missing data, and unknown number of motions. It first formulates the 3-D motion segmentation from two perspective views as a subspace clustering problem, utilizing the epipolar constraint of an image pair. It then combines the point correspondence information across multiple image frames via a collaborative clustering step, in which tight integration is achieved via a mixed norm optimization scheme. For model selection, wepropose an over-segment and merge approach, where the merging step is based on the property of the ?1-norm ofthe mutual sparse representation oftwo oversegmented groups. The resulting algorithm can deal with incomplete trajectories and perspective effects substantially better than state-of-the-art two-frame and multi-frame methods. Experiments on a 62-clip dataset show the significant superiority of the proposed idea in both segmentation accuracy and model selection.
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