Report

2012 Moving Object Segmentation by Pursuing Local SpatioTemporal Manifolds Yuanlu Xu Problem Segmenting moving foreground in a video Related work & intuitions Dynamic background ~ dynamic textures Image sequences of certain textures moving and changing under certain properties. S. Soatto, G. Doretto, and Y. Wu. “Dynamic textures”. IJCV 2003 Related work & intuitions Dynamic background ~ dynamic textures How to model? The output of a linear dynamic system driven by IID Gaussian noises. Intuition for moving object segmentation: A complex scene containing dynamic background is composed of several independent dynamic textures. Related work & intuitions Illumination changes ~ modeling illumination Observing eigenvalue curves of different state bricks, (a) background, (b) foreground occlusion Y. Zhao et al. “Spatiotemporal patches for night background modeling by subspace learning”. ICPR 2008 Related work & intuitions Illumination changes ~ modeling illumination Intuition for handling illumination changes: The set of bricks of a given background location under various lighting conditions lies in a low-dimensional manifold. Related work & intuitions Indistinctive changes Similar appearance incorporating extra information Intuition for distinguishing indistinctive moving objects: Modeling background appearance variations, estimating next state, distinguishing moving objects not following the similar changes Intuitions & assumptions 1. A complex scene containing dynamic background is composed of several independent dynamic textures. 2. The set of bricks of a given background location under various lighting conditions lies in a lowdimensional manifold. 3. Modeling background appearance variations. 1. Given a background location, the sequence of bricks (under dynamic changes, illumination changes) lies in a lowdimensional manifold, and the variations satisfy local linear. 2. The bricks with indistinctive and distinctive foreground occlusions can be well separated from the background by distinguishing differences in both appearance and variations. Representation Segmenting Brick in Video: For each frame, we divide it into patches with size ℎ ⋅ . At each location, t patches are combined together to form a brick Representation Center Symmetric – Spatio Temporal LTP (CS-STLTP) Descriptor 156 178 182 0 尺度阈值 70 101 89 193 251 126 t = 0.2 1 0 -1 4个时空平面 85 178 124 81 101 63 Y T . . . 146 251 145 特征向量 0 1 0 -1 56 178 76 X 123 101 251 53 251 142 . . . . . . -1 1 -1 53 178 78 3x3x3 立方体 246 101 198 43 251 20 -1 1 -1 1 1 Mathematical formulation Given a brick sequence = 1 , 2 , … , ∈ m∗nof a background location, we assume the dimension of the manifold in is . The structure of this manifold: = , + =1 = 1 , 2 , … , : bases of the manifold. , : coefficient of basis given . : structural residual . Mathematical formulation Given the corresponding coding = 1 , 2 , … , ∈ ∗ for = 1 , 2 , … , , the coding variation is local linear, according to the assumption. The coding variation within this manifold: +1 = + +1 , : two successive state. ∈ ∗ : description of the coding variation. : state residual. Mathematical formulation The problem of pursuing the structure of and the variation within a manifold is formulated as minimizing the empirical energy function: 1 . , = =1 1 ( − 2 1 + − −1 2 2 2 ( = 1 , 2 , … , ∈ ∗ , ∈ ∗ , ∈ ∗ , ∈ ∗ ) min. structural residual min. state residual 2 2 ) Mathematical formulation Because is unknown, we rewrite the problem as a joint optimization problem with , , : 1 . , , = =1 1 ( − 2 1 + − −1 2 2 2 2 2 ) Not jointly convex, but convex with respect to , and when the other is fixed. A numerical solution: alternate between the two variables, minimizing over one while keeping the other one fixed. Representation 1 . , , = =1 1 ( − 2 1 + − −1 2 2 2 2 2 ) Rewritten as a linear dynamic system (LDS) ∼ structural residual structural noise = + , +1 = + 0, , ∼ (0, ) state residual state noise Learning = + , +1 = + ∼ 0, , ∼ (0, ) Initial Learning Given a training sequence = {1 , 2 , … , }, identify , , , = + , +1 = + Online Learning Given a new brick +1 , incrementally learn +1 , +1 , +1 , +1 +1 = +1 + +1 , +2 = +1 +1 + +1 Learning Initial Learning Sub-optimal analytical solution S. Soatto, G. Doretto, and Y. Wu. “Dynamic textures”. IJCV 2003. Online Learning Learning +1 : incremental subspace learning Candid Covariance-free IPCA (CCIPCA) and IPCA J. Weng et al. “Candid covariance-free incremental principal component analysis”. TPAMI 2003. Y. Li. “On incremental and robust subspace learning”. Pattern Recognition 2004. Learning +1 : Linear problem of the latest states Inference For a new brick +1 , the segmentation of moving object is decided by the structural noise and state noise. Structural noise: ′ +1 = +1 = +1 − ′+1 +1 State noise: = ′ +1 − Experimental Results Datasets Busy scenes Dynamic scenes Water Surface Illumination changes Swaying Trees Sudden Light Airport Heavy Rain Active Fountain Train Station Gradual Light Waving Curtain Floating Bottle Experimental Results Scene GMM 1# Airport 2# Floating Bottle 3# Waving Curtain 4# Active Fountain 5# Heavy Rain 6# Sudden Light 7# Gradual Light 8# Train Station 9# Swaying Trees 10# Water Surface Average 46.99 57.91 62.75 52.77 71.11 47.11 51.10 65.12 19.51 79.54 55.39 ImGMM 47.36 57.77 74.58 60.11 81.54 51.37 50.12 68.80 23.25 86.01 59.56 OnlineAR 62.72 43.79 77.86 70.41 78.68 37.30 13.16 36.01 63.54 77.31 57.02 JDR 60.23 45.64 72.72 68.53 75.88 52.26 47.48 57.68 45.61 84.27 60.23 Struct1 -SVM 65.35 47.87 77.34 74.94 82.62 47.61 62.44 61.79 24.38 83.13 59.79 SILTP 68.14 59.57 78.01 76.33 76.71 52.63 54.86 67.05 42.54 74.30 63.08 STDB (RGB) 75.52 69.04 87.74 76.85 86.86 51.56 54.84 73.43 43.70 88.54 70.81 STDB (Ftr.) 66.40 75.85 79.57 79.68 81.35 70.23 72.52 66.46 48.49 87.88 72.84 Experimental Results Experimental Results Experimental Results Experimental Results Experimental Results Experimental Results Selection of structural update approach Scene 1# Airport 2# Floating Bottle 3# Waving Curtain 4# Active Fountain 5# Heavy Rain 6# Sudden Light 7# Gradual Light 8# Train Station 9# Swaying Trees 10# Water Surface Average CCIPCA Accuracy Efficiency (%) (fps) 75.52 69.04 87.74 76.85 86.86 51.56 4.1 54.84 73.43 43.70 88.54 70.81 IPCA Efficiency Accuracy (%) (fps) 65.13 70.02 78.47 81.38 79.84 53.63 2.3 59.79 68.69 70.17 89.43 71.66 Dynamic scenes: IPCA is much better than CCIPCA Busy scenes: CCIPCA is much better than IPCA Illumination changes: IPCA slightly better than CCIPCA Efficiency: CCIPCA is much faster than IPCA Contribution 1. Formulating the problem of modeling background by pursuing local spatio-temporal manifolds of video brick sequences. 2. Representing spatio-temporal statistics in video bricks with CSSTLTP descriptor. 3. Pursuing local spatio-temporal manifolds with two LDSs: a timeinvariant LDS for initial learning and a time-variant LDS for online learning. 4. Online learning the structure of local spatio-temporal manifolds with incremental subspace learning and the state variations with re-solving linear problems. Problems 1. CS-STLTP behaves well in handling illumination changes, but not sufficient to capture variation statistics. 2. In highly dynamics scenes, the assumption of local linear variation can hardly hold. 3. CCIPCA suffers updating the great changes of the structure of the manifold. IPCA behaves better than CCIPCA but suffers the computational complexity. Published Papers 1. Yuanlu Xu, Hongfei Zhou, Qing Wang, Liang Lin. “Realtime Objectof-Interest Tracking by Learning Composite Patch-based Templates”. ICIP 2012 (accepted) 2. Liang Lin, Yuanlu Xu, Xiaodan Liang. “Complex Background Subtraction by Pursuing Dynamic Spatio-temporal Manifolds”. ECCV 2012 (submitted) QUESTIONS? Difficulties Dynamic backgrounds Illumination changes (especially sudden changes) Difficulties Indistinctive moving objects Moving camera (e.g., shaking, hand-held) Contribution 1. Formulating the problem of modeling background by pursuing local spatio-temporal manifolds of video brick sequences. 2. Representing spatio-temporal statistics in video bricks. 3. Pursuing local spatio-temporal manifolds. 4. Maintaining local spatio-temporal manifolds online. Mathematical formulation Similar to sparse coding, to prevent being arbitrarily large, which results arbitrarily small, we add the constraint 2 ≤ 1, and the constraint set is formulated as: ≜ ∈ ∗ , ∀ = 1,2, … , , 2 ≤1 ∀ 1 2 ≤ 1, 2 2 ≤ 1, ∀ 0 ≤ ≤ 1, 1 + 1 − 2 2 ≤ 1 2 + 1 − 2 ≤ 1 2 + 1 − 2 ≤+ 1− ≤1 Thus is a convex set. 2 2 Mathematical formulation Because is unknown, we rewrite the problem as a joint optimization problem with , , : 1 . , , = =1 1 ( − 2 1 + − −1 2 2 2 2 2 ) ∈ Γ Not jointly convex, but convex with respect to , and when the other is fixed. A numerical solution: alternate between the two variables, minimizing over one while keeping the other one fixed. Mathematical formulation In practice, above joint optimization problem is simplified as a two step optimization: 1. Rewrite the problem as a time-variant linear dynamic system, solve the structure of the system, ignore the state (coding) variation. 2. Given the structure of the system, solve the state variation, based on the corresponding state for each brick. Representation Local Binary Pattern (LBP) / Local Ternary Pattern (LTP) Representation Scale Invariant LTP (SILTP) S. Liao et al. “Modeling pixel process with scale invariant local patterns for background subtraction in complex scenes”. CVPR 2010 Representation Scale Invariant LTP (SILTP) SILTP is more robust in handling scale changes (illumination changes). Representation 156 178 182 0 尺度阈值 70 101 89 193 251 126 t = 0.2 1 0 -1 4个时空平面 85 178 124 81 101 63 Y T . . . 146 251 145 特征向量 0 1 0 -1 56 178 76 X 123 101 251 53 251 142 . . . . . . -1 1 -1 53 178 78 3x3x3 立方体 246 101 198 43 251 20 -1 1 -1 1 1 Representation Center Symmetric Coding P0 P1 P2 P7 Pc P3 P6 P5 P4 Comparison S0 S1 S2 8 neighboring pixels S3 around the center are formed into 4 pairs (0 , 4 ), (1 , 5 ), (2 , 6 ), (3 , 7 ). Representation 1 . , , = structure of the manifold appearance matrix =1 1 ( − 2 1 + − −1 2 2 2 2 2 ) Rewritten as a linear dynamic system (LDS) structural noise ∼ 0, = + , structural residual +1 = + state variations of the manifold dynamics matrix state noise ∼ (0, ) state residual Initial learning Sub-optimal analytical solution Assumption: 1. The dimension of the manifold is , the dimension of the state noise is , > . The appearance matrix satisfies = . 2. The analytical solution for the structure of the manifold is The decomposition is simulated by SVD. = , = 1: , : , = (1: , 1: ) (1: , : ) S. Soatto, G. Doretto, and Y. Wu. “Dynamic textures”. IJCV 2003. Initial learning Given the states 1 2 … , solving the dynamics matrix by linear programming: To estimate noise covariance , we treat as the reconstruction error = +1 − , and is represented as = 1 = lim →+∞ 1 ≈ −1 =1 −1 =1 To reduce the dimension of , let = = −1 . and apply PCA to , Initial learning Since different manifold has different dynamic properties, the dimension of the manifold is determined by the training samples. Static Dimension Low Dynamic Dimension High Online learning Against foreground occlusions We define a noise-free video brick under the current model to compensate the missing background samples. The noise-free video brick +1 is defined as Online learning To update the structure of the manifold, we regard +1 as the extension by adding a new column (update sample) to . The problem of updating +1 is formulated as incremental subspace learning. To find a more effective approach, we employ two incremental subspace learning methods: 1. Candid Covariance-free Incremental PCA (CCIPCA), without estimating the covariance matrix. 2. Incremental PCA (IPCA), estimating the covariance matrix. Online learning CCIPCA J. Weng et al. “Candid covariance-free incremental principal component analysis”. IEEE TPAMI 2003. Online learning IPCA For a -dimension manifold, with eigenvectors , and eigenvalues Λ , the covariance matrix is estimated as With the new sample, the new covariance matrix is estimated as Using the new covariance matrix to estimate the new eigenvectors +1 , Λ+1 . Y. Li. “On incremental and robust subspace learning”. Pattern Recognition 2004. Online learning Update the state variation +1 , +1 by re-estimating the new state +1 , +1 is updated by re-computing the linear problem, +1 by re-estimating the covariance matrix, [ −+1 −+2 ⋯ ] = [ −+2 −+3 ⋯ +1 ] − [ −+1 −+2 ⋯ ] +1 = 1 = =−+1 Online learning Anti-degeneration Algorithm Experimental Results Behave poorly on highly dynamic backgrounds!