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Edge Preserving Spatially Varying Mixtures for Image Segmentation Giorgos Sfikas, Christophoros Nikou, Nikolaos Galatsanos (CVPR 2008) Presented by Lihan.

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Presentation on theme: "Edge Preserving Spatially Varying Mixtures for Image Segmentation Giorgos Sfikas, Christophoros Nikou, Nikolaos Galatsanos (CVPR 2008) Presented by Lihan."— Presentation transcript:

1 Edge Preserving Spatially Varying Mixtures for Image Segmentation Giorgos Sfikas, Christophoros Nikou, Nikolaos Galatsanos (CVPR 2008) Presented by Lihan He ECE, Duke University Feb 23, 2009 by

2 Introduction Edge preserving spatially varying GMM Inference using MAP-EM Experimental results Conclusion Outline 2/15

3 Introduction 3/15 Image segmentation GMM: no prior knowledge is exploited  Adjacent pixels most likely belong to the same cluster;  Edge of objectives. SVGMM (spatially variant GMM): Clustering pixels or super pixels such that the same group has common characteristics (same objective, similar texture)  Spatial smoothness is imposed in the neighborhood of each pixel based on the Markov random field;  Without considering the edge of textures

4 Introduction 4/15 In this paper  Hierarchical Bayesian model;  Spatially varying GMM: mixing weights are different for different pixels;  Difference of mixing weights for two neighbored pixels follows a student-t distribution;  Heavy tailed student-t preserves edges of textures;  MAP-EM is used for model inference.

5 St-SVGMM Feature vector for each pixel: SVGMM: Each pixel has its own mixing weights Each pixel x n : weights indicator variables Likelihood: Prior: 5/15

6 St-SVGMM Prior for mixing weight π: d=2 d=1 d: neighborhood adjacency type d=1: horizontal d=2: vertical γ d (n): the set of neighbors of pixel n, with respect to the d th adjacency type K×D different student-t distributions are introduced, with hyperparameters Joint prior for π: 6/15

7 St-SVGMM The student-t distribution can be modeled by introducing the latent variable plays an important role: neighboring pixels n, k belong to the same cluster n, k are at the edge of two clusters n – edge location k (d) – adjacency type (horizontal or vertical) j – cluster index (edges of which cluster) 7/15

8 St-SVGMM Model summary 8/15

9 Inference MAP-EM algorithm for model inference. Complete log-likelihood Model parameters: E-step (update Z, U) 9/15

10 Inference M-step ( update ) = 10/15

11 Results U-variable maps j=1: sky j=2: roof & shadows j=3: building d=1: horizontal d=2: vertical n – edge location k (d) – adjacency type j – cluster index K=3 clusters Brighter regions represent lower values – edges. 11/15

12 Results Comparison on 300 images of the Berkeley image database Statistics on the Rand Index (RI) (measuring the consistency between the ground truth and the segmentation map); higher is better. Statistics on the boundary displacement error (BDE) (measuring error of boundary displacement with respect to the ground truth); lower is better. 12/15

13 Results Segmentation examples K=5 K=15 K=10 original image 13/15

14 Results K=5 K=15 K=10 original image 14/15

15 Conclusion 15/15  Proposed a GMM-based clustering algorithm for image segmentation;  Used smoothness prior to consider the adjacent pixels belonging to the same cluster;  Also captured the image edge structure (no smoothness enforced across segment boundaries);  All required parameters are estimated from the data (no requirement of empirical parameter selection).  Next: automatically estimating the number of components K.


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