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Proposed Dissimilarity Measure

Proposed Dissimilarity Measure. We chose the SDF as our shape descriptor because: Convergence condition of gradient descent methods is satisfied (Huang et al PAMI’06). Invariance to rotations and translations. Ability to handle topological changes. Its relative simplicity.

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Proposed Dissimilarity Measure

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  1. Proposed Dissimilarity Measure • We chose the SDF as our shape descriptor because: • Convergence condition of gradient descent methods is satisfied(Huang et al PAMI’06). • Invariance to rotations and translations. • Ability to handle topological changes. • Its relative simplicity. To deal with the dimension added by the SDF definition • Proposed SSD Measure where: or

  2. Convexity of the proposed SSD measure • Empirical Evaluation (2D case): • Pick a shape: • Fix 3 parameters and vary the remaining 2. • The ranges of the 2 unknown parameters are uniformly quantized using 100 samples: • Convexity in full dimensionality is not guaranteed

  3. Empirical Evaluation of the Proposed SSD

  4. Euler Lagrange Equations • For each parameter where: • Implementation consideration: different time steps may need to be used for different parameters

  5. Comparisons with the other models Initial position Isotropic scale-based model VDF-based model 208.67 sec 300.57 sec 141.26 sec 221.35sec Our results 139.67 sec 206.82sec 180.68sec 102.23sec

  6. More comparisons Initial position Isotropic scale-based model VDF-based model 538.67sec 271.57 sec 263.69 sec 219.87 sec 296.67sec 157.76 sec 147.20 sec Our results 169.77 sec

  7. Recovered parameters • GT: Ground truth • M1: Our model • M2:VDF-model • M3: Homogeneous scale-based model

  8. 3D Experiments

  9. Model shape variations using PCA Align Shapes Application: Statistical modeling of shapes Shape Model = Mean Shape + Basic Variations Implicit Rep. Training data

  10. Before alignments Overlap After alignments Overlap Alignments Goal: Establish correspondences among shapes over the training set

  11. Qualitative Evaluation • Correlation Coefficient

  12. Modeling shape variations using PCA • Compute the mean of the aligned data and mean offsets and • SVD of covariance matrix with • New shape, within the variance observed in training set, can be approximated chose k s.t.

  13. First four principal modes Mode 1 Mode 2 Mode 3 Mode 4

  14. Application: Shape-based segmentation • Generate an Active Shape Model (ASM) and use it to locate objects in hard to segment images (Cootes and Taylor’95) Isotropic scale-based model Our model

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