1CVIP LaboratoryCVIP Laboratory1

Proposed Dissimilarity Measure

where:

or

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. Proposed SSD Measure

To deal with the dimension added by the SDF definition

2CVIP LaboratoryCVIP Laboratory2

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/,3/[ ]25.1,7.0[, yx ss ]20,20[, yx tt

Convexity of the proposed SSD measure

3CVIP LaboratoryCVIP Laboratory3

Empirical Evaluation of the Proposed SSD

4CVIP LaboratoryCVIP Laboratory4

Euler Lagrange Equations

where:

For each parameter

Implementation consideration: different time steps may need to be used for different parameters

5CVIP LaboratoryCVIP Laboratory5

Initial positio

n

Isotropic scale-based model

Our result

s

VDF-based model

Comparisons with the other models

208.67 sec

139.67 sec

300.57 sec

206.82 sec

141.26 sec

102.23 sec

221.35sec

180.68 sec

6CVIP LaboratoryCVIP Laboratory6

Initial positio

n

Isotropic scale-based model

Our result

s

VDF-based model

More comparisons

271.57 sec

219.87 sec

538.67sec

147.20 sec

157.76 sec

296.67sec

263.69 sec

169.77 sec

7CVIP LaboratoryCVIP Laboratory7

Recovered parameters•GT: Ground truth

•M1: Our model

•M2:VDF-model

•M3: Homogeneous scale-based model

8CVIP LaboratoryCVIP Laboratory8

3D Experiments

9CVIP LaboratoryCVIP Laboratory9

Implicit Rep..

1

2

3

n

Application: Statistical modeling of shapes

Training data

Align Shapes

Model shape

variations using

PCA

Shape Model

=

Mean Shape

+

Basic Variatio

ns

10CVIP LaboratoryCVIP Laboratory10

Alignments

OverlapOverlap

Before alignments

OverlapOverlap

After alignments

Goal: Establish correspondences among shapes over the

training set

11CVIP LaboratoryCVIP Laboratory11

Qualitative Evaluation Correlation Coefficient

12CVIP LaboratoryCVIP Laboratory12

Modeling shape variations using PCA Compute the mean of the aligned data and

mean offsetsand

SVD of covariance matrix

New shape, within the variance observed in training set, can be approximated

chose k s.t.

with

13CVIP LaboratoryCVIP Laboratory13

First four principal modes

Mode 1

Mode 2

Mode 3

Mode 4

i2 i2i0 i1

i2

14CVIP LaboratoryCVIP Laboratory14

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

sss yx

yx ss