Statistical Shape Models Eigenpatches model regions Assume shape is - - PowerPoint PPT Presentation

Statistical Shape Models

• Eigenpatches model regions

– Assume shape is fixed – What if it isn’t?

• Faces with expression changes,
• organs in medical images etc
• Need a method of modelling shape and

shape variation

Shape Models

• We will represent the shape using a set of

points

• We will model the variation by computing

the PDF of the distribution of shapes in a training set

• This allows us to generate new shapes

similar to the training set

Building Models

• Require labelled training images

– landmarks represent correspondences

Suitable Landmarks

• Define correspondences

– Well defined corners – `T’ junctions – Easily located biological landmarks – Use additional points along boundaries to define shape more accurately

Building Shape Models

• For each example

x = (x1,y1, … , xn, yn)T

Shape

• Need to model the variability in shape
• What is shape?

– Geometric information that remains when location, scale and rotational effects removed (Kendall)

Same Shape Different Shape

Statistical Shape Models

• Given a set of shapes:
• Align shapes into common frame

– Procrustes analysis

• Estimate shape distribution p(x)

– Single gaussian often sufficient – Mixture models sometimes necessary

Principal Component Analysis

• Compute eigenvectors of covariance,S
• Eigenvectors : main directions
• Eigenvalue : variance along eigenvector

1

p

2

p

1

λ ∝

2

λ ∝

Dimensionality Reduction

• Data lies in subspace of reduced dim.
• However, for some t,

i

λ

i

n nb

b p p x x + + + = 

1 1

t j bj > ≈ if

t

) is

• f

(Variance

j j

b λ

Hand shape model

• 72 points placed around boundary of hand

– 18 hand outlines obtained by thresholding images of hand on a white background

• Primary landmarks chosen at tips of fingers and

joint between fingers

– Other points placed equally between

1 2 3 4 5 6

Active Shape Models

• Suppose we have a statistical shape model

– Trained from sets of examples

• How do we use it to interpret new images?
• Use an “Active Shape Model”
• Iterative method of matching model to

image

Active Shape Models

• Match shape model to new image
• Require:

– Statistical shape model – Model of image structure at each point

Model Point Model of Profile

ASM Search Overview

• Local optimisation
• Initialise near target

– Search along profiles for best match,X’ – Update parameters to match to X’.

) , (

i i Y

X

Searching for strong edges

) (x g

x

dx x dg ) ( )) 1 ( ) 1 ( ( 5 . ) ( − − + = x g x g dx x dg

Select point along profile at strongest edge

Multi-Resolution Search

• Train models at each level of pyramid

– Gaussian pyramid with step size 2 – Use same points but different local models

• Start search at coarse resolution

– Refine at finer resolution

Gaussian Pyramids

• To generate image at level L

– Smooth image at level L-1 with gaussian filter (eg (1 5 8 5 1)/20) – Sub-sample every other pixel

Each level half the size of the

• ne below

Multi-Resolution Search

• Start at coarse resolution
• For each resolution

– Search along profiles for best matches – Update parameters to fit matches – (Apply constraints to parameters) – Until converge at this resolution

ASM Example : Brain

ASM Example: Spine

Genkendelse af ukrudtsarter ”Træning” af ASM

(ASM = Active Shape Model)

• Pt. 10 arter

(>100 planter)

Genkendelse af ukrudtsarter ASM-ukrudtsmodel

Weed shape model CHEAL

TRUE Pose parameters Horizontal translation 10

• 8

Vertical translation 10

• 12

Rotation 36 0 ° Scale 50 1,20 Shape parameters Mode

• 3

+3 Value (s.d.) 1 28 0,7 2 20 0,0 3 28

• 0,8

4 27

• 0,3

5 30 0,5 6 30

• 2,0

7 30 0,3 8 30 0,8 9 30

• 1,2

10 30

• 1,4

11 30

• 0,5

12 30

• 1,1

13 30 1,5 14 30

• 2,3

15 30

• 1,8
• 200
• 150
• 100
• 50

50 100 150 200

• 200
• 150
• 100
• 50

50 100 150 200

Use predefined Use scroll bars

Genkendelse af ukrudtsarter

Algoritme - Matlab og ASM Toolkit

Søgning øgning med med ASM ASM

Gennemsnitsmodel for VERSS Deformeret VERSS-model

Scor core

CHEAL 24% SINAR 14% LAMSS 87% VERSS 90%

Active Shape Models

• Advantages

– Fast, simple, accurate – Efficient to extend to 3D

• Disadvantages

– Only sparse use of image information

Active Appearance Models - examples