Analysis of Contour Motions Ce Liu William T. Freeman Edward H. Adelson Computer Science and Artificial Intelligence Laboratory Massachusetts Institute

Analysis of Contour Motions

Ce Liu William T. Freeman Edward H. Adelson

Computer Science and Artificial Intelligence Laboratory

Massachusetts Institute of Technology

Neural Information Processing Systems 2006

Visual Motion Analysis in Computer Vision

• Motion analysis is essential in– Video processing – Geometry reconstruction– Object tracking, segmentation and recognition– Graphics applications

• Is motion analysis solved?

• Do we have good representation for motion analysis?

• Is it computationally feasible to infer the representation from the raw video data?

• What is a good representation for motion?

Seemingly Simple Examples

Kanizsa square

From real video

Output from the State-of-the-Art Optical Flow Algorithm

T. Brox et al. High accuracy optical flow estimation based on a theory for warping. ECCV 2004

Optical flow fieldKanizsa square

Output from the State-of-the-Art Optical Flow Algorithm

T. Brox et al. High accuracy optical flow estimation based on a theory for warping. ECCV 2004

Optical flow field

Dancer

Optical flow representation: aperture problem

Corners Lines Flat regions

Spurious junctions Boundary ownership Illusory boundaries

Optical Flow Representation

Corners Lines Flat regions

Spurious junctions Boundary ownership Illusory boundaries

We need motion representation beyond pixel level!

Layer Representation

• Video is a composite of layers

• Layer segmentation assumes sufficient textures for each layer to represent motion

• A true success?

J. Wang & E. H. Adelson 1994

Y. Weiss & E. H. Adelson 1994

Achieved with the help of spatial segmentation

Layer Representation

• Video is a composite of layers

• Layer segmentation assumes sufficient textures for each layer to represent motion

• A true success?

J. Wang & E. H. Adelson 1994

Y. Weiss & E. H. Adelson 1994

Achieved with the help of spatial segmentation

Layer representation is good, but the existing layersegmentation algorithms cannot find the right layersfor textureless objects

Challenge: Textureless Objects under Occlusion

• Corners are not always trustworthy (junctions)

• Flat regions do not always move smoothly (discontinuous at illusory boundaries)

• How about boundaries?– Easy to detect and track for textureless

objects

– Able to handle junctions with illusory boundaries


• Our approach: simultaneous grouping and motion analysis– Multi-level contour representation

– Junctions are appropriated handled

– Formulate graphical model that favors good contour and motion criteria

– Inference using importance sampling

• Contribution– An important component in motion analysis toolbox for

textureless objects under occlusion

Three Levels of Contour Representation

– Edgelets: edge particles

– Boundary fragments: a chain of edgelets with small curvatures

– Contours: a chain of boundary fragments

Forming boundary fragments: easy (for textureless objects)

Forming contours: hard (the focus of our work)

Overview of our system

1. Extract boundary fragments 2. Edgelet tracking with uncertainty.

3. Boundary grouping and illusory boundary 4. Motion estimation based on the grouping

Forming Boundary Fragments

• Boundary fragments extraction in frame 1– Steerable filters to obtain edge energy for each

orientation band– Spatially trace boundary fragments– Boundary fragments: lines or curves with small curvature

• Temporal edgelet tracking with uncertainties

(a) (b)

(c) (d)

– Frame 1: edgelet (x, y, )

– Frame 2: orientation energy of

– A Gaussian pdf is fit with the weight of orientation energy

– 1D uncertainty of motion (even for T-junctions)

Forming Contours: Boundary Fragments Grouping

• Grouping representation: switch variables (attached to every end of the fragments)– Exclusive: one end connects to at most one other end

– Reversible: if end (i,ti) connects to (j,tj), then (j,tj) connects to (i,ti)

Arbitrarily possible connection

1b 2b

3b

Reversibility

A legal contour grouping

Another legal contour grouping

0

1

0

1

1

0

Local Spatial-Temporal Cues for Grouping

Motion stimulus

Illusory boundaries corresponding to the groupings (generated by spline interpolation)

Local spatial-temporal cues for grouping: (a) Motion similarity

Motion stimulus

xv

yv

Velocity space

KL( ) < KL( )

The grouping with higher motion similarity is favored

Local spatial-temporal cues for grouping: (b) Curve smoothness

Motion stimulus

The grouping with smoother and shorter illusory boundary is favored

Local spatial-temporal cues for grouping: (c) Contrast consistency

Motion stimulus

The grouping with consistent local contrast is favored

The Graphical Model for Grouping

• Affinity metric terms

– (a) Motion similarity

– (b) Curve smoothness

– (c) Contrast consistency

• The graphical model for grouping

1b

2b

),( 1111

),( 2121

1b

r

2b

reversibilityaffinity

11h

12h

21h

22h

1b

2b

no self-intersection

Motion estimation for grouped contours

• Gaussian MRF (GMRF) within a boundary fragment

• The motions of two end edgelets are similar if they are grouped together

• The graphical model of motion: joint Gaussian given the grouping

This problem is solved in early work: Y. Weiss, Interpreting images by propagating Bayesian beliefs, NIPS, 1997.

Inference

• Two-step inference– Grouping (switch variables)

– Motion based on grouping (easy, least square)

• Grouping: importance sampling to estimate the marginal of the switch variables– Bidirectional proposal density

– Toss the sample if self-intersection is detected

• Obtain the optimal grouping from the marginal

1b2b

3b4b

Why bidirectional proposal in sampling?


1b2b

3b4b

b1b2: 0.39

b1b3: 0.01

b1b4: 0.60

Normalized affinity metrics

b4b1: 0.20

b4b2: 0.05

b4b3: 0.85

b2b1: 0.50

b2b3: 0.45

b2b4: 0.05

b3b1: 0.01

b3b2: 0.45

b3b4: 0.54

b1b2: 0.1750

b1b3: 0.0001

b1b4: 0.1200

Affinity metric of the switch variable (darker, thicker means larger affinity)

Bidirectional proposal


b1b2: 0.39

b1b3: 0.01

b1b4: 0.60

Normalized affinity metrics Bidirectional proposal(Normalized)

b4b1: 0.20

b4b2: 0.05

b4b3: 0.85

b2b1: 0.50

b2b3: 0.45

b2b4: 0.05

b3b1: 0.01

b3b2: 0.45

b3b4: 0.54

b1b2: 0.62

b1b3: 0.00

b1b4: 0.38

Bidirectional proposal of the switch variable (darker, thicker means larger affinity)

1b2b

3b4b

Example of Sampling

Motion stimulusSelf intersection

Example of Sampling

Motion stimulus

A valid grouping

Example of Sampling

Motion stimulus

More valid groupings

Example of Sampling

Motion stimulus

More valid groupings

From Affinity to Marginals


Motion stimulus

From Affinity to Marginals

Marginal distribution of the switch variable (darker, thicker means larger affinity)

Motion stimulus

Greedy algorithm to search for the best grouping based on the marginals

Experiments

• All the results are generated using the same parameter settings

• Running time depends on the number of boundary fragments, varying from ten seconds to a few minutes in MATLAB

Frame 1

Two Moving Bars

Frame 2

Two Moving Bars

Extracted boundary fragments. The green circles are the boundary fragment end points.

Two Moving Bars

Optical flow from Lucas-Kanade algorithm. The flow vectors are only plotted at the edgelets

Two Moving Bars

Estimated motion by our system after grouping

Two Moving Bars

Boundary grouping and illusory boundaries (frame 1). The fragments belonging to the same contour are

plotted in one color.

Two Moving Bars

Boundary grouping and illusory boundaries (frame 2). The fragments belonging to the same contour are

plotted in one color.

Two Moving Bars

Kanizsa Square

Frame 1

Frame 2

Extracted boundary fragments

Optical flow from Lucas-Kanade algorithm

Estimated motion by our system, after grouping

Boundary grouping and illusory boundaries (frame 1)


Dancer

Frame 1

Frame 2


Optical flow from Lucas-Kanade

algorithm

Estimated motion by our system, after

grouping

Lucas-Kanade flow field


Boundary grouping and illusory boundaries

(frame 1)

Boundary grouping and illusory boundaries

(frame 2)

Rotating Chair

Frame 1

Frame 2


Estimated flow field from Brox et al.




Conclusion

• A contour-based representation to estimate motion for textureless objects under occlusion

• Motion ambiguities are preserved and resolved through appropriate contour grouping

• An important component in motion analysis toolbox

• To be combined with the classical motion estimation techniques to analyze complex scenes

Thanks!


Ce Liu William T. Freeman Edward H. Adelson

Computer Science and Artificial Intelligence LaboratoryMassachusetts Institute of Technology

http://people.csail.mit.edu/celiu/contourmotions/

Backup Slides

1b2b

3b4b



1b2b

3b4b

b1b2: 0.39

b1b3: 0.01

b1b4: 0.60

Normalized affinity metrics

b4b1: 0.20

b4b2: 0.05

b4b3: 0.85

b2b1: 0.50

b2b3: 0.45

b2b4: 0.05

b3b1: 0.01

b3b2: 0.45

b3b4: 0.54

b1b2: 0.1750

b1b3: 0.0001

b1b4: 0.1200


Bidirectional proposal


b1b2: 0.39

b1b3: 0.01

b1b4: 0.60

Normalized affinity metrics Bidirectional proposal(Normalized)

b4b1: 0.20

b4b2: 0.05

b4b3: 0.85

b2b1: 0.50

b2b3: 0.45

b2b4: 0.05

b3b1: 0.01

b3b2: 0.45

b3b4: 0.54

b1b2: 0.62

b1b3: 0.00

b1b4: 0.38

Bidirectional proposal of the switch variable (darker, thicker means larger affinity)

1b2b

3b4b

Sampling Grouping (Switch Variables)

Motion stimulus

Lucas-Kanade flow field


Documents

Analysis of Contour Motions Ce Liu William T. Freeman Edward H. Adelson Computer Science and Artificial Intelligence Laboratory Massachusetts Institute