Application of Bayesian Network in Human Motion Analysis

Ping Liu & Shizhong Han

What is Bayesian Network?

A Bayesian network is a probabilistic graphical model that represents a set of random variables

and their conditional dependencies via a directed acyclic graph (DAG).

It is a combination of Graph algorithm and Probabilistic theory

In Bayesian Network

The node—random variables

The edge—conditional dependencies

The directed edge & undirected edge

A sample of Bayesian Network

A sample of Bayesian Network

Three nodes in this example: sprinkler, raining and grass wet.

From the edges, we can conclude:

--Rain can lead to grass wet, and also open the sprinkler

--Open the sprinkler can lead to grass wet

So The joint probability function is:

P(G,S,R) = P(G | S,R)P(S | R)P(R)

G = Grass wet, S = Sprinkler, and R = Rain.

A sample of Bayesian Network

Here is a question based on the sample:

“What is the probability that it is raining, given the grass is wet?”

We can solve this problem by using the conditional probability formula:

A sample of Bayesian Network

What does this mean? How should we use the conclusion?

How to apply BN into human motion analysis?

How to apply BN into human motion analysis?-- a more complex example

How to apply BN into human motion analysis?-- a more complex example

H5: Vertical pose of the outermost leg

H6: Horizontal pose of the outermost leg

V8: Vertical position of maximum curvature point of lowerbody convex hull

V9: Lower-body ellipse aspect ratio of major to minor axes

V10: Lower-body ellipse rotation on image plane

V11: Horizontal position of maximum curvature point of lowerbody convex hull

How to apply BN into human motion analysis?-- a more complex example

How we get the dependence probability between each node? How we get the prior information of corresponding node?

The answer is :

Use the information from the “training” data set.

From the training data set, we will get the information about the prior probability of node, the conditional dependence probability between nodes.

How to apply BN into human motion analysis?--Estimation & Inference

We can predict the action based on the observation

-- If Jack holds a baseball bat in his hand, is he playing base ball or swimming?

-- If Jack nods his head, does he mean ”yes” or “no”?

We can estimate the “observation” based on the action

--If Jack is playing base ball, it is probable that he holds a baseball bat in his

hand

-- If Jack agrees with my opinion, it is not likely that he shakes his head

Arm Pose Estimation H3: Vertical pos of the

outermost arm H4: Horizontal pose of

the outermost arm V4: Vertical position of

maximum curvature point of upper-body convex hull.

V5:Torso ellipse aspect ratio of major to minor axes

V6: Torso ellipse rotation on image plan

V7: Horizontal position of maximum curvature point of upper-body convex hull.

Observation for the arm pose estimation. Individual upper body is represented by an ellipse A and B in (a) and the corresponding convex hull in (b). The maximum curvature points C and D in (b) are detected as candidate hand positions

Our goal is to estimate the posterior probability probability P(H3:4|V4:7):

P(H3:4|V4:7)=P(V4:7|H3:4)P(H3:4) The hidden node's states are defined

bellow: H3={'low', 'mid-low', 'mid-high', 'high'} H4={'withdrawn','intermediate','stretching'}

Leg Pose Estimation H5:Vertical pos of the

outermost leg H6:Horizontal pose of the

outermost leg V8:Vertical position of

maximum curvature point of lower-body convex hull.

V9:Lower-body ellipse aspect ratio of major to minor axes

V10:Lower-body ellipse rotation on image plan

V11: Horizontal position of maximum curvature point of lower-body convex hull.

Observation for the leg pose estimation. Individual lower body is represented by an ellipse A and B in (a) and the corresponding convex hull in (b). The maximum curvature points C and D in (b) are detected as candidate leg positions

Our goal is to estimate the posterior probability P(H5:6|V8:11):

P(H5:6|V8:11)=P(V8:11|H5:6)P(H5:6) The hidden node's states are defined bellow: H5={'low', 'mid-low', 'high'} H6={'withdrawn','intermediate','stretching'}

Bayesian network for pose estimation of an interacting person. The BN is composed of 6 hidden nodes H1:6 and 11 visible nodes V1:11 .

H1(the torso pose)= {‘front-view’, ‘left-view’, ‘right-view’, ‘rear-view’}.

V3:the median width of the torso in an image

Our goal is to estimate the posterior probabilities P(H1|H2:6,V3):

P(H1|H2:6,V3 )=P(H2:6 ,V3|H1)P(H1 )

Reference

Recognition of two-person interactions using a hierarchical Bayesian network

--Park, S. and Aggarwal, JK

http://en.wikipedia.org/wiki/Bayesian_network

Graphical Models: Methods for Data Analysis and Mining

-- Borgelt, Christian; Kruse, Rudolf