Image Parsing:Unifying Segmentation, Detection and Recognition

Z. Tu, X. Chen, A. Yuille and S. Zhu

Presented by:

Khurram Hassan Shafique

Related Work

Z. Tu and S.C. Zhu, “Image segmentation by Data Driven Markov Chain Monte Carlo,” PAMI, vol. 24, no. 5, 2002.

Z. Tu and S. C. Zhu, “Parsing images into regions and curve processes,” ECCV, June 2002.

S. C. Zhu and A. L. Yuille, “Region Competition,” PAMI, vol. 18, no. 9, 1996

Organization of Presentation

Problem Definition

Pre-requisites Probabilistic Inference

Monte Carlo Simulation

Markov Chain Monte Carlo Simulation

Unifying Segmentation, Detection and Recognition.

Problem Definition

Given an image,

Locate and identify text (if any) in the image.

Locate and identify faces (if any) in the image.

Partition the image into generic regions that best describe the image.

Probabilistic Inference

Obtaining representation of the parameters from the dataset is known as inference.

Maximum Likelihood Principle

Choose the world parameters that maximize the probability of

the measurement observed.

In the general case, we are choosing

(where the maximum is only over the world parameters

because the measurements are known)

arg max P(measurements|parameters)

Bayes Theorem APABPBPBAPBAP ||

BP

APABPBAP

|| Bayes Theorem

tsmeasuremenP

parametersPparameterstsmeasuremenPtsmeasuremenparametersP

||

Posterior DataPriors

Maximum a posteriori (MAP) inference

tsmeasuremenparametersPparameters

|maxarg

Choose the world parameters that maximize the conditional probability

of the parameters, conditioned on the measurements taking the observed

values.

Monte Carlo SimulationIn Monte Carlo simulation, the random selection process is repeated many times to create multiple scenarios. Each time a value is randomly selected, it forms one possible scenario and solution to the problem. Together, these scenarios give a range of possible solutions, some of which are more probable and some less probable

Monte Carlo Simulation

Randomly select a location within the rectangle

If it is within the blue area, record this instance a hit

Generate a new location and repeat 10,000 times

Monte Carlo Simulation

What is the area of blue region?

Monte Carlo Simulation

Given a set of random variables X={Xi} taking on values {xi},

The expectation of a function a(X) can be approximated by

Monte Carlo Simulation

Monte Carlo Simulation

Use I.I.D generated by distribution f(x), then we have

Monte Carlo Standard Error

Problems

It is not possible to obtain a sample of independent points from the distribution defined by f(x).

The probability density defined by f(x) may not only be concentrated in a tiny volume of the parameter space but also be distriuted across this space in a complex pattern.

Other Techniques

Rejection Sampling

Importance Sampling

Methods ased on finding the modes.

Markov Chain Monte Carlo Sampling (MCMC)

Markov Chains

A Markov chain is a series of random variables, X(0), X(1), … in which the influence of the values of X(0), …, X(n) on the distribution of X(n+1) is mediated entirely by the value of X(n). More formally,

where

Markov Chains

A Markov chain can e specified by giving the

Initial probabilities p0(x) of various states x and

The transition probabilities Tn(x,x’)for one state x’ to follow another state x at time n.

Using the transition probabilities, one can find the probability of state x occurring at time n+1.

Markov Chains (Basic Definitions)

If the transition probabilities do not depend on the time, the Markov chain is said to be homogeneous or stationary.

A distribution (x) is invariant with respect to the Markov chain with transition probabilities Tn(x,x’), if for all n,

Markov Chains(Basic Definitions)

Detailed Balance:

this implies that is an invariant distribution

Markov Chains(Basic Definitions)

Ergodic Markov Chains:

Markov chain is ergodic if the probabilities at time n, pn(x) converge to this invariant distribution as n, regardless of the choice of initial probabilities. The invariant distribution is also called equilibrium distribution.

Markov Chain Monte Carlo

Markov Chain Monte Carlo

MCMC: Metropolis Algorithm

Proposal: Select a candidate state, x*, picked at random from a proposal distribution.

Metropolis Acceptance: Accpet this candidate state with probability A(x,x*); otherwise reject it and retain the current state.