Hidden Markov Model based 2D Shape

Classification

Ninad Thakoor1 and Jean Gao2

1 Electrical Engineering, University of Texas at Arlington, TX-76013, USA

2 Computer Science and Engineering, University of Texas at Arlington, TX-76013, USA

Introduction

Problem of object recognition Shape recognition Shape classification

Shape classification techniques Dynamic programming based Hidden Markov Model (HMM) based

Advantages of HMM Time warping capability Robustness Probabilistic framework

Introduction (cont.)

Limitations of HMM Unable to distinguish between similar shapes No mechanism to select important parts of

shape Does not guarantee minimum classification

error Proposed method deals with these

limitations by designing a weighted likelihood discriminant function and formulates a minimum error training algorithm for it.

Terminology

S, set of HMM states. State of HMM at instance t is denoted by qt.

A, state transition probability distribution. A = {aij}, aij denotes the probability of changing the state from Si to Sj .

B, observation symbol probability distribution. B={bj(o)}, bj(o) gives probability of observing the symbol o in state Sj at instance t.

, initial state distribution. = {i}, i gives probability of HMM being in state Si at instance t = 1.

Cj is jth shape class where j=1,2, … ,M. HMM for Cj can be denoted compactly as

Shape description with HMM

Shape is assumed to be formed by multiple constant curvature segments. These are hidden states of HMM.

Each state is assumed to have Gaussian distribution. Mean of the distribution is the constant curvature of the segment.

Noise and details of the shape are standard deviation of the state distribution.

HMM construction

Preprocessing Filter the shape Normalize the shape length to T Calculate discrete curvature (,i.e., turn

angles) which will be treated as observations for the HMM

Initialization Gaussian mixture model with N clusters

built from unrolled example sequences

HMM construction (cont.)

Training Individual HMM are trained by Baum-Welch

algorithm for varying number of states N

Model selection (,i.e, optimum N) is carried out with Bayesian Information Criterion (BIC)

N is selected to maximize BIC.

Weighted likelihood (WtL) discriminant Motivation

Similar objects can be discriminated by comparing only part of the shapes

No point wise comparison is required for shape classification

Maximum likelihood criterion gives equal importance to all shape points

WtL function weights likelihoods of individual observations such that the ones important for classifications are weighted higher.

WtL discriminant (Cont.)

Log likelihood of the optimal path Q* followed by observation O is given by

Where

A simple weighted likelihood discriminant can be defined as

WtL discriminant (Cont.)

We use the following weighting function which is sum of S Gaussian windows

Parameter pi,j governs the height, i,j controls the position, while si,j determines spread of ith window of jth class.

GPD algorithm

Misclassification measure

Cost function Re-estimation rule

Experimental results

Plane shapes:

Classification accuracies (in %):

Experimental results (cont.)

Discriminant function comparison:

HMM ML HMM WtL

Questions?

Please email your questions to ninad.thakoor@uta.edu OR ninad.thakoor@ieee.org

Copy of the presentation is available at

http://visionlab.uta.edu/~ninad/acivs2005/

THANK YOU!!!!!