Hidden Markov Model based 2D Shape Classification

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Hidden Markov Model based 2D Shape Classification

• Ninad Thakoor1 and Jean Gao21 Electrical
  Engineering, University of Texas at Arlington,
  TX-76013, USA2 Computer Science and Engineering,
  University of Texas at Arlington, TX-76013, USA

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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

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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.

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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.
  Bbj(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 j1,2, ,M. HMM for
  Cj can be denoted compactly as

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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.

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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

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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.

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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.

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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

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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.

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GPD algorithm

• Misclassification measure
• Cost function
• Re-estimation rule

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Experimental results

• Plane shapes
• Classification accuracies (in )

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Experimental results (cont.)

• Discriminant function comparison

HMM WtL
HMM ML
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Questions?

• Please email your questions to ninad.thakoor_at_uta.e
  du OR ninad.thakoor_at_ieee.org
• Copy of the presentation is available at
• http//visionlab.uta.edu/ninad/acivs2005/
• THANK YOU!!!!!