HMM(Hidden Markov Model)을 이용한 Wiimote 제스쳐 인식

http://wiki.jienew.twbbs.org/project:wiimote-gesture-recognition 참조.

Wiimote Gesture Recognition

Projects » Wiimote Gesture Recognition

foldunfold Table of Contents Architecture Wiimote Acceleration Sensor Raw Data from Sensor Calibration Gesture Analysis Quantization Pseudo code Training Hidden Markov Models Training with Multiple Sequence Pseudo Code Real Time Recognition Forward Algorithm Pseudo code Demo & Source Code Wiimote Driver Reference Wiimote HMM library Bibliography

Architecture

Wiimote Acceleration Sensor

Raw Data from Sensor

Ranged from 0 to 255.

• About 130 when no acceleration.
• About 155 when .
• About 105 when .

(: acceleration, : gravity)

Calibration

are raw data when on axes. About 154~156.

are raw data when on axes. About 128~130.

(1)

Then calibrated = 1.0 when on axes.

and are constants built in wiimote. So wiimote dirvers can get calibrated data by above computation.

Gesture Analysis

Quantization

Pseudo code

size_t Quantize(const Acceleration& acc) const{
    double rho = sqrt(acc.x*acc.x+acc.y*acc.y+acc.z*acc.z);
    return (rho>3.0? 3<<3 : rho>2.0? 2<<3 : rho>1.0? 1<<3 :0)
        | (acc.x>acc.y? 1<<2 : 0)
        | (acc.y>acc.z? 1<<1 : 0)
        | (acc.z>acc.x? 1 : 0);
}

Training

Hidden Markov Models

5 state L-to-R or circular both works.

Training with Multiple Sequence

Method modified from Rabiner & Juang^[1]:

(2)

Pseudo Code

// reestimate transition matrix and prob of symbols to states
for(i = 0; i < hmm.N; i++) {
    denominatorA = 0.0;
    denominatorB = 0.0;
    for(curSeq = seqs.begin(); curSeq < seqs.end(); curSeq++){
        double& logProb = curSeq->logProb[&hmm];
        vector< vector<double> >& gamma = curSeq->gamma;
        T = curSeq->o.size();
        denominatorA_partial = 0.0;
        for(t = 0; t < T - 1; t++)
            denominatorA_partial += gamma[t][i];
        denominatorB_partial = denominatorA_partial + gamma[T-1][i];
        denominatorA += denominatorA_partial/exp(logProb);
        denominatorB += denominatorB_partial/exp(logProb);
    }
 
    for(j = 0; j < hmm.N; j++) {
        numeratorA = 0.0;
        for(curSeq = seqs.begin(); curSeq < seqs.end(); curSeq++){
            vector< vector< vector<double> > >& xi = curSeq->xi;
            T = curSeq->o.size();
            numeratorA_partial = 0.0;
            for(t = 0; t < T - 1; t++)
                numeratorA_partial += xi[t][i][j];
            numeratorA += numeratorA_partial/exp(curSeq->logProb[&hmm]);
        }
        hmm.TranProb(i,j) = 0.0001 + 0.9999*numeratorA/denominatorA;
    }
 
    for(k = 0; k < hmm.M; k++) {
        numeratorB = 0.0;
        for(curSeq = seqs.begin(); curSeq < seqs.end(); curSeq++){
            vector< vector<double> >& gamma = curSeq->gamma;
            vector<size_t>& o = curSeq->o;
            T = o.size();
            numeratorB_partial = 0.0;
            for(t = 0; t < T; t++) {
                if(o[t] == k)
                    numeratorB_partial += gamma[t][i];
            }
            numeratorB += numeratorB_partial/exp(curSeq->logProb[&hmm]);
        }
        hmm.ObsProb(i,k) = 0.0001 + 0.9999*numeratorB/denominatorB;
    }
}

Real Time Recognition

Forward Algorithm

Pseudo code

/*
Only do iteration necessary for newly added
symbols of input sequence.
*/
for(t = t_begin; t < T; t++) {
    /*
    Do initialization if forward algorithm haven't been applied to
    the input sequence before.
    */
    if(t == 0){
        logProb = 0.0;
        scale[0] = 0.0;
        alpha[0].resize(hmm.N);
        for(i = 0; i < hmm.N; i++) {
            alpha[0][i] = hmm.pi[i] * hmm.ObsProb(i,o[0]);
            scale[0] += alpha[0][i];
        }
        for(i = 0; i < hmm.N; i++)
            alpha[0][i] /= scale[0];
    }else{
        scale[t] = 0.0;
        alpha[t].resize(hmm.N);
        for(j = 0; j < hmm.N; j++) {
            sum = 0.0;
            for(i = 0; i < hmm.N; i++)
                sum += alpha[t-1][i] * hmm.TranProb(i,j);
 
            alpha[t][j] = sum * hmm.ObsProb(j,o[t]);
            scale[t] += alpha[t][j];
        }
        for(j = 0; j < hmm.N; j++)
            alpha[t][j] /= scale[t];
    }
}
 
/*
Compute sequence probability
*/
for(t = t_begin; t < T; t++){
    logProb += log(scale[t]);
}

Demo & Source Code

WiimoteGR.zip

Wiimote Driver

WiiYourself!

See Building WiiYourself! Library

Reference

Wiimote

WiiBrew

HMM library

UMDHMM

UMDHMM (C library)

C++ HMM Library

A C++ Implementation of Hidden Markov Model

Bibliography

1. Fundamentals of Speech Recognition - by Lawrence Rabiner , Biing-Hwang Juang

2. Pattern Recognition and Machine Learning - by Christopher M. Bishop

3. Hidden Markov Models: Applications in Computer Vision - by Horst Bunke (Author), Terry Caelli (Editor)