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PARAFAC Analysis of 3-D Tongue Shape

Yanli Zheng, Mark Hasegawa-Johnson

ECE Department

University of Illinois at Urbana-Champaign

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Part I. Background

WHY is the factor analysis of tongue shape meaningful?

1. Speech Motor System

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Part I. Background (cont. Why?)2. Representing Vowel

• Anatomical View Basic Vowel Diagram

• Frequency Domain

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Part I. Background

X-ray images

HOW to analysis the vowels in the context of anatomy? 2-D PARAFAC analysis by Richard Harshman(1977)

Measuring Scheme

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Background (cont. Results of Harshman)

Grids Factors Vowels Loading

Results:Two Factors account for 92% variance.

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Part I. Background Why is 3D Different from 2D?

1. Linear Source-Filter Theory:• Vowel Quality is Determined by Areas• Area Correlated w/Midsagittal Width

2. Distinguish important in Speech Synthesis

3. Clinic Application

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Part II. Algorithms Introduction

1. PARAFAC (Parallel Factor Analysis) xijk: tongue shape measurement for ith data point, jth vowel and kth speaker.

aif: fth factor contribution to ith data point

bjf: loading of phoneme j on fth factor

ckf: loading of speaker k on fth facotor

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Part II. Algorithms Introduction

2. Tucker3 Model(used in the validation of PARAFAC model)

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Part III. 3-D Factor Analysis of MRI-Derived Tongue Shapes

1. Subjects: 5 subjects successfully imaged (three male speaker: m1,m2, m3; and two female speaker: f1,f2).

2. MRI Image Collection

•T1-weighted•GE Signa 1.5T•3mm slices•24 cm FOV•256 x 256 pixels•Coronal, Axial •11-18 Sounds per Subject.•Breath-hold in vowel position for 25 seconds

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Part III. 3-D Factor Analysis of MRI-Derived Tongue Shapes 3. Image Viewing and Segmentation: the CTMRedit GUI and toolbox

• Display series of CT or MR image slices

• Segment ROI manually or automatically

• Interpolate and reconstruct ROI in 3D space

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Part III. 3-D Factor Analysis of MRI-Derived Tongue Shapes 4. PARAFAC Analysis1) 3D-Tongue Shape 2) How to define the

measuring grid?

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x-axis (from right to left)

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Part III. 3-D Factor Analysis of MRI-Derived Tongue Shapes 4. PARAFAC Analysis(cont.)

3) Result: 2 Factors are extracted, with 83.8729 % variance explained

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0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.370.1

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Part III. 3-D Factor Analysis of MRI-Derived Tongue Shapes 4)Validation of the Result

a) Split-half test (example for f1,f2 and m3)

Correlation Coefficients

Grid Contribution 0.9646

Vowel Loading 0.9279

0.28 0.3 0.32 0.34 0.36 0.38 0.4-0.1

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4)Validation of the Result

b) Check the reliability of the solution• Try different start points, check whether all the solutions

converge to the same solution.

c) Core Consistency Testing (by Rasmus Bro,1998)

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1.2Core consistency 99.9955% (yellow target)

Core elements (green should be zero/red non-zero)

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Degenerated result for 3-factor PARAFAC Model

Correlation Coefficients

1&2 2&3 1&3

Grid Contribution -0.5362 0.9632 -0.6045

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Part IV. Conclusion

• 3-D PARAFAC Analysis of Tongue Shape suggests the “Hierarchical Control”

• This research and the follow-up expected research in the MR Microscopy, and Dynamic Imaging aim to : 1. Provide new anatomical information to speech scientists and

speech pathologists

2. Lay the foundation for future research with disordered populations.