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### Factor Analysis of MRI-Derived Tongue Shapes

Mark Hasegawa-Johnson

ECE Department and Beckman Institute

University of Illinois at Urbana-Champaign

Background

The vowel sounds of English are classified in two dimensions: “high/low” and “front/back.”

u

High

i

e

o

ae

a

Low

Front

Back

Background

Tongue is composed of about 9 muscles (4 intrinsic, 5 extrinsic)

Superior

Longitudinalis

Palatoglossus

Styloglossus

Verticalis

Superior Phar.

Constrictor

Transversus

Genioglossus

Inferior

Longitudinalis

Hyoglossus

Factor Analysis of X-Ray ImagesHarshman, Ladefoged, &Goldstein, 1977

Factor Analysis of X-Ray ImagesHarshman, Ladefoged, &Goldstein, 1977

Factor Analysis of X-Ray ImagesHarshman, Ladefoged, &Goldstein, 1977

Factor Analysis of X-Ray ImagesHarshman, Ladefoged, &Goldstein, 1977

Finding: Two factors account for 92% of variance.

Can Three-Dimensional TongueShape be Explained Using ShapeFactors?

Hypothesis 1

3D tongue shape during speech = weighted sum of 2-3 factors.

Hypothesis 2

Shape of the factors t1(i), t2(i) is speaker-dependent. (??)

Why is 3D Different from 2D?

Linear Source-Filter Theory:

- Vowel Quality is Determined by Areas

- Area Correlated w/Midsagittal Width

Do Shape Factors Exist in 3D?

- If inter-speaker shape similarity is governed by desire for acoustic similarity, and...
- If acoustic similarity depends on cross-sectional area, not cross-sectional shape...
- Then

Variation in 3D Shape May Not Have

a Shape Factor Basis

Factor Analysis of MRI-Derived Tongue Shapes: Methodology

1. Recruit Subjects

2. Collect MRI Images

3. Segment the Images

4. Interpolate ROI to Create 3D Tongue Shapes for Each Vowel

5. Speaker-Dependent Factor Analysis

6. Speaker-Independent Factor Analysis

Subject Recruitment:

- Ten subjects recruited; five successfully imaged (3 male, 2 female).
- Subjects were college undergrads and grads with no metal fillings and no claustrophobia.
- Subjects were trained to sustain vowel sounds with little variation.
- Human subjects approval: both UCLA and Cedars-Sinai Medical Center.

MRI Image Collection

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

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

Calibration: Segmentation of Phantom (J. Cha)

- Test tubes of 3 sizes
- Radius estimated from manual segmentation has an absolute error of
- typical case: 0.1mm
- worst case: 0.4mm

Calibration: Articulatory Speech Synthesis (J. Cha)

- /a,i,u/ synthesized using Maeda articulatory synthesizer
- F1-F4 errors:
- worst case: +/- 30%
- mean error: +2.8%
- std dev: 19.5%

Reconstruction of ROI

- Interpolate between image slices to create 3D object.

Speaker Normalization: VT Length,

Inter-Molar Width (S. Pizza)

Speaker-Dependent Factor Analysis

- 12 tongue shapes from one speaker:
- Each tongue shape modeled as a 25 point x 40 point rubber sheet.
- Principal Components Analysis:
- 11 Non-Zero Factors (12 vowels - 1 mean vector = 11 degrees of freedom).
- 2 Factors: 78% of variance
- 3 Factors: 88% of variance

“Excuses:” Why Didn’t it Work?

- Tongue Length changes from /ao/ to /iy/.
- Human Transcriber Error?
- Interpolation to Form 3D Image Causes Error
- Spline & Sinc interpolation: very large errors
- Linear interpolation: smaller errors, but still too large.

New Approaches: ---- Avoid Interpolation

General Method: Avoid interpolation by modeling the measured data directly.

- J. Huang: Control factor shape using an a priori probability distribution.
- Y. Zheng: Limit factor to the set of polynomial surfaces.

Polynomial Smoothing (Y. Zheng)

- Polynomial Surface Modeling
- Tongue shape = polynomial surface
- 4D surface model enforces smoothness constraints.
- Hybrid Polynomial/Factor model
- Midsagittal tongue shape is as predicted by Harshman et al.
- 3D shape = (midsag. shape)X(polynomial)

Conclusions

- X-ray analysis suggests hierarchical motor control, but...
- “Hierarchical control” might reflect structure of the acoustic space.
- MRI analysis does not find hierarchical control (yet), but...
- Negative finding might be result of methodological weakness.

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