This document discusses using hemispherical photography to estimate carbon distribution along tree stems without cutting down trees. It finds that measurement error when using hemispherical photography is: - Precise to within 5 mm below 5 meters height but biased between 10-40 mm at higher sections of the stem. - Distributed along the stem in a Weibull pattern related to height and diameter. - Faster than normal photography techniques, taking around 15 minutes per tree both in the field and office, but less accurate than normal 3D photography which can achieve sub-5mm accuracy.

1. Distribution of errors along stem in
carbon estimation using hemispherical
photography
Bogdan Strimbu
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2. Overview
 Taper and Hemispherical
 Carbon estimation
 Measurements
 Error distribution along stem
 Application – loblolly pine (P. taeda)
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3. Objective
 Impact of measurements error in estimation of
carbon along stem WITHOUT cutting trees
 Accuracy
 Precision
 Expedite
 Equipment / software cost
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4. Carbon distribution
• Depends on:
− Height on the stem
− Distance to pith
• Related to:
− Specific gravity
 Solution: use taper → diameter along stem
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( , )Cerror f height diameter

5. Measurement Techniques
• Close range photogrammetry
1. Wide-angle lenses: angle of view 180°
2. Normal lenses: angle of view ~ 50°
• Cut trees
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6. Ultra wide - angle lenses
 Fisheye lens
o Hemispherical lenses
 Strong distortion
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7. Study area
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8. Field - Normal lenses
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9. Field– hemispherical photo
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10. Field - Hemispherical photo
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11. Data - Ground
• Carbon – estimated thru specific gravity
− Linearly related
• Cookies – 2.5 m
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12. Specific gravity / Carbon content
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0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0 5 10 15 20
SpecificGravity
Height [m]
( , )SG f height diameter
• SG linearly related to height (R2=0.82)
• FOCUS: error in height

13. Data – Photo processing
• Hemispherical photography:
− Equations & Custom software
− Photo enhancement: super-resolution (PhotoAcute)
• Normal photos: Pix4D or Agisoft and Civil3D
− Build 3D model
− Calibrate model
− Measure 3D object
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14. Normal photos
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15. Normal photos - Issues
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16. Hemispherical photos
• PhotoAcute – enhance from 12M to 50M
• Diameter
• Height
• Precision
• Time to measure
• 10 min/tree - field
• 15 min/tree - office
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17. Taper
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18. Taper Assessment
• 3D model
− Precision and Accuracy: ≤ 2 mm any height
• Hemispherical photo
− Precise: ≤ 5 mm bellow 5 m
− Biased: 10 – 40 mm
o Concentrated on higher sections of the stem
• Bias induced by human errors → identify stem
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19. Errors - Hemispherical photo
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20. Error distribution – Hemispherical photo
e ~ Weibull distributed
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( , )SGerror f height e diameter e  

21. Summary
Item Cut Fisheye Normal-3D
Time – Field 30 min 10 min 2 min
Time – Office 0 min 15 min 25 - 120 min
Time - Total 30 min 25 min ½ hour–2 hours
Precision
Height / diam. 1 mm 0.1 mm–10mm 0.1 mm
Accuracy
Height / diam. 0 mm 10 - 40 mm 1 - 5 mm
Price $500+trees
(paperwork)
$1,500
(little training)
$10,000
(significant training)
measurement
error distrib.
None Weibull unsignificant
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Normal-3D
2 min
25 - 120 min
½ hour–2 hours
0.1 mm
1 - 5 mm
$10,000
(significant training)
unsignificant

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