The document analyzes the distribution of errors in carbon estimation along tree stems using hemispherical photography, particularly focusing on loblolly pine. It discusses various measurement techniques, equipment costs, and the impact of errors on accuracy and precision. It also explores the relationship between specific gravity, height, and diameter in carbon content assessment, highlighting the advantages and drawbacks of different photographic methods.

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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