1. Computer Vision II Chapter 20 Accuracy
Presented by: 王夏果 and Dr. Fuh
Digital Camera and Computer Vision Laboratory
Department of Computer Science and Information Engineering
National Taiwan University, Taipei, Taiwan, R.O.C.

2. Introduction Expect of positional inaccuracy due to quantizing error
Estimate false alarm and misdetection rate
Experimental protocols for describing the experiments and analysis
Determine the repeatability and positional accuracy
Assess the performance of a near-perfect vision system
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3. Mensuration Quantizing Error
Position on digital grid has inherent quantizing error due to discreteness
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4. Definition B: coordinate of line’s right endpoint
Δc: spacing between pixel centers
q: uniform random variable, 0≦q≦1
B = Δc ( B* q)
B* = Ceiling( )
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5. DC & CV Lab.
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6. Quantizing Model β*: digital coordinate of the line’s right most pixel
Natural quantizing model:
letting x be a random variable where
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7. Quantizing Model (cont.)
Thus, we can restate the quantizing model:
note that E(x) = q and E(x2) = q
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8. Quantizing Model (cont.)
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9. Automated Position Inspection
In industrial position inspection, an automated mechanism machines a part to given specifications
Ensures machining or part placement is correct
Automated inspector: consists of machine identifying critical object points
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10. Ideal Condition
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11. Real Condition
Actual position x is not known
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12. False Alarm and Misdetection
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13. False Alarm and Misdetection (cont.)
The entire probability model is characterized by five parameters: t, σx, σy, α, β
Problem: how to compute false-alarm and misdetection probabilities
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14. Analysis
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15. Analysis (cont.) ≦ ≦ ≦ ≦
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16. Take a Break
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17. Discussion Failure probability: Relative precision: DC & CV Lab.
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18. Discussion (cont.)
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19. DC & CV Lab.
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20. Discussion (cont.)
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21. DC & CV Lab.
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22. Discussion (cont.)
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23. DC & CV Lab.
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24. Discussion (cont.)
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25. Experiment Protocol
Make experiment repeated and evidence verified by another researcher
Protocol: gives experimental design and data analysis plan
Experiment protocol states:
Quantity (or quantities) to be measured
Accuracy of measurement
Population of scenes/images or artificially generated data
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26. Experiment Protocol (cont.)
Experimental design: how a suitably random, independent, and representative set of images from the specified population is to be sampled, generated, or acquired
Experimental data analysis plan:
How hypothesis meets specified requirement
How observed data analyzed
Detailed enough for another researcher
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27. Experiment Protocol (cont.)
Accuracy criterion: how comparison between true, measured values evaluated
Analysis plan: supported by theoretically developed statistical analysis
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28. Determining the Repeatability of Vision Sensor Measuring Positions
Vision sensors measure position or location in 1D, 2D, 3D
Some number of points are exposed to the sensor, each some number of times
Repeatability is computed in terms of the degree to which the measured position for each point agrees with the corresponding mean measured position for each point
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29. The Model
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30. Derivation
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31. Performance Assessment of Near-Perfect Machines
Machines in recognition and defect inspection required to be nearly flawless
Error rate:
Fraction of time that machine’s judgment incorrect
Contains false detection and misdetection error
False-detection rate (false-alarm rate): unflawed part judged flawed
Misdetection rate: flaw part judged unflawed
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32. Derivation
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33. Balancing the Acceptance Test
If the buyer and seller balance their own self-interests exactly in a middle compromise, the operating chosen for the acceptance test will be the one for which the false-acceptance rate (which the buyer wants to be small) equals the missed-acceptance rate (which the seller wants to be small)
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34. Lot Assessment
In the usual lot inspection approach, a quality control inspector makes a complete inspection on a randomly chosen small sample from each lot
For cost reason, we cannot inspect all of the lot
If more than specified number of defective products fount, the entire lot will be rejected
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35. Summary
Mensuration quantizing error model computes variance due to random error
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