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Quantizing Error Analysis in Computer Vision Systems

Explore the impact of quantizing errors on positional accuracy in computer vision systems, with a focus on false alarms, misdetection rates, and automated position inspection.

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Quantizing Error Analysis in Computer Vision Systems

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  1. Computer Vision IIChapter 20 Accuracy Presented by: 王夏果 and Dr. Fuh r94922103@ntu.edu.tw 0937384214 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 DC & CV Lab. NTU CSIE

  3. Mensuration Quantizing Error • Position on digital grid has inherent quantizing error due to discreteness DC & CV Lab. NTU CSIE

  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( ) DC & CV Lab. NTU CSIE

  5. DC & CV Lab. NTU CSIE

  6. Quantizing Model • β*: digital coordinate of the line’s right most pixel • Natural quantizing model: letting x be a random variable where DC & CV Lab. NTU CSIE

  7. Quantizing Model (cont.) • Thus, we can restate the quantizing model: note that E(x) = q and E(x2) = q DC & CV Lab. NTU CSIE

  8. Quantizing Model (cont.) DC & CV Lab. NTU CSIE

  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 DC & CV Lab. NTU CSIE

  10. Ideal Condition DC & CV Lab. NTU CSIE

  11. Real Condition • Actual position x is not known DC & CV Lab. NTU CSIE

  12. False Alarm and Misdetection DC & CV Lab. NTU CSIE

  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 DC & CV Lab. NTU CSIE

  14. Analysis DC & CV Lab. NTU CSIE

  15. Analysis (cont.) ≦ ≦ ≦ ≦ DC & CV Lab. NTU CSIE

  16. Take a Break DC & CV Lab. NTU CSIE

  17. Discussion • Failure probability: • Relative precision: DC & CV Lab. NTU CSIE

  18. Discussion (cont.) DC & CV Lab. NTU CSIE

  19. DC & CV Lab. NTU CSIE

  20. Discussion (cont.) DC & CV Lab. NTU CSIE

  21. DC & CV Lab. NTU CSIE

  22. Discussion (cont.) DC & CV Lab. NTU CSIE

  23. DC & CV Lab. NTU CSIE

  24. Discussion (cont.) DC & CV Lab. NTU CSIE

  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 DC & CV Lab. NTU CSIE

  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 DC & CV Lab. NTU CSIE

  27. Experiment Protocol (cont.) • Accuracy criterion: how comparison between true, measured values evaluated • Analysis plan: supported by theoretically developed statistical analysis DC & CV Lab. NTU CSIE

  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 DC & CV Lab. NTU CSIE

  29. The Model DC & CV Lab. NTU CSIE

  30. Derivation DC & CV Lab. NTU CSIE

  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 DC & CV Lab. NTU CSIE

  32. Derivation DC & CV Lab. NTU CSIE

  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) DC & CV Lab. NTU CSIE

  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 DC & CV Lab. NTU CSIE

  35. Summary • Mensuration quantizing error model computes variance due to random error DC & CV Lab. NTU CSIE

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