Video Distance Measurement Technique Using Least Squares Based Sharpness Cost Function
Abstract
:1. Introduction
2. Materials and Methods
2.1. Method Description
- establishing the dependence of the sharpness, for each position of the lens, on the position of the object of interest. A (n,m) mapping matrix is obtained with n and m being the number of the positions of the focus lens and the number of positions of the object of interest, respectively;
- approximating each dependency by a polynomial function Si and identification of the function coefficients.
- taking a set of images of the object (stack) and calculating the sharpness for each position of the lens, Si_measured;
- calculating the Cost Function as being the square deviations between the measured sharpness and the sharpness obtained by calibration for each of the m possible positions of the object;
- ;
- establishing the index of the minimum of the square deviations, which yield the calculated distance;
- .
2.2. Experimental Setup
3. Results
3.1. Calibration Stage
3.2. Measurement Stage
4. Discussion
5. Conclusions
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Lens’ Position (i) | Polynomial Coefficients | ||||||
---|---|---|---|---|---|---|---|
a0 | a1 | a2 | a3 | a4 | a5 | a6 | |
0 | 1.00242 | −3.41879 × 10−3 | −292321 × 10−4 | 4.05166 × 10−6 | −2.16663 × 10−8 | 5.22761 × 10−11 | −4.74343 × 10−14 |
1 | 0.898721 | 6.36388 × 10−3 | −4.76928 × 10−4 | 5.53824 × 10−6 | −2.7626 × 10−8 | 6.40214 × 10−11 | −5.65194 × 10−14 |
2 | 0.802894 | 1.44673 × 10−2 | −5.99068 × 10−4 | 6.25795 × 10−6 | −2.94182 × 10−8 | 6.53407 × 10−11 | −5.57859 × 10−14 |
3 | 0.704034 | 1.85123 × 10−2 | −5.59871 × 10−4 | 5.0166 × 10−6 | −2.07422 × 10−8 | 4.09188 × 10−11 | −3.11744 × 10−14 |
4 | 0.672847 | 1.47299 × 10−2 | −3.34911 × 10−4 | 2.04935 × 10−6 | −4.44685 × 10−8 | 3.8416 × 10−11 | 6.60522 × 10−15 |
5 | 0.684477 | 6.57673 × 10−3 | −2.49564 × 10−5 | −1.41218 × 10−6 | 1.24868 × 10−8 | −3.79673 × 10−11 | 3.95845 × 10−14 |
6 | 0.707126 | −1.54146 × 10−3 | 2.0778 × 10−4 | −3.24671 × 10−6 | 1.81618 × 10−8 | −4.42197 × 10−11 | 3.99154 × 10−14 |
7 | 0.745179 | −9.34635 × 10−3 | 3.99719 × 10−4 | −4.82945 × 10−6 | 2.47073 × 10−8 | −5.8496 × 10−11 | 5.28991 × 10−14 |
8 | 0.831732 | −2.12925 × 10−2 | 6.80613 × 10−4 | −7.49486 × 10−6 | 3.79759 × 10−8 | −9.16576 × 10−11 | 8.50388 × 10−14 |
9 | 0.706765 | −4.9561 × 10−3 | 1.48598 × 10−4 | −1.44829 × 10−6 | 7.39629 × 10−9 | −1.89172 × 10−11 | 1.82406 × 10−14 |
10 | 0.704984 | −6.61971 × 10−3 | 1.71546 × 10−4 | −1.6138 × 10−6 | 7.1569 × 10−9 | −1.44787 × 10−11 | 1.04764 × 10−14 |
11 | 0.690874 | −4.97126 × 10−3 | 1.07935 × 10−4 | −8.17178 × 10−7 | 2.66015 × 10−9 | −2.95716 × 10−12 | −3.20389 × 10−16 |
12 | 0.687389 | −4.74209 × 10−3 | 9.63782 × 10−5 | −6.6829 × 10−7 | 1.82623 × 10−9 | −8.70554 × 10−13 | −2.20633 × 10−15 |
13 | 0.682394 | −4.54304 × 10−3 | 8.85567 × 10−5 | −5.72535 × 10−7 | 1.29942 × 10−9 | 4.56257 × 10−13 | −3.44156 × 10−15 |
14 | 0.677695 | −4.47291 × 10−3 | 8.77463 × 10−5 | −5.72904 × 10−7 | 1.33118 × 10−9 | 3.31304 × 10−13 | −3.29169 × 10−15 |
15 | 0.674817 | −4.50933 × 10−3 | 8.79664 × 10−5 | −5.6798 × 10−7 | 1.27092 × 10−9 | 5.60098 × 10−13 | −3.57643 × 10−15 |
Distance [mm] | Zuckerman M., et al. 2017 [39] | Yankin C., et al. 2017 [40] | Hahne C., et al. 2014 [41] | Setyawan R.A., et al. 2018 [42] | Megalingam R.K., et al. 2016 [43] | Dragne C., et al. 2022 [44] | Proposed Method |
---|---|---|---|---|---|---|---|
50 | 6% | 2% | |||||
100 | 23 % | 6.3% | 1% | ||||
150 | 0.2% | 2.7% | 10.6% | 0.7% | |||
200 | 7% | 1.5% | 4.7% | 3.5% | 2.72% | 2.5% | |
250 | 7.2% | 5.3% | 1.2% | ||||
300 | 11% | 1.7% | 5.9% | 6.22% | 0.4% | ||
350 | 7% | 1.5% | |||||
400 | 2% | 3.7% | |||||
450 | 1.3% | 2% | 6.7% | 0.3% | |||
500 | 2% | 2.5% | 4% | ||||
550 | 6.1% | 0.3% | |||||
600 | 9% | 2.4% | 7% | 2.1% | 1.7% | ||
650 | 5.3% |
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Serea, E.; Penciuc, M.; Temneanu, M.C.; Donciu, C. Video Distance Measurement Technique Using Least Squares Based Sharpness Cost Function. Mathematics 2022, 10, 3273. https://doi.org/10.3390/math10183273
Serea E, Penciuc M, Temneanu MC, Donciu C. Video Distance Measurement Technique Using Least Squares Based Sharpness Cost Function. Mathematics. 2022; 10(18):3273. https://doi.org/10.3390/math10183273
Chicago/Turabian StyleSerea, Elena, Mihai Penciuc, Marinel Costel Temneanu, and Codrin Donciu. 2022. "Video Distance Measurement Technique Using Least Squares Based Sharpness Cost Function" Mathematics 10, no. 18: 3273. https://doi.org/10.3390/math10183273
APA StyleSerea, E., Penciuc, M., Temneanu, M. C., & Donciu, C. (2022). Video Distance Measurement Technique Using Least Squares Based Sharpness Cost Function. Mathematics, 10(18), 3273. https://doi.org/10.3390/math10183273