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Technical Brief

Complete Sensitivity Analysis in a LiDAR-Camera Calibration Model

[+] Author and Article Information
Angel-Iván García-Moreno, Alfonso Ramírez-Pedraza, Juan B. Hurtado-Ramos, Francisco-Javier Ornelas-Rodríguez

Department of Image Analysis,
Research Center for Applied Science and Advanced Technology (CICATA),
Instituto Politécnico Nacional,
Cerro Blanco 141 Col. Colinas del Cimatario,
Quéretaro 76090, México

Jose-Joel González-Barbosa

Department of Image Analysis,
Research Center for Applied Science and Advanced Technology (CICATA),
Instituto Politécnico Nacional,
Cerro Blanco 141 Col. Colinas del Cimatario,
Quéretaro 76090, México
e-mail: jgonzalezba@ipn.mx

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received June 3, 2015; final manuscript received October 30, 2015; published online December 11, 2015. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 16(1), 014501 (Dec 11, 2015) (10 pages) Paper No: JCISE-15-1184; doi: 10.1115/1.4032026 History: Received June 03, 2015; Revised October 30, 2015

This paper presents a sensitivity analysis in the calibration of two sensors: a laser sensor Velodyne HDL-64E and a panoramic camera Point Grey Ladybug2; both sensors are used for three-dimensional urban reconstruction and were calibrated by two techniques; their results are compared in the sensitivity analysis. The effect of each parameter on the errors propagated in our platform reconstruction was analyzed using the simulated and experimental data sets. To compare the calibration parameters, we implement simulation techniques like Monte Carlo (MC) and Latin hypercube sampling (LHS). The sensitivity index for each parameter was calculated by two methods. The Sobol method, which is based on the analysis of the variance breakdown and the Fourier amplitude sensitivity test (FAST) method, based on Fourier analysis. Measures of variability on the simulated and experimental calibration parameters are shown for the calibration techniques implemented. Results on parameters and factors causing higher uncertainty in the calibration process are presented.

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References

Figures

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Fig. 3

LiDAR Velodyne HDL-64E configuration

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Fig. 2

LiDAR framework L and the multicamera system C1,…,C5. [R,T]WCi represents the world-camera transformation, [R,T]WL represents the world-LiDAR transformation, and [R,T]LCi represents the LiDAR-camera transformation.

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Fig. 1

Sensor platform composed of LiDAR Velodyne HDL-64E (L) Ladybug2 (LB) and GPS. Ladybug2 spherical digital video camera system has six cameras (Ci). [R,T]LCi represents rotation and translation of the LiDAR and six camera frames of the Ladybug2.

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Fig. 4

Tsai's calibration method analyzed by Sobol technique: blue bars are the global sensitivity (Si) and red bars are the total sensitivity (Sitot). Simulated data by MC and LHS with six different distributions. The most relevant parameters are tz and β, i.e., with more sensitive. Parameter identification is indicated in Table 2. (a) Sobol sequence by MC, (b) Halton sequence by MC, (c) normal distribution by MC, (d) normal distribution by LHS, (e) uniform distribution by LHS, and (f) multivariate distribution by LHS. (See online version for color.)

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Fig. 5

Zhang's calibration method analyzed by Sobol technique: blue bars are the global sensitivity (Si) and red bars are the total sensitivity (Sitot). Simulated data by MC and LHS with six different distributions. The most relevant parameters are tz and β, i.e., with more sensitive. Parameter identification is indicated in Table 2. (a) Sobol sequence by MC, (b) Halton sequence by MC, (c) normal distribution by MC, (d) normal distribution by LHS, (e) uniform distribution by LHS, and (f) multivariate distribution by LHS. (See online version for color.)

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Fig. 6

Experimental camera calibration results. Twenty sets of images were taken. For each set, our calibration algorithms were run 100 times. The left side of the graphs displays the average per parameter calibrated (dashed line). The right side shows the variability of these results (chain line). The greater the variability, the greater the sensitivity. The tz − ty and α−β parameters show greater change, similar results to those calculated by the FAST and Sobol techniques.

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Fig. 7

LiDAR sensitivity analysis by Sobol method: blue bars are the global sensitivity (Si) and red bars are the total sensitivity (Sitot). Simulated data by MC and LHS with six different distributions. The most relevant parameters are θ and Δθ. Parameter identification is indicated in Table 3. (a) Sobol sequence by MC, (b) Halton sequence by MC, (c) normal distribution by MC, (d) normal distribution by LHS, (e) uniform distribution by LHS, and (f) multivariate distribution by LHS.

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Fig. 8

Experimental LiDAR results. The left side of the graphs shows the average of each laser to calibrate 100 datasets (dashed line). The right side shows the variability of these results (chain line). The greater the variability, the greater the sensitivity. The Δvosc−Δθ parameters show greater change, similar results to those calculated by FAST and Sobol techniques.

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