Calibration of Structured Light Area Based on Distortion Shift Vector

Ying Lu; Zemin Wang; Borui Yang

doi:10.3788/LOP202259.0214002

Journals >Laser & Optoelectronics Progress >Volume 59 >Issue 2 >Page 0214002 > Article

Laser & Optoelectronics Progress
Vol. 59, Issue 2, 0214002 (2022)

Calibration of Structured Light Area Based on Distortion Shift Vector

Ying Lu^*, Zemin Wang^**, and Borui Yang

Author Affiliations

College of Electronic Information Engineering, Xi'an Technological University, Xi'an , Shaanxi 712021, China

show less

DOI: 10.3788/LOP202259.0214002 Cite this Article Set citation alerts

Ying Lu, Zemin Wang, Borui Yang. Calibration of Structured Light Area Based on Distortion Shift Vector[J]. Laser & Optoelectronics Progress, 2022, 59(2): 0214002 Copy Citation Text

show less

Abstract

Aiming at the problem of poor global applicability of the object image mapping model in the direct calibration method of structured light measurement system, this paper proposes a subarea calibration method based on the distortion model. First, the projection matrix of camera linear imaging is estimated by using Zhang Zhengyou's plane calibration rule. Then, the matrix as the initial value is taken to solve the camera distortion parameters by ordinary least square. Finally, the image subarea is divided according to the distribution law of distortion shift vector for calibration. The experimental results in the same scene show that compared with the global direct calibration method, the calibration accuracies of the method in X direction and Y direction are increased by 37.40% and 56.20%, respectively, and it has wide applicability in the field of structural light measurement.

Keywords

distortion shift vector finite element laser array laser optics structural light measurement subarea calibration

X = Z \cdot c o t α

，（1）

Y = \frac{Z \cdot t a n θ \cdot m / M}{s i n δ - c o s δ \cdot t a n β \cdot n / N}

，（2）

Z = \frac{B}{c o t α + \frac{c o t δ + t a n β \cdot n / N}{1 - t a n β \cdot c o t δ \cdot n / N}}

，（3）

\{\begin{array}{l} X_{w i} = a_{0} + a_{1} u_{i} + a_{2} v_{i} + a_{3} u_{i}^{2} + a_{4} u_{i} v_{i} + a_{5} v_{i}^{2} + a_{6} u_{i}^{3} + . . . \\ Y_{w i} = b_{0} + b_{1} u_{i} + b_{2} v_{i} + b_{3} u_{i}^{2} + b_{4} u_{i} v_{i} + b_{5} v_{i}^{2} + b_{6} u_{i}^{3} + . . . \\ Z_{w i} = c_{0} + c_{1} u_{i} + c_{2} v_{i} + c_{3} u_{i}^{2} + c_{4} u_{i} v_{i} + c_{5} v_{i}^{2} + c_{6} u_{i}^{3} + . . . \end{array}

，（4）

\sum_{i = 1}^{m} δ_{i}^{2} = {\sum_{i = 1}^{m} [X_{w i} - X_{i}]}^{2}

，（5）

C^{T} C a = C^{T} γ_{x}

，（6）

C = [\begin{matrix} 1 & u_{1} & v_{1} & u_{1} v_{1} & . . . & u_{1}^{n} v_{1}^{q} \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ 1 & u_{m} & v_{m} & u_{m} v_{m} & . . . & u_{m}^{n} v_{m}^{q} \end{matrix}]

，（7）

γ_{x} = {[X_{1}, \dots, X_{m}]}^{T}

，

a = {[a_{1}, \dots, a_{n}]}^{T}

，（8）

m i n s (a) = {\sum_{h = 1}^{r} (j_{h} - \sum_{k = 1}^{t} i_{h k} a_{k})}^{2}

，（9）

\hat{c} = c ({\hat{a}}_{k}) = I' (j - {\hat{a}}_{k})

，（10）

\bar{y} (γ) = y - μ_{A} - γ μ_{A}

，（11）

\hat{C} = \underset{k}{m a x} \{|{\hat{a}}_{k}|\}

，（12）

A = \{k : |{\hat{a}}_{k}| = \hat{C}\}

，（13）

A_{+} = A ⋃ \{\hat{j}\}

，（14）

\{\begin{matrix} u_{u} = \frac{x_{d} + x_{d} (k_{1} r_{d}^{2} + k_{2} r_{d}^{4})}{d x} + u_{0} \\ v_{u} = \frac{y_{d} + y_{d} (k_{1} r_{d}^{2} + k_{2} r_{d}^{4})}{d y} + v_{0} \end{matrix}

，（15）

H = A [\begin{matrix} r_{1} & r_{2} & t \end{matrix}]

，（16）

[\begin{matrix} (u_{u}^{1} - u_{u 0}^{1}) [{(x_{u}^{1})}^{2} + {(y_{u}^{1})}^{2}] & (u_{u}^{1} - u_{u 0}^{1}) \{{[{(x_{u}^{1})}^{2} + {(y_{u}^{1})}^{2}]}^{2}\} \\ (v_{u}^{1} - v_{u 0}^{1}) [{(x_{u}^{1})}^{2} + {(y_{u}^{1})}^{2}] & (v_{u}^{1} - v_{u 0}^{1}) \{{[{(x_{u}^{1})}^{2} + {(y_{u}^{1})}^{2}]}^{2}\} \\ ⋮ & ⋮ \\ (u_{u}^{n} - u_{u 0}^{n}) [{(x_{u}^{n})}^{2} + {(y_{u}^{n})}^{2}] & (u_{u}^{n} - u_{u 0}^{n}) \{{[{(x_{u}^{n})}^{2} + {(y_{u}^{n})}^{2}]}^{2}\} \\ (v_{u}^{n} - v_{u 0}^{n}) [{(x_{u}^{n})}^{2} + {(y_{u}^{n})}^{2}] & (v_{u}^{n} - v_{u 0}^{n}) \{{[{(x_{u}^{n})}^{2} + {(y_{u}^{n})}^{2}]}^{2}\} \end{matrix}] [\begin{matrix} k_{1} \\ k_{2} \end{matrix}] = [\begin{matrix} u_{d}^{1} - u_{u}^{1} \\ v_{d}^{1} - v_{u}^{1} \\ ⋮ \\ u_{d}^{n} - u_{u}^{n} \\ v_{d}^{n} - v_{u}^{n} \end{matrix}]

，（17）

D k = d

，（18）

k = {[\begin{matrix} k_{1} & k_{2} \end{matrix}]}^{T} = {(D^{T} D)}^{- 1} D^{T} d

。（19）

\{\begin{matrix} Δ x = |x_{u} - x_{d}| \\ Δ y = |y_{u} - y_{d}| \end{matrix}

。（20）

d = 0

，（21）

\{\begin{array}{l} R O I X 1 、 R O I X 3, Δ x \geq Δ y \\ R O X I 2, Δ x < Δ y o r Δ x = Δ y = 0 \end{array}

。（22）

\{\begin{array}{l} R O I X 1 、 R O I X 3, Δ y \geq Δ x \\ R O X I 2, Δ y < Δ x o r Δ x = Δ y = 0 \end{array}

。（23）

Ying Lu, Zemin Wang, Borui Yang. Calibration of Structured Light Area Based on Distortion Shift Vector[J]. Laser & Optoelectronics Progress, 2022, 59(2): 0214002

Download Citation

Set citation alerts for the article

Tools

Set citation alerts for the article

Save the article for my favorites

Paper Information