基于一维查找表的相移结构光实时相位计算

应松霖; 胡丹; 刘凯

doi:10.11884/HPLPB202234.220159

基于一维查找表的相移结构光实时相位计算

doi: 10.11884/HPLPB202234.220159

应松霖^1,,
胡丹^2, ,,
刘凯^1,

1.
四川大学电气工程学院，成都 610065
2.
四川省产品质量监督检验检测院，成都 610199

基金项目: 四川省科技厅重点研发项目(2022YFG0233)、四川大学理科特色方向培育计划项目（2020SCUNL204）

详细信息

作者简介:
应松霖，yingsonlin@163.com

刘　凯，kailiu@scu.edu.cn

通讯作者:
胡　丹，demyd03@163.com

中图分类号: TN247
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- 被引次数: 0
出版历程
- 收稿日期: 2022-05-16
- 修回日期: 2022-05-29
- 录用日期: 2022-06-20
- 网络出版日期: 2022-11-02
- 刊出日期: 2022-11-02

Real time phase calculation of phase shifted structured light based on one-dimensional look-up table

Ying Songlin^1
,,
Hu Dan^{2
, ,},
Liu Kai^1
,

1.
College of Electrical Engineering, Sichuan University, Chengdu 610065, China
2.
Chengdu Institute of Product Quality Inspection, Chengdu 610199, China

摘要

摘要: 针对相移结构光中相位计算环节，提出了一种基于一维查找表的相位实时解码算法。首先根据相位计算公式中的反正切函数性质，得到四个象限之间的相位转化关系。基于得到的转换关系，使用线性函数将第一象限中的所有坐标点映射至某个离散整数区间中，结合该区间与线性函数提前建立相位的一维查找表。在相位计算过程中，首先利用相关信息计算一维查找表的索引，直接获取相位值，然后利用线性插值法与相位转换关系调整该相位值，得到最终的真实相位。通过实验验证了所提算法的有效性，与使用传统相位计算方法相比，本文提出的方法最快可提升3.97倍，使用线性插值后，相位精度可达${10^{ - 8}}$。与传统的多项式逼近算法相比，该算法速度提升了1.29倍；与传统的一维查找表算法相比，该算法速度提升了1.22倍。
- 相移结构光 /
- 相位计算 /
- 反正切函数 /
- 查找表 /
- 实时计算
Abstract: We propose a fast phase decoding algorithm based on a one-dimensional look-up table. Firstly, according to the property of the arctangent function in the phase calculation formula, the phase relationship between the four quadrants is obtained. A linear function is used to map the coordinate points in the first quadrant to a discrete integer interval, and a one-dimensional look-up table of phases is established in advance by combining the interval with the linear function. In the process of phase calculation, firstly, the index of the one-dimensional look-up table is calculated by using relevant information to directly obtain the phase value, and then the phase value is adjusted by the linear interpolation method and phase relationship to obtain the final real phase. Experiments have verified the effectiveness of the proposed algorithm. Compared with the traditional phase calculation method, the proposed method can improve the speed by 3.97 times, 1.29 times compared with the traditional polynomial approximation algorithm, and 1.20 times compared with the traditional one-dimensional look-up table algorithm.
- phase shifted structured light /
- phase calculation /
- arctangent function /
- look-up table /
- real-time calculation

HTML全文

图 1 第一象限空间中的坐标映射至坐标轴上

Figure 1. The coordinates in the first quadrant space are mapped to the coordinate axis

下载: 全尺寸图片幻灯片

图 2 扫描对象标靶

Figure 2. Target of scanning object

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图 3 参数a与参数b的变化对相位精度的影响

Figure 3. Influence of parameter a and parameter b on phase accuracy

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图 4 各算法的相位结果误差

Figure 4. Phase error comparison of the algorithms

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图 5 标靶三维重建结果

Figure 5. Target 3D reconstruction results

下载: 全尺寸图片幻灯片

表 1 各算法计算复杂度

Table 1. Calculation complexity of each algorithm

method	compare	multiplication	division	addition/subtraction	round
Eq(19) in Ref [14]	3	7	1	5	0
L_ut(8)	3	2	2	5	1
L_ut(12)	2	2	1	5	1

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表 2 各算法相位计算速度对比

Table 2. Comparison of phase calculation speed of each algorithm

step		Eq(2)	Eq(16) in Ref [14]	L_ut(8)	L_ut(12)
N=3	speed	189.92 fps	585.80 fps	619.84 fps	754.83 fps
N=3	improvement	−	3.08×	3.26×	3.97×
N=5	speed	166.13 fps	462.63 fps	493.83 fps	588.49 fps
N=5	improvement	−	2.78×	2.97×	3.54×
N=16	speed	50.06 fps	54.08 fps	57.32 fps	59.02 fps
N=16	improvement	−	1.08×	1.15×	1.18×

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表 3 各算法计算反正切值时间

Table 3. Calculation time of arctangent value by each algorithm

method	Eq(2)	Eq(19) in Ref [14]	L_ut(8)	L_ut(12)
time	17.08 ns	3.20 ns	2.75 ns	2.31 ns
improvement	−	5.34×	6.21×	7.39×

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