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Lens distortion practically presents in a real optical imaging system causing nonuniform geometric distortion in the images and gives rise to additional errors in the vision measurement. In this paper, a planar-dimensions vision measurement method is proposed by improving camera calibration, in which the lens distortion is corrected on the pixel plane of image. The method can be divided into three steps: firstly, the feature points, only in the small central region of the image, are used to get a more accurate perspective projection model; secondly, rather than defining a uniform model, the smoothing spline function is used to describe the lens distortion in the measurement region of image, and two correction functions can be obtained by fitting two deviation surfaces; finally, a measurement method for planar dimensions is proposed, in which accurate magnification factor of imaging system can be obtained by using the correction functions. The effectiveness of the method is demonstrated by applying the proposed method to the test of measuring shaft diameter. Experimental data prove that the accurate planar-dimensions measurements can be performed using the proposed method even if images are deformed by lens distortion.

Image measurement has advantages of noncontact, fast speed, and high precision and has applications in industry, medicine, and other fields [

In fact, for real camera lenses, such as a fixed length lens, a zoom lens, or even an expensive high-quality telecentric lens, image distortions unavoidably exist due to lens aberrations and misalignment of optical elements [

In practice, lens distortion can be regarded as a system error since camera and lens are fixed. Therefore, it is not necessary that uniform model of image distortions is used for the camera calibration [

The organization of the paper is as follows: Section

At present, the pinhole projective model was calibrated by mapping 3D scenes to the 2D camera image plane in the literature [

In the experiment, nine patterns of a check board are acquired by the camera with a 25 mm fixed lens, and the image resolution is

The residuals of the proposed and Zhang’s methods in the central region (

Patterns | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|

Proposed method | 3.0 | 4.1 | 4.8 | 4.4 | 4.6 | 3.8 | 3.6 | 3.3 | 3.3 |

Zhang’s method | 5.3 | 5.8 | 6.1 | 5.9 | 6.0 | 5.6 | 5.5 | 5.4 | 5.4 |

Patterns for the calibration.

The feather points in the central region of

The small central region in the image

The local region

Data of Table

In practice, the image region used for the measurement is usually larger than that for the calibration. This may affect the measurement accuracy since the imaging system is not perfect, such as the lens distortion. Now, deviation between corner positions on the board pattern and ones calculated by (

Deviation in

Regarding the correction, the previous papers [

As an example, the deviation in center region of

Deviation surface in coordinate

The deviation surface in

Total deviation distribution in coordinate

Deviation surface in coordinate

The deviation surface in

Total deviation distribution in coordinate

Deviation surface after correction.

A planar-dimensions measurement method is proposed by means of the distortion correction functions and used to measure the shaft diameter as an example in this section. Although the shaft is a 3D object, the measurement of shaft diameter can be considered as a 2D measurement when the optical axis of the imaging lens is perpendicular to center line of shaft approximatively.

It can be seen in Figure

using the proposed calibration method, the central image region of

two edges of the shaft are detected using sub-pixel edge detection method [

two parallel lines are fitted using the corrected points in the plane of pixel, and pixel distance between the two lines can be obtained.

The measurement region of shaft diameter.

A four-segment shaft, whose diameters are known, should be measured using the above measurement procedures firstly, as shown in Figure

Measurement results of segments of shaft (mm).

Segment of shaft | 1 | 2 | 3 | 4 | 5 | 6 |
---|---|---|---|---|---|---|

Known values | 32.441 | 31.467 | 30.459 | 34.422 | 31.589 | 37.725 |

Proposed method | 32.447 | 31.469 | 30.463 | 34.426 | 31.593 | 37.732 |

Without correction | 32.506 | 31.526 | 30.520 | 34.501 | 31.650 | 37.827 |

The imaging of four-segment shaft.

The imaging of three-segment shaft.

The imaging of two-segment shaft.

The imaging of one-segment shaft.

This study develops a machine vision method for high-precision 2D measurement. In the method, a novel algorithm is proposed by improving the calibration model. In this way, the lens distortion can be corrected on the pixel plane before measuring, and accurate magnification factor of imaging system can be obtained. Experimental results indicate that the proposed method possesses a precision of 0.005 mm for measuring shaft diameter about 40 mm.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The work described in this paper is partially supported by the National Nature Science Foundation of China under Grant nos. 61201084 and 11226335.