Precise distance measurement with stereo camera: experimental results

The method used in the experimental study

The triangulation method is used in distance measurement studies conducted with stereo cameras in the literature. In the triangulation method, the measurement error increases non-linearly depending on the distance. The non-linear increase in the measurement error as the distance increases is due to the pixel-based operation of the triangulation method. The motivation of the study is the non-linear increase in the measurement error due to the triangulation method. With this motivation, it is thought that the triangulation method is a pixel-dependent method and that distance measurement should be freed from pixel dependency. The triangulation method in the literature is given in Fig. 4.

In the triangulation method in the literature, the short side information in the right triangle equation is found with the pixel difference data and used. In this study, the method proposed by Yanik & Turan (2023) as the improved triangulation method was used. In the improved triangulation method, the real measure of the short side information is found. This allows the distance to be found precisely. The improved triangulation method consists of two stages.

In the first stage, the moving camera is moved angularly and thus the target object location in the camera images is matched. This ensures that the pixel difference used in the triangulation method is 0. However, having a pixel difference of 0 does not guarantee that the image acquisition axes of the cameras intersect on the target object. Because pixels cover an area. In other words, they have a width. For this reason, the distance cannot be measured precisely/exactly in a measurement calculation made using only the angle. In the second stage of the improved triangulation method, the moving camera, which has completed the angular movement, is moved linearly on the horizontal axis. With the linear movement, the distance between the lenses that ensure that the image acquisition axes of the cameras coincide on the target object is determined. This distance is also the short side length of the right triangle to be used in the triangulation method. And its precise/exact determination also ensures that the long side value (object distance) is found precisely/exactly. The details of the method are given under the title of performing the measurement process.

Performing the measurement process

A target is determined by the user in the reference camera screen image. Any pixel belonging to the target object is marked by the user with the help of a marker. The marked pixel and this pixel are considered the center, and a 71 × 71 pixel template is created around them. This template is a 3D matrix of 71 × 71 pixels. This matrix is reduced to binary image level and single dimension. The entire screen image belonging to the moving camera is 3D, and the entirety is 4,608 × 3,456 pixels. This image is reduced to binary image level and single dimension. The template is started to be searched in Camera B image screen. The similarities between the found image set and the target image set are compared, and a coefficient is determined. Thanks to this coefficient, the search image (camera B image screen) is reduced to 4,608 × 71 pixels. The target image search is now performed using the newly created search image. The target image is moved with angular movement until the difference between the centre pixels in the found image falls below 0 pixels. The last angle that makes the difference greater than zero will be the B camera angle. Then, the linear movement of the system will start by keeping this angle fixed. Here, the moving camera is first moved away from the reference camera (in the l+ direction), and the camera position that makes the pixel difference between the two images −1 and, therefore, the distance between the moving camera and the fixed camera lenses is found. Then, the moving camera moves to the other side (in the l-direction), and the camera coordinate makes the pixel difference between the two images 1 pixel. Therefore, the distance between the moving camera and the fixed camera lenses is obtained by the electromechanical system. The electromechanical system trigonometrically calculates the distance of the target object to the system by using the average of the two-distance information and the angle information. The system algorithm (Yanik & Turan, 2023) is given in Algorithm 1, and calculation details are given below.

In Eq. (1), the field of view (FoV) of a camera with a viewing angle of α at a distance of Z (m) is calculated.

(1) $$FoV=tan\left({\displaystyle \frac{a}{2}}\right)\ast Z\ast 2$$

In Eq. (2), the number of pixels per meter in a camera with a field of view FoV is calculated. The horizontal resolution of the camera is taken as wp.

(2) $$PPM={\displaystyle \frac{wp}{FoV}}$$

In Eq. (3), the position difference of the target object in images belonging to cameras at different positions on the same axis is calculated in pixels.

(3) $$\mathrm{\Delta }x=PPM\ast l$$

In Eq. (4), the equation used in calculating the distance in a stereo camera rangefinder, where the distance between the lenses is determined as $l_g$and the moving camera angle is β, is given.

(4) $$Z={\displaystyle \frac{l_g}{tan\beta }}$$

If the moving camera angle and the distance between the lenses in Eq. (4) are taken from the electromechanical system with precision, the distance information can also be calculated with that precision.

Eqs. (1), (2), (3), (4) are the equations used in distance information and processing this information.

In stereo camera distance detection studies, pixels must, of course, be present, and when two different cameras with different positions are used, the same object will be displayed in different positions in both cameras. However, by changing the camera’s image acquisition axis angles, the object images can be moved to the same position.

The study focused on this. In our study, fixed (A) and mobile (B) cameras were used at different points. The image taken from camera B was superimposed with the image taken from the reference camera (Camera A). Thus, the difference between the target object positions in the camera screen images can be changed with the angular movement of camera B. If the image acquisition axis angle of camera B and the distance between the lenses can be precisely determined at the moment when this difference is 0, the distance of the object to the cameras can be precisely determined.

The overlapping process of the object images formed on cameras A and B is provided by the angular and linear movements of the mobile camera B. First, the distance between the lenses is kept constant (0.25 m). Camera B is moved angularly, and Δx = 0 is captured. Thus, the angle β is found. Then, the system starts the movement between the lenses by keeping the β angle constant. The distance between the lenses, which is 0.25 m, is increased by 0.001 m and the $l_{+}$ that provides the condition ∆x > 0 on the camera’s image is received by the system. Then, the lenses come back to their initial position of 0.25 m and the second movement between the lenses begins, which is the reduction process of 0.001 m. The value that makes ∆x < 0 becomes the $l_{-}$ value of the system. This situation finds how much distance the width corresponds to linearly between −1 and +1 pixels on the image screens of the cameras. The average value will be the midpoint of these two values. This value is the real distance between the lenses that we will use in the trigonometric calculation. Then, the angle and distance information between the lenses obtained electromechanically are substituted in “Eq. (4)”, and the system calculates the actual distance. The image meter theoretical diagram is given in Fig. 5.

In Fig. 5, the distances of 1 pixel belonging to the target object on the image screens and the distance between these distances are given symbolically. The distance between the two cameras is initially 0.25 m, and the angles of the two cameras are positioned parallel to each other. The user marks the target with a marker from the screen accepted as the reference image. The pixel selected by the user represents a unit belonging to the target object. A 71 × 71 matrix is created with this selected pixel and neighbouring pixels. Then, this 71 × 71 matrix is searched in the target image. This first part, which is outside the vertical axes, is removed from the image. The search is now made in 4,608 × 71 pixels. In the following steps, the search continues by narrowing down the searched image set. In the last stage, the template searched for is found in the image. Thus, the location of the target object is determined on both image screens. In the initial state, the angular movement of the moving (B) camera starts until the difference between the two positions becomes 0 in the image screens belonging to the two cameras that are 0.25 m away from each other. The angle value (β) that makes Δx = 0 will be the angle value of the system. Then the system is moved linearly so that the first value $l_{+}$ that makes Δx > 0 and the first value $l_{-}$ that makes Δx < 0 are calculated.

(5) $$l_g={\displaystyle \frac{\left(l_{+}\right)+\left(l_{-}\right)}{2}.}$$

The $l_g$ value calculated according to Eq. (5) becomes the real l value of the system. Then, the $l_g$ and β values obtained by the system are substituted into Eq. (4) and the real distance is calculated.

The target object sketch and capture of the target object image with the image meter are given in Fig. 6.

In Fig. 6, the distance diagram between the target object and the platform and the images of the target object are given.

Determining the angle of the moving camera

The moving camera, moves angularly until the locations of the target object (the specified template representing the target object) in the two images (reference and moving camera images) coincide. When the target object locations coincide, the angular movement is stopped, and the moving camera angle is recorded. During the determination of the moving camera angle, the distance between the lenses is kept constant at 0.25 m. The angle information in the measurements is given in Table 1. Since the values given in Table 1 are calculated with the fixed distance information between the lenses, the error rates are high.

The distance information calculated with the distance between fixed lenses and the specified angle information is not precise. Because pixels in the image have an area (horizontal and vertical dimensions). When the moving camera takes an image with the specified angle, even if the image acquisition axis coincides with any part of the horizontal edge of the pixel, the object images coincide with the information according to the target object location calculation. However, for precise distance measurement, the image acquisition axes of the moving camera and the fixed camera must coincide at the centre point of the specified pixel on the target object (the specified pixel belonging to the target object). In order to ensure this, the moving camera is precisely moved linearly on the horizontal axis, keeping the specified angle constant. The optimum distance between lenses is determined, and the calculation is made based on these two features.

When the data obtained in the table was evaluated, it was seen that the error rates in the measurements were variable. However, a linear increase was not observed depending on the distance. These measurements were the first stage of the experiment only as a result of the angular movement of the system. After each measurement, these angle values were kept constant, and the distances between the lenses were found again.

For example, In Table 1, the measured β angle value for the target distance at 6.723 m, which was measured by keeping the distance between the lens’s constant (lb = 0.25 m), was 1.74254870 degrees. When the system processed this data, the distance was approximately 8.21m, and the margin of error was 22.23%. When the angle information measured in Table 1 was kept constant for the same distance, and the recalculated distance between the lenses was taken into account, the result would be as in Table 2. In other words, when the β value for the target at 6.723 m was kept constant at 1.74254870, the distance between the lenses was recalculated by moving the moving camera linearly, and the average distance between the lenses was found, $l_g$ = 206.485 mm. When the β calculated in Table 1 and $l_g$ calculated in Table 2 were taken into account again, the real measurement result would be 6.787 m. In this case, our margin of error will decrease from 22.23% to 0.96%. The low margin of error for some measurements in Table 1 was coincidental for the calculated distances. In these measurements, the moving camera image acquisition axis coincided with a region close to the centre point of the target pixel.

As another example, the β value in Table 1 for the distance of 801.955 m was found to be 0.01657540 degrees, and when lb = 0.25 m was taken, the calculated distance was calculated as 864.16886 m. Our margin of error here was 7.76%. If we look at the measurement values in Table 2 for this distance, the $l_g$value measured in the second case was 236.030 mm, and the distance measured by the system was 815.87 m. Our margin of error in this measurement is also 1.74%. The distances between the lenses, which were recalculated by keeping the β angle in Table 1 constant, the measurement results of the electromechanical system and the margins of error are given in Table 2.

When the measurement errors made at the fixed lens distances measured by the electromechanical system are compared, a significant decrease in the margin of error is observed. This is due to the precise acquisition of the real angle and the distance between the lenses required to find the distance information.

When the results from measurements made at different distances are examined, it is seen that the margin of error is different from the systems found in the literature and does not increase with distance.

The results of the image meter measurement device developed in our study were also compared with the results of the laser meter measurement device. In the comparison phase, the results of the Total Station measurement device were used as a reference. The comparison results are given in Table 3.

Table 3 shows the GM, LM and TS measurement values of the same target. According to GM, the largest error was detected at 225,617 m with a 2.22% error rate. The best results were obtained at 16,288 m with 0.30% and 511,367 m with 0.48%.

In addition, the errors mean were determined. The standard deviations and confidence intervals of the determined error means were also determined. Since the errors included negative and positive results, the meaning of the absolute error values was taken into account in terms of significance. However, real values were used in determining the standard deviation and confidence interval. For GM, the error mean was found to be 1.245%, the standard deviation as 1.403 and the confidence interval as −0.73 < μ< 0.63. For LM, the error mean was found to be 1.426%, the standard deviation as 1.782 and the confidence interval as −0.94 < μ < 0.78. When both the errors mean, the standard deviation and the confidence interval were taken into account, GM had better results than LM.

Target object sizes were selected to be visible to the camera. The measurements were made by determining the objects in the natural environment. For this reason, the measurement distances do not have a standard range. And they do not consist of exact values.