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Defense & Security

Ranging with a small stereoscopic system

Compact stereoscopic systems used for passive target ranging show promise in covert target distance estimation in a realistic field environment.

12 July 2006, SPIE Newsroom. DOI: 10.1117/2.1200606.0293

Laser rangers are widely used today for distance measurement. However, they require more energy than passive systems and are not covert. In some applications, stereoscopic passive vision systems can provide accurate ranging while remaining hidden. Here we summarize the elements of a compact stereoscopic system and examine its performance in a realistic scenario. The investigated parameters are the distance between the two cameras, the kernel size used for correlation between the two images, and the quality of the image measured by the standard deviation of pixel values.

A stereoscopic system operates with two images of the same scene taken by closely spaced cameras on parallel optical axes, as shown in Figure 1. The target at point P appears at different positions, xr and xl in the right and left images respectively, and the distance to the target object is determined using the disparity N = xr - xl. The disparity is found by correlating a kernel of pixels around the target in one image to the same kernel in the other image. The slant range to the target is given by:


Figure 1. Top view of a stereoscopic vision system with two cameras.
 

The effect of kernel size was examined using the D = 12in image pair. Larger kernels, 30 or 40 pixels in width, allowed more accurate correlation and lower range errors than smaller kernels. However, if the kernel is too large, it may require unwarranted computation time and include parts of the image that are at different distances, degrading the results. The choice of kernel size is therefore an important factor that depends on the application.

Table 1 summarizes the results concerned only with target distance and camera spacing. The percent error in range is much lower for D = 12in than D = 6in. Greater camera spacing and closer targets produce greater disparity, which minimizes the effect of a one or two pixel error in the correlation algorithm.

Table 1. Slant Range (R) and its Percent Error by Camera Distance (D) and Actual Range
D=6in D=12in
Object Actual range (ft) Estimated rangeR (ft) Percent error Estimated R (ft) Percent error
1 136 187.84 38% 132.59 2.5%
2 31.06 35.21 13% 31.41 1.1%
3 25.17 26.99 7% 25.47 1.2%
4 20.33 21.66 7% 20.31 0.1%
 

The effect of image quality was found by numerically lowering the standard deviation of pixel values in a neighborhood around the target, until the correlation algorithm would no longer operate. Lowered standard deviation simulates darkness or haze in the image. Table 2 illustrates the effect of image contrast on range estimation error.

Table 2. Percentage error in slant range (R) by standard deviation (STD) in pixel values and actual range.
Actual range (ft) Initial STD Minimum Viable STD Percent Error at Minimum STD
136 44.68 1 18%
31.06 42.52 1 1%
25.17 33.73 12 1%
20.33 63.02 12 0%
 

The initial standard deviation (STD) shows the standard deviation of a pixel neighborhood encompassing the target in the original image. The minimum viable STD is the lowest standard deviation that the correlation algorithm could operate on, and the following column shows the corresponding percentage error. The results showed that the correlation algorithm acts robustly up to a certain level of image degradation, after which it fails completely.

Using the standard expressions for propagated error in results based on the individual uncertainties of all parameters, it is possible to derive the formula for the error in the slant range estimation as,

Figure 2 shows the analytical upper bound for range error when D = 12in (solid line). The measured error for D = 6in is closer to the curve with 2 pixel disparity error (dotted line) than the curve with 1 pixel disparity error (dashed line). For a 12-inch camera spacing, the compact stereoscopic vision system determined the range to an object 100 feet away within an error of six feet.


Figure 2. Theoretical and experimental trends in range error as a function of range. The dashed and solid lines show the curves for propagated error in range with a camera spacing of 6in and 12in respectively, using an error in correlation of 1 pixel. The dotted line shows the curve for propagated error using an error in correlation of 2 pixels, for a camera spacing of 6in. The plus signs show experimental results for a camera spacing of 6in, and the circles show results for a camera spacing of 12in.
 

Results show how camera spacing, kernel size, and image quality affect the error in the estimated range. It is also possible to magnify targets to obtain viable accuracy beyond ranges reported here. For example, a target at 1000 feet magnified 10 times can produce similar results to a target at 100 feet. This study suggests that stereoscopic vision systems are a viable option for covert target distance estimation in a realistic field environment.


Author
Daniel Bankman
National Security Technology, Applied Physics Laboratory
Laurel, MD
Daniel Bankman is a junior at Atholton High School in Columbia, Maryland. He has been an intern at the Johns Hopkins Applied Physics Lab for almost a year, and works mainly in the fields of robotics and computer vision. In addition, He wrote one conference paper on stereoscopic vision and gave a presentation at the Defense and Security Symposium in Orlando, Florida in the spring of 2006.