Theory of Stereo vision system

Introduction

Stereo vision is a technique aimed at extracting depth information of a scene from two camera images. Difference in

pixel position in two image produces the depth output. There are several other methods to measure depth of a scene,

stereo vision is one among technique.

Left image Right Image

Depth Image

Intended Audience

The document is intended for audience to help in understanding the concept of stereo vision system and estimating

depth range of a system theoretically.

Theory

Below image depicts the working of stereo vision system.

The above image depicts that two cameras capture a particular scene. The scene or image captured by the cameras are

with a difference due to the distance the cameras are placed. The difference in pixel position of identical pixel in the

images are called disparity. Disparity value will be high for nearer distance and will be low for far distance. Depth is

inversely propositional to disparity. Since depth range depends on hardware parameters like focal length, baseline and

pixel size also the equation is formulated as below.

f=Focal length

b=Baseline

d=Disparity value

ps=Pixel size

D=Depth

Focal length

Focal length is the lens parameter of the camera system. It is the point where light rays converges to form a sharp image

to the digital sensor. Focal length is represented in millimetre. Change in focal length of the cameras affects directly the

depth range of stereo vision system, since stereo vision system is with two cameras both the cameras must be with

identical focal length.

Baseline

Baseline refers to the distance between left and right camera. Change in baseline directly affects the depth range of the

stereo vision system. Baseline is represented in centimetre or millimetre.

Pixel size

Pixel size is the size of the individual pixel in an image sensor. Pixel size is represented in micrometre. Since stereo

vision system uses two cameras the pixel size of the image sensor must be identical. As the pixel size decreases the

depth range of the system increases.

Disparity value

Disparity refers to difference in pixel position between two camera images. Assuming left image in stereo vision camera

has a pixel at position (1, 30) and the same pixel is present at position (4, 30) in right image, the disparity value or

difference is (4 – 1) =3. Disparity value is inversely proportional to depth as per the above formula.

Diagrammatic representation of Depth Range

Above image depicts the depth range of a stereo vision system by applying disparity value from maximum to minimum.

Graphical Representation of depth Range

Depth Range of stereo vision system is represented graphically below and the depth at minimum distance alone is

plotted in the second graph.

Disparity value

d=3

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61

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Disparity

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Graph for Depth vs Disparity

0 20 40 60 80

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Short Range Accuracy Graph

Short range in graph or disparity plane at minimum distance are the range where the depth is more accurate in stereo

vision system. Disparity value is plotted in x axis and depth is plotted in y axis.

Manual disparity calculation from stereo image pair

The below scene is captured with a stereo vision system.

In the above image, (303,232) is the pixel in the left image which is the edge of the bottle taken for validating the

disparity value manually and in the same row searching for the identical pixel in the right image we could identify the

pixel at (879,232) position. Since two images are concatenated the pixel value of second image is subtracted from the

value 640(size of the image) i.e. (879-640 =239). So the identical pixel position in the left and right image are in

(303,232) and (239,232).The disparity between pixels of the bottle(object) present in the scene(303-239 =64).

By applying the below value in Depth formula.

Focal length =4.3

Baseline =60 mm

Disparity value =64

Pixel size = 0.006

=(4.3 *60)/(64*0.006) =671.875 mm =0.67 meter =67 centimetre.

From the above result we could conclude that the bottle is kept at a distance of 67 centimetre.

Conclusion

The above article helps the user to refer when estimating the depth range of stereo vision system theoretically before

designing or using a stereo vision system. Manual Disparity evaluation, Graphical and Diagrammatic representation of

depth helps the reader to understand the concept more in detail.

About Author

Prashanth.R working as a senior engineer at e-con systems and working with the customers to choose the right camera

for their end application scenarios. Prashanth holds Bachelors in Instrumentation Engineering worked in domains like

IOT and robotics and can be reached at prashanth.r@e-consystems.com