Find the height of a person caught on a CCTV camera

Question

A CCTV camera was installed on the roadside. A suspected person was caught on the CCTV doing something illegal. The height of the person in CCTV footage/monitor is 4 cm. The CCTV camera was installed at a distance of 17 meters from the suspected person. Can you find the original height of the suspected person?

If you know the original height of another person is 5 feet, and if the person is caught on the same CCTV from the exact same spot, then the height of the person in CCTV footage/monitor is 3.7 cm, then can you find the height of the suspected person using proportion?

score 0 · Accepted Answer · answered Apr 21 '22 at 20:43

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I shall assume that the CCTV thingy is a pinhole camera. The 'law' followed by a pinhole camera can be stated as: $$\frac{h_r}{h_i} = \frac{z_r}{f}$$ where $h_r, h_i$ are the heights of the person in real-world and image resp., $z_r$ is the distance from the camera and $f$ is the focus of the camera. Since the perpetrator was caught at the same distance $z_r$ we have $$\frac{h_{r1}}{h_{i1}} = \frac{z_r}{f} = \frac{h_{r2}}{h_{i2}} = \text{a constant}$$ where 1 and 2 refer to the two people in your question. You can easily solve it from here to get $h_{r2} = 4.625$ ft.

answered Apr 21 '22 at 20:43

cybershiptrooper

753

What is the value of f ? – Sann Apr 22 '22 at 06:44
You don't need $f$ to solve this question, but you can solve for it using $z_r$ = 17m in the first equation @SanniddhaChakrabarti – cybershiptrooper Apr 22 '22 at 17:00
I tried to solve the problem using this equation: (5/3.7) = (h/4). I get the result, h= 5.4054 ft. @cybershiptrooper – Sann Apr 22 '22 at 19:01
@SanniddhaChakrabarti if the 5-foot person is seen as 3.7cm in the image, it is correct. I took it the other way round – cybershiptrooper Apr 23 '22 at 10:13
Thanks @cybershiptrooper – Sann Apr 23 '22 at 14:37

Find the height of a person caught on a CCTV camera

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