Is it possible to convert 2D coordinates of point to 3D form ?

[ramdas]

Hello everyone ,i have captured car positons at differents frames.http://www.imagesup.net/pt-7140205392313.png%5D%5BIMG%5Dhttp://www.imagesup.net/dt-7140205392313.png
Suppose car's(left side car which is coming towards us) centroid is at video frame1 is P(x1,y1) and Q(x2,y2) at video frame4.

1.Is it possible to represent P and Q points into 3D? so that i can calculate correct pixel distance d(PQ)?
Note:u can assume that camera is stationary, placed at height 10 m from ground level .u can also assume any suitable data if u want

 

[HallsofIvy]

Not without additional assumptions. When you convert from 3D to 2D (e.g. taking a photograph) you lose information. You would have to have information not in the photo to recover that lost information.

 

[WWGD]

To add to what HallsofIvy said, if your transformation is linear, it is not invertible, by dimension reasons. And similarly for homeomorphisms (or local homeomorphisms/diffeomorphisms ,which I assume you would want if you want to preserve some properties), not even injective (i.e., 1-1) , continuous maps, by a kind of difficult result called invariance of domain. So you basically cannot go from 3D to 2D without causing distortions. To go from 2D to 3D, you may use an embedding, like, say, (a,b) -->(a,b,0). There are many embeddings, and your choice would depend on the properties you want to preserve.

 

[ramdas]

sir its getting difficult to understand Homographic transformation

To add to what HallsofIvy said, if your transformation is linear, it is not invertible, by dimension reasons. And similarly for homeomorphisms (or local homeomorphisms/diffeomorphisms ,which I assume you would want if you want to preserve some properties), not even injective (i.e., 1-1) , continuous maps, by a kind of difficult result called invariance of domain. So you basically cannot go from 3D to 2D without causing distortions. To go from 2D to 3D, you may use an embedding, like, say, (a,b) -->(a,b,0). There are many embeddings, and your choice would depend on the properties you want to preserve.

sir its getting difficult to understand Homographic transformation and Perspective Mapping.i searched pdf on google,but not getting idea about it.

 

[blue_raver22]

Yes, it is possible to convert 2D coordinates of a point to 3D form. This process is known as 3D coordinate transformation and involves using mathematical equations and data from the camera to determine the 3D coordinates of the point.

To calculate the correct pixel distance between P and Q, we would need additional information such as the focal length of the camera, the camera's field of view, and the resolution of the image. With this information, we can use trigonometry and other mathematical techniques to determine the 3D coordinates of P and Q and then calculate the distance between them in 3D space.

Assuming the camera is stationary and placed at a height of 10 meters from the ground level, we can use this information to help determine the 3D coordinates of P and Q. However, we would still need the other necessary data mentioned above to accurately calculate the distance between them in 3D space.

In conclusion, it is possible to convert 2D coordinates of a point to 3D form and calculate the correct pixel distance between two points, but it requires the use of additional data and mathematical techniques.