Mathematical relationship to control camera heading

In summary, the conversation discusses the difficulty of finding a mathematical relationship between the direction of one's head and a camera placed at a distance in order to make the camera point towards the same point the head is looking at. Various methods such as reference transformation and using sensors or a mounted camera are suggested, but the exact solution depends on the specifics of the situation.
  • #1
naser1234
1
0
Hi everyone, I want to find a mathematical relationship between my head direction and the direction of a camera placed at a distance. The objective is to make the camera heading to same point where my head is looking at. Both my head and the camera are in the horizontal plane and the motion will be Pan (yaw) motion. Some type of reference transformation has to be applied but I don’t know how to find the relation of my heading verses the camera heading.
 
Physics news on Phys.org
  • #2
If I understand the question, I think the answer is unpleasant: your demands are self-contradictory.

Even if we assume you are always looking "forward" relative to your heads position, that only determines a line -- you could be looking at any particular point along that line, and each one would require a different orientation from the camera.

So, for each orientation, you need some way to decide upon a distance from your head as well. Once you have that, it's straightforward trigonometry.

Alas, whether or not it's feasible to get that distance, or at least a passable approximation, is something that is closely tied to the specifics of your situation. :frown:
 
  • #3
You can't slave your camera that way. It will just look in a parallel direction to your line of sight.

You need to find the intersection point between your line of sight and the first object encountered/nearest object. You will obtain a point. Let's call this point the 'target'.

http://sonyafterdark.webs.com/Diverse/RayTracing.pdf" you compute the target. Sc is the field of view constant.

The camera must look at the target. This might be the way to do it, if you work with angles to describe orientation. Try and see if it's correct.

[tex]\alpha = \arcsin(\frac{target.x - camera.x}{target.z - camera.z})[/tex]

α is the heading you need.

[tex]\beta = \arcsin(\frac{target.y - camera.y}{target.z - camera.z})[/tex]

β is the elevation you need.
 
Last edited by a moderator:
  • #4
Hurkyl said:
If I understand the question, I think the answer is unpleasant: your demands are self-contradictory.

Even if we assume you are always looking "forward" relative to your heads position, that only determines a line -- you could be looking at any particular point along that line, and each one would require a different orientation from the camera.

So, for each orientation, you need some way to decide upon a distance from your head as well. Once you have that, it's straightforward trigonometry.

Alas, whether or not it's feasible to get that distance, or at least a passable approximation, is something that is closely tied to the specifics of your situation. :frown:

If you use sensors to track the direction and dilation of your pupils, you might be able to do it since I believe that pupil dilation relates to focus. I know the eye doctor can tell when you've focused on something and determine your prescription just by watching your pupils.

It might be easier to mount a small low resolution camera to your head and then use digital image processing to match the image from the horizontal displaced camera with the image from the head mounted camera.
 
Last edited:
  • #5


I would first suggest considering the principles of trigonometry and geometry to find a mathematical relationship between your head direction and the camera heading. The horizontal plane can be represented as a two-dimensional coordinate system, with your head position and the camera position as points on the plane. By using the distance between these points and the angle of rotation (pan motion) needed to align the camera heading with your head direction, a trigonometric function such as tangent or sine could be used to calculate the relationship between the two.

Additionally, depending on the specific setup and equipment being used, there may be other factors to consider such as the focal length of the camera lens and its field of view. These could also be incorporated into the mathematical relationship to ensure the camera accurately captures the same point as your head.

In terms of finding the reference transformation, this could involve experimenting with different transformations and measuring the resulting camera heading in relation to your head direction. Data from these experiments could then be used to determine the most accurate and consistent transformation to apply in order to achieve the desired result.

Overall, finding the mathematical relationship between your head direction and the camera heading will likely involve a combination of principles from trigonometry, geometry, and experimentation. It may also be helpful to consult with other scientists or experts in the field of camera control for additional insights and guidance.
 

1. What is the mathematical relationship between camera heading and object tracking?

The mathematical relationship between camera heading and object tracking can be described using geometry, trigonometry, and linear algebra. Essentially, the camera heading is the angle at which the camera is pointed in relation to the object being tracked. This angle can be calculated using the coordinates of the object and the camera, as well as the orientation of the camera.

2. How does changing the camera heading affect the accuracy of object tracking?

Changing the camera heading can significantly affect the accuracy of object tracking. If the camera heading is not aligned with the direction of movement of the object, it can lead to errors in the tracking algorithm. Additionally, if the camera heading changes too quickly, it can cause the object to appear to jump or move erratically in the video feed, making it difficult for the tracking algorithm to accurately track its movement.

3. Can the mathematical relationship between camera heading and object tracking be used to predict the future position of an object?

Yes, the mathematical relationship between camera heading and object tracking can be used to predict the future position of an object. By analyzing the movement of the object and the camera heading, it is possible to calculate the trajectory of the object and predict where it will be in the future. This can be useful in applications such as autonomous vehicles or sports analysis.

4. How does the distance between the camera and the object impact the mathematical relationship to control camera heading?

The distance between the camera and the object can impact the mathematical relationship to control camera heading in several ways. Firstly, the farther the object is from the camera, the smaller the angle between the camera heading and the direction of movement of the object will be. This can make it more difficult for the tracking algorithm to accurately predict the object's movement. Additionally, as the distance increases, the accuracy of the camera's measurements may decrease, leading to errors in the calculation of the camera heading.

5. Are there any limitations to using the mathematical relationship between camera heading and object tracking?

Yes, there are limitations to using the mathematical relationship between camera heading and object tracking. One limitation is that it assumes a stationary camera and a moving object. If the camera is also moving, the calculations become more complex and may require additional information such as the camera's velocity and orientation. Additionally, factors such as lighting conditions, occlusions, and object shape can also affect the accuracy of the tracking algorithm and the resulting mathematical relationship.

Similar threads

  • DIY Projects
Replies
6
Views
3K
Replies
1
Views
905
Replies
3
Views
2K
  • Other Physics Topics
Replies
12
Views
3K
  • Introductory Physics Homework Help
Replies
12
Views
729
Replies
1
Views
2K
Replies
152
Views
4K
  • Mechanical Engineering
Replies
5
Views
1K
  • Sci-Fi Writing and World Building
Replies
1
Views
428
  • Introductory Physics Homework Help
Replies
5
Views
766
Back
Top