Finding the Camera’s Position Tutorial

Finding the Camera’s Position Tutorial

| May 8, 2004

Though it’s a good idea to survey and capture camera information on a shoot, it’s not always possible. Also sometimes we are supplied with stock footage or already shot material and we need to find out where the camera was. Photogrammetry programs can help us with that but before we had them, it was still possible to do so using basic geometry.

There are a few things that are very helpful in visual effects to know about the camera used on a given shot.

First what is the camera position relative to subject?

  • height from ground plane?
  • tilt angle (up or down)?
  • twist (dutch tilt) angle?

Secondly, what lens was used?

  • vertical lens angle?
  • horizontal lens angle?

This information can be really helpful in setting up for adding 3D to a shot or even preparing digital matte paintings.

What do we mean by saying … doing it “old school” ? Well for starters we were kind of loosely including use of computer / photoshop in that ! The process could be done with a photographic print and a drawing board but it’s easier to have a digital image and photoshop!

You’ll need the image to be uncropped – to see the whole image area.

If it came from a film camera, it’s good to get right up to the edges of the exposed piece of film to make sure it isn’t cropped. This will give us the correct aspect ratio of the image.

You must have an object in the scene that has visible lines that are at 90 degrees to one another – such as the building in our shot. Could also be a flagpole or other structure but preferably man made.

OK so you have your image now in photoshop – first thing is to find the “center of vision” which is the geometric center of the frame. This is done by drawing diagonal lines from top left (TL) to bottom right (BR) and top right (TR) to bottom left ( BL). The center of vision is where those lines cross in the exact center of the frame. Now draw horizontal and vertical lines that both pass through that center line – which will give you an image like this.

Next is to find the left and right vanishing points as per the principles of two point perspective. To make this easier, expand your photoshop canvas further out to the left and right – this will give you area to draw outside the image area. Drag down from the Image menu in photoshop to the canvas size, select percent as the measure and enter something like 300. This will expand the canvas around your image with an area made from your background colour which should be ideally a mid tone, not black or white.

Now find and follow perspective lines from your man-made object outside the image frame to where they converge – both left and right.

The left one is called Left Vanishing Point, the right one Right Vanishing Point. Now draw a line between these two points – this is your horizon line. If this is lower than the center of vision, your camera is tilted up. If the horizon is higher, your camera is tilted down. Just how much this tilt is, we will find out soon.

Drop a line down from the Left Vanishing Point (LVP) and Right Vanishing Point (RVP) to below your image, and draw a perfectly horizontal line between them. Lets call this line the VP distance (VPD). Bisect this to find the exact center of that line. Draw an arc from one line to the other from the center point which we will call Vanishing Point Center (VPC).

Draw a line now from the center of vision down to where it meets the Vanishing Point (VP) arc.

The distance between this point and the line VPD is the focal distance, ie. the distance from camera to point of focus. Let’s call this the Focal Distance or FD.

Drop another line from the left edge of frame down to where the FD intersects the VPC arc, and also from the right edge of frame. Label these points LV and RV. Draw another line from FD to LV and from FD to LR. Find the angle between these lines (in this case, 50degrees). This is our horizontal lens angle.

The same process is used to work out the vertical lens angle. Use the same focal distance FD – extended from the H and then draw lines from the left-most point of the FD to both the top and bottom of frame.

In this example, the vertical lens angle is about 40 degrees.

We can now work out the lens tilt angle. Draw a line from the leftmost point of the FD to where the horizon line meets the rightmost FD. The angle between the FD and this line is the angle of camera tilt. We know the camera is tilted up so in our example, it is about 3.2 degrees.

What is the cameras height above ground ? Well, we can see the horizontal horizon line (between vanishing points). We need to find a detail in the shot that we can reasonably guess the scale of. Our horizon crosses about half way up the windows of the red brick building, or just below the windows of the dark grey building. I am guessing that the horizon is about 1.7 meters or 5 feet 3 inches from the ground and assuming that the roadway is fairly level then that is our approximate camera height.

This is kind of verified by counting the number of brick courses – there are about 20 and as they are around 85mm per course, our 1.7 meters is still good.

Submitter: Peter Webb

One Response to “Finding the Camera’s Position Tutorial”

  1. Anonymous

    Hi Peter

    Really interesting information and nice diagrams. I am wondering if you could use this technique to derive a camera’s position relative to an oblique aerial photograph. I am working with a series of images taken from a helicopter looking down on a valley. I have information on focal length and 3D geographic coordinates for ground control points (buildings) but I am trying to derive my camera’s position. Any thoughts- I don’t have clear horizontal and vertical objects in the image because it is taken from an aerial view.




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