Representing the lens distortion mathematically Now if you were asked to find the height of the right door, which two points would you consider ? Things become even more difficult when you are performing SLAM or making some augmented reality application with cameras having high distortion effect in the image. You can relate figure 3 with figure 1 and say that it is a barrel distortion effect, a type of radial distortion effect. The above figure is an example of distortion effect that a lens can introduce. Note how the edges of the wall and doors are curved due to distortion. Nothing comes for free!įigure 3 : Image showing the distortion effect. The problem is solved? Right? Not so fast. This makes the image brighter.Īwesome! So we have bright and sharp, focused image using a lens. A lens allows larger number of rays to pass through the hole and because of its optical properties it can also focus them on the screen. We replace the pinhole by a lens thus increasing the size of the aperture through which light rays can pass. How do we get a sharp image but at the same time capture more light rays to make the image bright? This leads to a bright image with only a small amount of noise. On the other hand, with a larger aperture, the image sensor receives more photons ( and hence more signal ). So, smaller the aperture of the pinhole camera, more focused is the image but, at the same time, darker and noisier it is. On the other hand, if we make the aperture size small, only a small number of photons hit the image sensor. If we increase the size of the aperture, we know that rays from multiple points of the object would be incident on the same part of the screen creating a blurred image. To generate clear and sharp images the diameter of the aperture (hole) of a pinhole camera should be as small as possible. In this post we will answer the above questions. Have you ever wondered why we attach a lens to our cameras? Does it affect the transformation defining the projection of a 3D points to a corresponding pixel in an image? If yes, how do we model it mathematically? The model of image formation for any real world camera involves a lens. The only time you use a pinhole camera is probably during an eclipse. The model we used was based on the pinhole camera model. In a previous post, we went over the geometry of image formation and learned how a point in 3D gets projected on to the image plane of a camera.
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