Camera Models And Fundamental Concepts Used In Geometric Computer Vision
Geometric computer vision is a subfield of computer vision that deals with understanding the 3D structure of the world from 2D images. It is used in a wide range of applications such as robotics, augmented reality, and autonomous vehicles. Camera models are a fundamental concept in geometric computer vision as they are used to model the relationship between 3D points in the world and their corresponding 2D image projections.
Pinhole Camera Model
The pinhole camera model is a simple model that represents the camera as a single point (the pinhole) and a plane (the image plane) where the 2D projection of the world is formed. The pinhole camera model assumes that light travels in straight lines and that the image on the image plane is inverted.
The pinhole camera model can be described mathematically using the camera matrix which is a 3x4 matrix that relates the 3D world points to their corresponding 2D image points. The camera matrix can be decomposed into its intrinsic and extrinsic parameters which represent the camera's internal and external properties respectively.
Fisheye Camera Model
The fisheye camera model is used to model cameras with wide-angle lenses that can capture a wide field of view. The fisheye camera model assumes that light travels in curved paths and that the image on the image plane is distorted.
The fisheye camera model can also be described mathematically using the camera matrix which is a 3x4 matrix that relates the 3D world points to their corresponding 2D image points. However, the camera matrix for the fisheye camera model is much more complex than the pinhole camera model as it involves additional distortion parameters.
Stereo Camera Model
The stereo camera model is used to model multiple cameras that are placed at different positions and orientations to capture the same scene. The stereo camera model is used to derive information about the depth of the scene by analyzing the differences in the image projections from each camera.
The stereo camera model can be described mathematically using the camera matrices for each camera which are 3x4 matrices that relate the 3D world points to their corresponding 2D image points for each camera. The stereo camera model also involves a disparity map which represents the differences in the image projections from each camera at each pixel location.
Epipolar Geometry
Epipolar geometry is a fundamental concept in geometric computer vision that describes the relationship between two cameras that are observing the same scene. Epipolar geometry is used to derive information about the depth of the scene by analyzing the differences in the image projections from each camera.
Epipolar geometry can be described mathematically using the epipolar line which represents the line of intersection of the image planes of the two cameras. The epipolar line can be used to find the corresponding points in the other image by searching along the line of intersection.
Conclusion
Camera models and fundamental concepts used in geometric computer vision are important for understanding the 3D structure of the world from 2D images. The pinhole camera model is a simple model that represents the camera as a single point and a plane while the fisheye camera model is used to model wide-angle lenses. The stereo camera model is used to model multiple cameras and derive information about the depth of the scene while epipolar geometry describes the relationship between two cameras that are observing the same scene.
