general homography matrix such that . The cameras then transform as and likewise with still get us the same image points. Derivation of the fundamental matrix using coplanarity condition The fundamental matrix can also be derived using the coplanarity condition. For satellite images The fundamental matrix expresses the epipolar geometry in stereo images. The epipolar geometry in images taken with perspective cameras appears as straight lines. However, in satellite images, the image is formed during the sensor movement along its orbit (pushbroom sensor). Therefore, there are multiple projection centers for one image scene and the epipolar line is formed as an epipolar curve. However, in special conditions such as small image tiles, the satellite images could be rectified using the fundamental matrix. Properties The fundamental matrix is of rank 2. Its kernel defines the epipole. See also Epipolar geometry Essential matrix Trifocal tensor Eight-point algorithm Notes References Toolboxes fundest is a GPL C/C++ library for robust, non-linear (based on the Levenberg–Marquardt algorithm) fundamental matrix estimation from matched point pairs and various objective functions (Manolis Lourakis). Structure and Motion Toolkit in MATLAB (Philip H. S. Torr) Fundamental Matrix Estimation Toolbox (Joaquim Salvi) The Epipolar Geometry Toolbox (EGT) External links Epipolar Geometry and the Fundamental Matrix (chapter from Hartley & Zisserman) Determining the epipolar geometry and its uncertainty: A review (Zhengyou Zhang) Visualization of epipolar geometry (originally by Sylvain Bougnoux of INRIA Robotvis, requires Java) The Fundamental Matrix Song Video demonstrating laws of epipolar geometry. Geometry in computer vision