What is the difference between the fundamental, essential and homography matrices?

Without any extra assumption on the world scene geometry, you cannot affirm that there is a projective transformation between the two views. This is only true if the scene is planar. A good reference on that topic is the book Multiple View Geometry in Computer Vision by Hartley and Zisserman.

If the world scene is not planar, you should definitely not use the findHomography function. You can use the findFundamentalMat function, which will provide you an estimation of the fundamental matrix F. This matrix describes the epipolar geometry between the two views. You may use F to rectify your images in order to apply stereo algorithms to determine a dense correspondence map.

I assume you are using the expression “perspective transformation” to mean “projective transformation”. To the best of my knowledge, a perspective transformation is a world to image mapping, not an image to image mapping.

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