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Essential Matrix: Difference between revisions
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(Created page with "An essential matrix, denoted <math>\mathbf{E}</math>, is a <math>3 \times 3</math> matrix relating camera parameters.<br> You can compute the essential matrix based on feature...") |
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Given feature points <math>\mathbf{x}</math> and <math>\mathbf{x'}</math> from two images, | Given feature points <math>\mathbf{x}</math> and <math>\mathbf{x'}</math> from two images, | ||
the essential matrix satisfies the equation <math>\mathbf{x}'^T \mathbf{E} \mathbf{x} = 0</math> | the essential matrix satisfies the equation <math>\mathbf{x}'^T \mathbf{E} \mathbf{x} = 0</math> | ||
==Derivation== | |||
Given feature points <math>\mathbf{x}</math> and <math>\mathbf{x'}</math> from two images, | |||
we can relate them with a rotation <math>\mathbf{R}</math> and a translation <math>\mathbf{t}</math> | |||
such that <math>(\mathbf{R}\mathbf{x} + \mathbf{t}) = x'</math>. | |||
==Properties== | ==Properties== | ||
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==Calculating the Essential Matrix from two images== | ==Calculating the Essential Matrix from two images== | ||
===Planar Images=== | |||
===Spherical Images=== | |||
Here we assume an equirectangular projection. | |||
==Determining rotation <math>R</math> and translation <math>t</math>== | ==Determining rotation <math>\mathbf{R}</math> and translation <math>\mathbf{t}</math>== | ||
==3D points== | ==3D points== | ||