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Essential Matrix: Difference between revisions
→Calculating the Essential Matrix from two images
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{{main | Wikipedia:Eight-point algorithm}} | {{main | Wikipedia:Eight-point algorithm}} | ||
Copied from section 5 of Hartley<ref name="hartley"/>. | Copied from section 5 of Hartley<ref name="hartley"/>. | ||
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your correspondences are very accurate and are not linearly dependent. | your correspondences are very accurate and are not linearly dependent. | ||
For this, see section 5.1 of Hartley<ref name="hartley"/>. | For this, see section 5.1 of Hartley<ref name="hartley"/>. | ||
We assume we have list of correspondences between the two images, <math>\{\mathbf{u}_i\}</math> and <math>\{\mathbf{u}_i'\}</math>.<br> | |||
This can be build by extracting features (e.g. ORB, SIFT, SURF) and creating matches.<br> | |||
Each feature is of the form <math>\mathbf{u}_i = (u, v, 1)</math>. | |||
Here, <math>u \in [0, W]</math> and <math>v \in [0, H]</math> are pixel positions within the image. | |||
Ideally, each set of correspondences should be independently normalized such that the origin of each set is the centroid of all points and the mean distance is <math>\sqrt{2}</math>. | |||
This can be done with a single matrix for each set of points. | |||
For each correspondence <math>\mathbf{u}_i</math> and <math>\mathbf{u}'_i</math>., | For each correspondence <math>\mathbf{u}_i</math> and <math>\mathbf{u}'_i</math>., | ||
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The goal is to minimize <math>\Vert A\mathbf{x} \Vert </math> such that <math>\Vert \mathbf{x} \Vert = 1</math> | The goal is to minimize <math>\Vert A\mathbf{x} \Vert </math> such that <math>\Vert \mathbf{x} \Vert = 1</math> | ||
==Determining rotation <math>\mathbf{R}</math> and translation <math>\mathbf{t}</math>== | ==Determining rotation <math>\mathbf{R}</math> and translation <math>\mathbf{t}</math>== | ||