The Fundamental Matrix Song

最新推荐文章于 2024-04-18 22:18:19 发布

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最新推荐文章于 2024-04-18 22:18:19 发布

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分类专栏：三维视觉文章标签： Fundamental Matrix

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本文深入探讨了立体几何中基础矩阵的概念，该矩阵在3D视觉和计算机视觉中有重要作用。基础矩阵是一个3x3的方阵，拥有7个自由度，秩为2，其在两幅图像中对应点之间的极线约束起到关键作用。文章还提到了基础矩阵的估计方法，包括使用奇异值分解(SVD)从一组样本点中求解，并强调了共面点集的退化性以及估计过程中保持秩约束的重要性。

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The fundamental matrix
Used in stereo geometry
A matrix with nine entries
It's square with size 3 by 3
Has seven degrees of freedom
It has a rank deficiency
It's only of rank two
Call the matrix F and you'll see...

Two points that correspond
Column vectors called x and x-prime
x-prime transpose times F times x
Equals zero every time

The epipolar constraint
Involves epipolar lines
Postmultiplying F by x
Results in vector l-prime
It's the epipolar line
In the other view passing through x-prime
A three component vector
Of homogeneous design

The left and right nullspaces of F
Are the epipoles e-prime and e
All of the epipolar lines
Should pass through these

Here's a linear estimation example:
Take a set of 8 point samples
Construct a matrix, take the SVD
And the elements of F are in the last column of V

If you try to estimate
F with a coplanar set of points
Your sample set will be degenerate
And will not bring you joy

When doing the estimation
If you don't perform rank deprivation
Your epipolar lines
And the epipoles will not coincide

But if your scene has three views
The trifocal tensor is what you'd use
Constraints from the third view act like glue
That can't be determined from just two views

视频来自Youtube: http://www.youtube.com/watch?v=DgGV3l82NTk

附带RANSAC Song链接http://danielwedge.com/ransac/