CODEWITHSUNDEEP
matrixcamera-calibration
Mehdi Bahar
Mehdi Bahar

Reputation: 41

Singular value decomposition

I started to learn something about camera matrix and its solution method. There are some methods which in many of them I saw using of singular value decomposition of a matrix but I can't understand what is the aim for using that, Anybody can give some hints about that?

Upvotes: 3

Views: 598

Answers (2)

Sai Vinod
Sai Vinod

Reputation: 11

SVD is a method find the directions in an n-dimensional space, which can explain the maximum variance of the data. Observe the below figure, in this image the direction we choose [line between red dots] is not a good one. As the data points don't lie along the chosen direction. That's why the sum of projection errors of data points onto that line is maximum.

Data points projection when an inappropriate direction is used

But look at the second image, in this the direction we choose [line between red dots] is good choice. As it is aligning with the data points distribution. That's why the sum of projection errors of data points onto that line is minimum.

Data points projection when an appropriate direction is used

What SVD do?

SVD decomposes the dataset into three components, you can decide which direction you want to use for your data analysis. It is very helpful for data scientists when they can figure it out by looking at original data distribution given below.

Original Data distribution

When SVD is used, the data is transformed in such a manner that you can find a clear pattern. In the below figure the principal component 1 & 2 are the directions with fewer projection errors.

Plotting the data using those principal components

For further details

Upvotes: 1

Rob
Rob

Reputation: 2656

SVD is used to decompose a matrix into three matrices that multiplied together one way will give the original matrix, and if multiplied in reverse order will give you the inverted matrix.

This is very useful for example when trying to solve a system of equations of n equations with n unknowns.

In the case of the calibration of a camera I would assume the unknowns are the calibration parameters.

I will try and find you a good link that describes both processes.

Upvotes: 3

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