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## How many degrees of freedom are there in an affine transformation for transforming two dimensional points?

Generally, an affine transformation has **6 degrees** of freedom, warping any image to another location after matrix multiplication pixel by pixel.

## What is 2D projective transformation?

2D projective geometry is the study of properties of the projective plane P2 that are invariant under a group of transformation known as projectivities. That is, **an invertible mapping from points in P2 to points in P2 that maps lines to lines**.

## How many point correspondences are needed to fit a 2D translational model?

Why do they say you need **6 points** to get a 2D affine transform? opencv getAffineTransform only needs 3 data points to find a point in 2D, which is the intuitive number, since 3 points define a plane.

## How many degrees of freedom does a 2D rigid transform have?

Degrees of Freedom in Affine Transformation and Homogeneous Transformation. I understand that a 2D Affine Transformation has 6 DOF and a 2D Homogeneous Transformation has **8 DOF**.

## How many degrees of freedom does a affine transformation has?

An affine transformation has **12 degrees** of freedom: a rotation (3 dof): the matrix U determines scaling directions. an anisotropic scaling (3 dof): matrix S. a rotation (3 dof): matrix R.

## What is similarity transformation?

▫ A similarity transformation is **a composition of a finite number of dilations or rigid motions**. Similarity transformations precisely determine whether two figures have the same shape (i.e., two figures are similar).

## What is perspective transform?

: **the collineation set up in a plane by projecting on it the points of another plane from two different centers of projection**.

## What is the minimum number of 3d 2d point correspondences needed to estimate the projection matrix?

Basically we need only **three points** to estimate the pose of the camera (as you stated each point gives two constraints) however it is not going to give you a unique solution but you’re sure you have a finite number of solutions. So with at least four points you get a unique solution.

## How many points are needed to estimate a projective transform between two images?

Computing a projective transformation

A projective transformation of the (projective) plane is uniquely defined by **four** projected points, unless three of them are collinear.

## What is the minimum number of point correspondences required to compute the Homography of a set of point correspondences?

Homography can be estimated using at least **four point correspondences** [3].