How to Create a holographic display and camcorder
In the last part of the series "How to Create a Holographic Display and Camcorder", I talked about what the interest points, descriptors, and features to find the same object in two photos.
In this part of the series, I'll talk about how to extract the depth of the object in two photos by calculating the disparity between the photos.
In order to that, we need to construct a triangle mesh between correspondences.
To construct a mesh, we will use Delaunnay triagulation.
Delaunnay Triagulation
- It minimizes angles of all triangles, while the sigma of triangles is maximized.
The reason for the triangulation is to do a piece wise affine transformation for each triangle mapped from a projective plane A to a projective plane B.
A projective plane A is of a camera projective view at time t,
while a projective plane B is of a camera projective view at time t+1.
(or, at t-1. It really doesn't matter)
Piece wise Affine Transformation
For that, we need at least 3 correspondences. Why?
Because Affine transform support 6 DoF (degrees of freedom).
Why do piece-wise affine transform?
Because a full rectangular affine transform doesn't fit a convex rectangular form.
Why do homography?
What we just did is called Homography.
Ah = 0
With it, we can project a projective plane to any projective plane.
In the last part of the series "How to Create a Holographic Display and Camcorder", I talked about what the interest points, descriptors, and features to find the same object in two photos.
In this part of the series, I'll talk about how to extract the depth of the object in two photos by calculating the disparity between the photos.
In order to that, we need to construct a triangle mesh between correspondences.
To construct a mesh, we will use Delaunnay triagulation.
Delaunnay Triagulation
- It minimizes angles of all triangles, while the sigma of triangles is maximized.
The reason for the triangulation is to do a piece wise affine transformation for each triangle mapped from a projective plane A to a projective plane B.
A projective plane A is of a camera projective view at time t,
while a projective plane B is of a camera projective view at time t+1.
(or, at t-1. It really doesn't matter)
Piece wise Affine Transformation
For that, we need at least 3 correspondences. Why?
Because Affine transform support 6 DoF (degrees of freedom).
Why do piece-wise affine transform?
Because a full rectangular affine transform doesn't fit a convex rectangular form.
Why do homography?
What we just did is called Homography.
Ah = 0
With it, we can project a projective plane to any projective plane.
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