One way to warp one image to another is to implement a piecewise affine warp. Assume that we have a number of points in image 1 and their corresponding points in image 2. We first triangulate each set of points in the same way. We now represent the position x 1 in image 1 as a weighted sum of the three vertices of the triangle a 1 , b 1 , c 1 that it lies in so that x 1 = α a 1 + β b 1 + γ c 1 , where the weights are constrained to be positive with α + β + γ = 1. These weights are known as barycentric coordinates . To find the position in the second image, we then compute the position relative to the three vertices a 2 , b 2 , c 2 of the warped triangle so that x 2 = α a 2 + β b 2 + γ c 2 . How can we compute the weights α, β, γ ? Devise a method to warp the whole image in this manner.

One way to warp one image to another is to implement a piecewise affine warp. Assume that we have a number of points in image 1 and their corresponding points in image XXXXXXXXXXWe first triangulate...

^x
1
⁼

^α
^a
1
⁺

^β
^b
1
⁺

^γ
^c
1
^,

where the weights are constrained to be positive with

α

+

β

+

γ

= 1. These weights are known as

barycentric

coordinates

.

To find the position in the second image, we then compute the position relative to the three vertices

^a
2
^,

^b
2
^,

^c
2
^of

^the

^warped

^triangle

^so

^that

^x
2
⁼

^α
^a
2
⁺

^β
^b
2
⁺

^γ
^c
2
^.

How can we compute the weights

α,

β,

γ

? Devise a method to warp the whole image in this manner.

May 12, 2022