09/23/10. Image Morphing. Computational Photography Derek Hoiem, University of Illinois. Many slides from Alyosha Efros. Project 2. Class choice awards Jia -bin Huang Guenther Charwat. All 2D Linear Transformations. Linear transformations are combinations of … Scale, Rotation,
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09/23/10
Image Morphing
Computational Photography
Derek Hoiem, University of Illinois
Many slides from Alyosha Efros
Affine transformations are combinations of
Properties of affine transformations:
Will the last coordinate w ever change?
Projective transformations are combos of
Properties of projective transformations:
?
T(x,y)
y
y’
x
x’
f(x,y)
g(x’,y’)
?
T(x,y)
y
y’
x
x’
?
T(x,y)
y
y’
x
x’
9/23/2010
1) Suppose we have two triangles: ABC and A’B’C’. What transformation will map A to A’, B to B’, and C to C’? How can we get the parameters?
B’
B
?
T(x,y)
C’
A
C
A’
Source
Destination
Women in art
Aging
http://www.youtube.com/watch?v=L0GKp-uvjO0
T(x,y)
y
y’
x
x’
f(x,y)
g(x’,y’)
T(x,y)
y
y’
x
x’
f(x,y)
g(x’,y’)
What is the problem with this approach?
T(x,y)
y
y’
x
x’
f(x,y)
g(x’,y’)
Q: what if pixel lands “between” two pixels?
T-1(x,y)
y
y’
x
x
x’
f(x,y)
g(x’,y’)
Q: what if pixel comes from “between” two pixels?
T-1(x,y)
y
y’
x
x
x’
f(x,y)
g(x’,y’)
Q: what if pixel comes from “between” two pixels?
http://en.wikipedia.org/wiki/Bilinear_interpolation
Q
v= Q - P
What’s the average
of P and Q?
P
Extrapolation: t<0 or t>1
P+ 1.5v
= P + 1.5(Q – P)
= -0.5P+ 1.5 Q (t=1.5)
P + 0.5v
= P + 0.5(Q – P)
= 0.5P + 0.5 Q
Linear Interpolation
New point: (1-t)P + tQ
0<t<1
Specify corresponding spline control points
But we want to specify only a few points, not a grid
Specify corresponding points
How do we go from feature points to pixels?
good
bad
If an edge flip improves the triangulation, the first edge is called “illegal”.
p
q
How do we create an intermediate shape at time t?
Slide by Durand and Freeman
Black or White (MJ):
http://www.youtube.com/watch?v=l6GJd8xoe0k
Willow morph: http://www.youtube.com/watch?v=uLUyuWo3pG0