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Today: Image Morphing• Introduction to image morphing

• Basic idea• Beier-Neely morphing

• Photography session for A4 portraits • Only ONE tutorial this week• Photos to be taken during the tutorial• Location: RW 143 (TA:Fransisco Estrada)• You will only have 2 chances to get your picture taken:

in this week’s tutorial, or in next week’s tutorial

Image Morphing

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Extensions: View MorphingA combination of view synthesis & image morphing

Image MorphingA combination of generalized image warping with a cross-dissolve between pixels

Morphing involves two steps:• Pre-warp the two images• Cross-dissolve their colors

Source 1Source 1Image 1 Warp 2Warp 1 Image 2

Source 1Source 1

Morph

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Cross-dissolveA weighted combination of two images, pixel-by-pixel

Combination controlled by a single interpolation parameter t:

Image 1

Cross-Dissolving Two Images

Image 2

D(r,c) = I1(r,c) + t*[I2(r,c)-I1(r,c)]

Why warp first?In order to align features that appear in both images (e.g., eyes, mouth, hair, etc). Without such an alignment, we would get a “double-image” effect!!

Image pre-warpingRe-position all pixels in the source images to avoid the “double-image” effect as much as possible

Pre-warping implemented using Backward Mapping Algorithm

Image Pre-WarpingSource 1Source 1Image 1 Warp 1 No pre-warping Pre-warping Warp 2 Image 2

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Image MorphingA combination of generalized image warping with a cross-dissolve between pixels

Morphing involves two steps:• Pre-warp the two images• Cross-dissolve their colors

Source 1Source 1Source 1 Warp 2Warp 1 Source 2

Morph

Goal:Define a warp that moves every pixel in Image 1to its “corresponding” pixel in Image 2

Warping & cross-dissolve controlled by the same parameter t• For t near 0, pixels in morph are near their “original” position

in Image 1• For t near 1, they are near their “original” position in Image 2

Warping Between Two Images

Source 1Source 1Image 1 Image 2

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Image MorphingBoth morphing steps specified by same parameter t

• Warp the two images according to t• Cross-dissolve their colors according to t

Source 1Source 1Source 1 Warp 2Warp 1 Source 2

Morphing videos generated by creating a sequence of images, defined by a sequence of t-values (e.g., 0,0.1,0.2,…,0.9,1)

Morphing ExampleImage 1

Image 2

Intermediate Images

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Basic Question: How is the Morph Defined?Image 1 Intermediate Image

Today: Image Morphing• Introduction to image morphing

• Basic idea• Beier-Neely morphing

• Photography session for A4 portraits • Only ONE tutorial this week• Photos to be taken during the tutorial• Location: RW 143 (TA:Fransisco Estrada)• You will only have 2 chances to get your picture taken:

in this week’s tutorial, or in next week’s tutorial

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Backward mapping algorithm:

for r = rmin to rmaxfor c = cmin to cmax

u = U(r,c,t)v = V(r,c,t)copy pixel at source (u,v)to destination (r,c)

Morphing w/ Backward Mapping

(u,v)

To completely determine the morph we need to define the functions U(r,c,t), V(r,c,t)

(r,c)

SourceImage 1

IntermediateImage t

• A single parameter t defines two warps, one applied to image 1 and one to image 2

Intermediate Morphs

Image 1

Image 2

pixel (r,c) in Warp 1 and pixel(r,c) in Warp 2 are in exact

correspondence

(r,c)

(r,c)

Warp 1

Warp 2

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• Warped image computed using backward mappingalgorithm

• Image warp specified by interactively drawing lines in thetwo source images (Field Morphing)

Beier-Neely Field Morphing Algorithm (1992)

• Use corresponding lines in 2 images to define a re-positioning for every pixel according to parameter t

• Morphed image for t=0: Source image 1• Morphed image for t=1: Source image 2• Morphed image for 0<t<1: Intermediate morph

Beier-Neely’s Field Morphing Technique

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Coordinate Map:A function that takes pixel (r,c) in Image 2 & movesit to pixel (r’,c’) in Image 1

Two cases:1. Coordinate map defined by a single line pair2. Coordinate map defined by multiple line pairs

Coordinate Maps in Field Morphing

Steps: 1. Compute position of pixel X in Image 2 relative to

destination line(r,c) → (u,v)

2. Compute (r’,c’) coordinates of pixel X’ in Image 1 whose position relative to source line is (u,v)(u,v) → (r’,c’)

Coordinate Maps from One Line Pair

destination line

source line

cc’

r’ r

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Position of pixel X in Image 2 relative to destination line(r,c) → (u,v)

given by

Computing Pixel Positions Relative to a Line

(r,c)2PQ

)PQ).(PX(u

−

−−=

(rP ,cP)

(rQ,cQ)

2PQ

2PQ )cc()rr( −+−

)cc)(cc()rr)(rr( PQPPQP −−+−−

PQ)PQ(larPerpendicu).PX(v

−−−=

)rr,cc( PQPQ +−−

Examples

Pixel Coordinates Relative to a Line

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Field warping algorithm (single -line case)For each pixel (r,c) in the destination image

find the corresponding (u,v) coordinates of the pixelfind the (r’,c’) in source image for that (u,v)color at destination pixel (r,c) = color at source pixel (r’,c’)

Coordinate Maps from One Line Pair

cc’

r’ r

Field warping algorithm (multiple-line case)1. Apply single-line field warping algorithm to each line

separately, to get N source pixel positions (ri’,ci’) for every destination pixel (N= # of line pairs)

2. Compute source position (r’,c’) as weighted average of positions (ri’,ci’)

Coordinate Maps from Multiple Line Pairs

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Computing the Averaging Weights

(r,c)bp

distalength

weight

+=

2PQ

2PQ )cc()rr( −+−

1u0 if )v(abs <<0u if P from c)(r, of distance <1u if Q from c)(r, of distance >

controls influence of linefor points near it

For each pixel (r,c) in destination image

DSUM=(0,0)

weightsum = 0

for each line (Pi,Qi)

calculate (ui,vi)based on Pi,Qi

calculate (ri’,ci’)based on u,v & Pi’,Qi’

calculate displacementDi=Xi’-Xi for this line

calculate weightfor line (Pi,Qi)

DSUM += Di*weightweightsum += weight

(r’,c’) = (r,c) + DSUM/weightsum

color at destination pixel (r,c) = color at source pixel (r’,c’)

Beier-Neely Field Warping Algorithm

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Warping Example

Morphing Example

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Morphing Dynamic Scenes