Image Morphing. Michael Kazhdan ( /657) HB Ch Feature Based Image Metamorphosis, Beier and Neely 1992

Transcription

1 Image Morphing Michael Kazhdan ( /657) HB Ch Feature Based Image Metamorphosis, Beier and Neely 1992

2 Image Morphing Animate transition between two images H&B Figure 16.9

3 Image Morphing Animate transition between two images Two Components: Cross-dissolving Warping H&B Figure 16.9

4 Cross-Dissolving / Blending Combine images using the α-channel: α of bottom image is 1.0 α of top image varies from 0.0 to 1.0 blend i, j, α = 1 α src(i, j) + α dst(i, j) (0 α 1) src blend dst α = 0.0 α = 0.5 α = 1.0 α

5 Image Warping Deform the source so that it looks like the target src dst α = 0.0 α = 0.5 α = 1.0 α

6 Image Warping Deform the source so that it looks like the target src warp warp warp warp dst α = 0.0 α = 0.5 α = 1.0 α

7 Image Morphing Warp and then cross-disolve src warp warp cross-dissolve warp warp dst α = 0.0 α = 0.5 α = 1.0 α

8 Image Morphing The warping step is the hard one Aim to align features in images How do we specify the mapping for the warp? H&B Figure 16.9

9 Feature-Based Warping Beier & Neeley use pairs of lines to specify warp Given p in destination image, where is p in the source? Mapping p u v p u v Source image Destination image u is a signed fraction v is a signed length (in pixels) Beier & Neeley SIGGRAPH 92

10 Feature-Based Warping How do we calculate u and v? Recall: v 1, v 2 = x 1 x 2 + y 1 y 2 = v 1 v 2 cos θ The (signed) length of the projection of v 1 on the line through v 2, scaled by the length of v 2. The signed length of the projection of v 1 onto the line through v 2 is: v 1, v 2 v 2 v 1 = (x 1, y 1 ) θ v 2 = x 2, y 2

11 Feature-Based Warping How do we calculate u and v? v 1, v 2 is the (signed) length of the projection of v 1 on the line through v 2, scaled by the length of v 2. v = v 1 v 2 p s, t s t s t v s p v

12 Feature-Based Warping How do we calculate u and v? v 1, v 2 is the (signed) length of the projection of v 1 on the line through v 2, scaled by the length of v 2. u = v 1 v 2 p s, t s t s 1 t s t p Remember: u is a fraction u s

13 Feature-Based Warping Beier & Neeley use pairs of lines to specify warp Given p in the destination, where is p in the source? Mapping p u v p u v Source image Destination image u is a fraction v is a length (in pixels) Beier & Neeley SIGGRAPH 92

14 Warping with One Line Pair What happens to the F? Translation!

15 Warping with One Line Pair What happens to the F? Non-uniform scale!

16 Warping with One Line Pair What happens to the F? Rotation!

17 Warping with One Line Pair What happens to the F? What types of (affine) transformations can t be specified?

18 Warping with One Line Pair Can t specify arbitrary scales, skews, mirrors, angular changes X

19 Warping with Multiple Line Pairs Use weighted combination of points defined by each pair of corresponding lines Beier & Neeley, Figure 4

20 Warping with Multiple Line Pairs Use weighted combination of points defined by each pair of corresponding lines L 1 L 2 p 2 Mapping p L 1 L 2 p 1 Source image Destination image

21 Warping with Multiple Line Pairs Use weighted combination of points defined by each pair of corresponding lines L 1 L 2 p Mapping p L 1 L 2 Source image Destination image p is a weighted average

22 Weighting Effect of Each Line Pair Given a set of lines {L 0,, L n }, to weight the contribution of each line pair, Beier & Neeley use: weight i p = length i c a + dist i p b where: length[i] is the length of line L[i] dist[i](p) is the distance from p to L[i] a (small), b [0.5,2.0], c [0.0,1.0] are constants that control the warp

23 Feature-Based Warping How do we calculate dist? v if u [0,1] dist p = ቐ p s if u < 0 p t if u > 1 t v p u s

24 Warping Pseudocode WarpImage(Image in, Image out, L in [ ], L out [ ]) { foreach destination pixel p out : { p in = (0,0) sum = 0 for i = 1 to number of line pairs: q in = p out transformed by (L in [i],l out [i]) p in += q in * weight[i](p out ) sum += weight[i](p out ) end p in /= sum Image out (p out ) = Image in (p in ) } }

25 Morphing Pseudocode Animate( Image 0, L 0 [ ], Image 1, L 1 [ ], Images out [ ] ) { foreach intermediate frame time t: { for i = 1 to number of line pairs: L[i] = line t-th of the way from L 0 [i] to L 1 [i] Warp 0 = WarpImage(Image 0, L 0 [], L[]) Warp 1 = WarpImage(Image 1, L 1 [], L[]) warp } } Images out [t] = (1-t)*Warp 0 + t*warp 1 cross-dissolve

26 Beier & Neeley Example Image 0 Warp 0 Result Image 1 Warp 1

27 Beier & Neeley Example Image 0 Warp 0 Result Image 1 Warp 1

28 Beier & Neeley Example Extensions: Apply to consecutive frames in a video to generate in-between frames (for slow-motion). Automate the calculation of correspondences.

29 Image Processing Quantization Uniform Quantization Random dither Ordered dither Floyd-Steinberg dither Pixel operations Add random noise Add luminance Add contrast Add saturation Filtering Blur Detect edges Warping Scale Rotate Warp Combining Composite Morph