Image Warping, Compositing & Morphing

Transcription

1 Image Processing Image Warping, Compositing & Morphing Adam Finkelstein Princeton Uniersit COS 426, Spring 2005 Image Processing Qantization Uniform Qantization Random dither Ordered dither Flod-Steinberg dither Piel operations Add random noise Add lminance Add contrast Add satration Qantization Filtering Uniform Qantization Random dither Ordered dither Flod-Steinberg dither Blr Detect edges Warping Scale Warp Piel operations Add random noise Add lminance Add contrast Add satration Combining Morph Composite Image Warping Filtering Blr Detect edges Moe piels of image Mapping Resampling Warping Scale Warp Warp Combining Morph Composite Sorce image Oeriew Mapping Forward Reerse Mapping Define transformation Describe the destination (,) for eer location (,) in the sorce (or ice-ersa, if inertible) Resampling Point sampling Triangle filter Gassian filter

2 Eample Mappings Eample Mappings Scale b factor: b " degrees: = factor * = factor * = cos" - sin" = sin" + cos" Scale Eample Mappings Other Mappings Shear in X b factor: = + factor * = An fnction of and : = f(,) = f(,) Shear X 1.3 Shear in Y b factor: = = + factor * Shear Y 1.3 Swirl Image Warping Implementation I Rain Forward Mapping Forward mapping: Iterate oer sorce image for (int = 0; < ma; ++) { for (int = 0; < ma; ++) { float = f(,); float = f(,); dst(,) = src(,); (,) Fish-ee f -30 (,) Sorce image

3 Forward Mapping - NOT Forward Mapping - NOT Iterate oer sorce image Man sorce piels can map to same destination piel Iterate oer sorce image Man sorce piels can map to same destination piel Some destination piels ma not be coered Image Warping Implementation II Reerse mapping: for (int = 0; < ma; ++) { for (int = 0; < ma; ++) { float = f -1 (,); float = f -1 (,); dst(,) = src(,); (,) f Sorce image (,) Reerse Mapping Iterate oer destination image Mst resample sorce Ma oersample, bt mch simpler -30 Resampling Ealate sorce image at arbitrar (,) (,) does not sall hae integer coordinates Oeriew Mapping Forward Reerse» Resampling Point sampling Triangle filter Gassian filter (,) Sorce image (,)

4 Point Sampling Take ale at closest piel: int i = trnc(+0.5); int i = trnc(+0.5); This method is simple, dst(,) = src(i,i); bt it cases aliasing Filtering Compte weighted sm of piel neighborhood Weights are normalized ales of kernel fnction Eqialent to conoltion at samples -30 Scale 0.5 k(i,j) represented b gra ale (,) Filtering Compte weighted sm of piel neighborhood Weights are normalized ales of kernel fnction Eqialent to conoltion at samples Triangle Filtering Kernel is triangle fnction s = 0; for (i = -w; i <= w; i++) for (j = -w; j <= w; j++) s += k(i,j)*i(+i, +j); (,) w (,) r w -w w Tent Fnction k( i, j) =1 k(i,j) represented b gra ale Filter Width = 2 Triangle Filtering Kernel is triangle fnction (,) w -w w Tent Fnction Triangle Filtering (with width = 1) Bilinearl interpolate for closest piels a = linear interpolation of src( 1, 2 ) and src( 2, 2 ) b = linear interpolation of src( 1, 1 ) and src( 2, 1 ) dst(,) = linear interpolation of a and b ( 1, 2 ) a (,) ( 2, 2 ) Filter Width = 1 Width of filter affects blrriness Filter Width = 1 ( 1, 1 ) b ( 2, 1 )

5 Gassian Filtering Filtering Methods Comparison Kernel is Gassian fnction Trade-offs Aliasing erss blrring Comptation speed w -w Gassian Fnction (,) Point Bilinear Gassian Filter Width = 2 Image Warping Implementation Image Warping Implementation Reerse mapping: Reerse mapping: for (int = 0; < ma; ++) { for (int = 0; < ma; ++) { float = f-1(,); float = f-1(,); dst(,) = resample_src(,,w); (,) for (int = 0; < ma; ++) { for (int = 0; < ma; ++) { float = f-1(,); float = f-1(,); dst(,) = resample_src(,,w); (,) f (,) Sorce image Eample: Scale f w (,) Sorce image Eample: Scale (src, dst, s, s): (src, dst, theta): float w # ma(1.0/s,1.0/s); for (int = 0; < ma; ++) { for (int = 0; < ma; ++) { float = / s; float = / s; dst(,) = resample_src(,,w); (,) (,) for (int = 0; < ma; ++) { for (int = 0; < ma; ++) { float = *cos(-") - *sin(-"); float = *sin(-") + *cos(-"); dst(,) = resample_src(,,w); (,) (,) = cos" - sin" = sin" + cos" Scale

6 Eample: Fn Image Processing Swirl (src, dst, theta): for (int = 0; < ma; ++) { for (int = 0; < ma; ++) { float = rot(dist(,center)*theta); float = rot(dist(,center)*theta); dst(,) = resample_src(,,w); (,) f (,) Swirl 45 Qantization Filtering Uniform Qantization Random dither Ordered dither Flod-Steinberg dither Blr Detect edges Warping Scale Warp Piel operations Add random noise Add lminance Add contrast Add satration Combining Morph Composite Oeriew: combining images Oeriew: combining images Image morphing Image morphing Specifing correspondences Warping Bling Specifing correspondences Warping Bling Image compositing Image compositing Ble-screen mattes Alpha channel Porter-Dff compositing algebra Ble-screen mattes Alpha channel Porter-Dff compositing algebra Image Morphing Cross-Dissoling Animate transition between two images Bl images with oer operator alpha of bottom image is 1.0 alpha of top image aries from 0.0 to 1.0 bl(i,j) = (1-t) src(i,j) + t dst(i,j) (0 $ t $ 1) src H&B Figre 16.9 t = 0.0 bl t = 0.5 dst t = 1.0 t

7 Image Morphing Combines warping and cross-dissoling src Image Morphing The warping step is the hard one Aim to align featres in images warp warp cross-dissole warp warp t = 0.0 t = 0.5 t = 1.0 dst t How specif mapping for the warp? H&B Figre 16.9 Featre-Based Warping Beier & Neele se pairs of lines to specif warp Gien p in dst image, where is p in sorce image? Warping with One Line Pair What happens to the F? Mapping p p Sorce image is a fraction is a length (in piels) Beier & Neele SIGGRAPH 92 Translation Warping with One Line Pair What happens to the F? Warping with One Line Pair What happens to the F? Scale Rotation

8 Warping with One Line Pair What happens to the F? Warping with Mltiple Line Pairs Use weighted combination of points defined b each pair of corresponding lines In general, similarit transformations What tpes of transformations can t be specified? Beier & Neele, Figre 4 Warping with Mltiple Line Pairs Use weighted combination of points defined b each pair of corresponding lines Weighting Effect of Each Line Pair To weight the contribtion of each line pair, Beier & Neele se: p Mapping p p weight & length[ i] i a dist i # [ ] = $ % + [ ] " b Sorce image p is a weighted aerage Where: length[i] is the length of L[i] dist[i] is the distance from X to L[i] a, b, p are constants that control the warp Warping Psedocode WarpImage(Image, L [ ], L[ ]) begin foreach destination piel p do psm = (0,0) wsm = 0 foreach line L[i] in destination do p [i] = p transformed b (L[i],L [i]) psm = psm + p [i] * weight[i] wsm += weight[i] p = psm / wsm Reslt(p) = Image(p ) Morphing Psedocode GenerateAnimation(Image 0, L 0 [ ], Image 1, L 1 [ ]) begin foreach intermediate frame time t do for i = 1 to nmber of line pairs do L[i] = line t-th of the wa from L 0 [i] to L 1 [i] Warp 0 = WarpImage(Image 0, L 0, L) Warp 1 = WarpImage(Image 1, L 1, L) foreach piel p in FinalImage do Reslt(p) = (1-t) Warp 0 + t Warp 1

9 Beier & Neele Eample Image0 Beier & Neele Eample Warp0 Reslt Image1 Oeriew Image0 Warp0 Reslt Warp1 Image1 Warp1 Een CG folks Can Win an Oscar Image compositing Ble-screen mattes Alpha channel Porter-Dff compositing algebra Image morphing Specifing correspondences Warping Bling Smith Image Compositing Separate an image into elements Rer indepentl Composite together Applications Cel animation Chroma-keing Ble-screen matting Dff Catmll Porter Ble-Screen Matting Composite foregrond and backgrond images Create backgrond image Create foregrond image with ble backgrond Insert non-ble foregrond piels into backgrond Problem: no partial coerage

10 Alpha Channel Compositing with Alpha Encodes piel coerage information % = 0: no coerage (or transparent) % = 1: fll coerage (or opaqe) 0 < % < 1: partial coerage (or semi-transparent) Controls the linear interpolation of foregrond and backgrond piels when elements are composited. %=0 Eample: % = 0.3 %=1 0<%<1 or Partial Coerage 0<%<1 SemiTransparent Semi-Transparent Objects Opaqe Objects Sppose we pt A oer B oer backgrond G A B G How do we combine 2 partiall coered piels? 3 possible colors (0, A, B) 4 regions (0, A, B, AB) AB A How mch of B is blocked b A? A %A B 0 How mch of B shows throgh A (1-%A ) B How mch of G shows throgh both A and B? (1-%A )(1-%B )??? Composition Algebra??? Eample: C = A Oer B 12 reasonable combinations Consider the areas coered: C = %A A + (1-%A) %B B % = %A + (1-%A) %B clear A B A oer B B oer A A in B (1-%A) %B %A B in A A ot B B ot A A atop B B atop A A or b A oer B Porter & Dff `84 Assmption: coerages of A and B are ncorrelated for each piel

11 Image Composition Eample Image Composition Eample [Porter&Dff Compter Graphics 18:3 1984] Image Composition Eample [Porter&Dff Compter Graphics 18:3 1984] Image Processing Qantization Uniform Qantization Random dither Ordered dither Flod-Steinberg dither Piel operations [Porter&Dff Compter Graphics 18:3 1984] Net Time: 3D Rering Misha Kazhdan, CS426, Fall99 Add random noise Add lminance Add contrast Add satration Filtering Blr Detect edges Warping Scale Warp Combining Composite Morph