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- 1. Digital Image Processing Digital Image Processing (UST 2007 Fall (UST 2007 Fall) ) (UST 2007 Fall (UST 2007 Fall) ) Sang Chul Ahn asc@imrc.kist.re.kr asc@imrc.kist.re.kr Dithering Dithering
- 2. Dithering Dithering Dithering Dithering Æ Dithering is a technique to simulate the display of colors g q p y that are not in the current color palette of an image Æ Full colors are usually represented with reduced number of colors Æ It accomplishes this by arranging adjacent pixels of different colors into a pattern which simulates colors that are not available Æ O i l l i t t Æ One simple example is to represent a gray scale image with black and white It is called (digital) halftone Æ It is called (digital) halftone image source: http://www.geocities.com/ResearchTriangle/Thinktank/5996/techpaps/introip/manual04.html Dithering Dithering Dithering Dithering Æ Dithering is possible because Æ Dithering is possible because Æ Your eyes will average over an area Æ S i l i Æ Spatial Integration Æ Dithering Methods g Æ Thresholding Æ Patterning Æ Patterning Æ Random dither(Robert’s algorithm) Æ Ordered dither Æ Error diffusion
- 3. Thresholding Thresholding Thresholding Thresholding Æ A simple fixed threshold can be used but Æ A simple fixed threshold can be used, but average intensity for a threshold can give a good(?) result Æ Average thresholding good(?) result Æ Average thresholding image source: http://en.wikipedia.org/wiki/Dither Patterning Patterning Patterning Patterning Æ Patterning is used when the spatial resolution Æ Patterning is used when the spatial resolution of an output is greater than that of a source image image Æ It generates an image that is of higher spatial resolution than the source image resolution than the source image Æ Compute the intensity of each sub-block(or pixel) and index a pattern pixel) and index a pattern Æ Pattern should grow as the intensity gets brighter Æ The 1’s pixels in the previous level pattern should b d i h l l be preserved in the next level
- 4. Patterning Patterning Patterning Patterning Æ Rylander pattern matrix Patterning Patterning Patterning Patterning input image LUT address output image generation pattern LUT
- 5. Random Dithering Random Dithering Random Dithering Random Dithering Æ Add a random amount to each pixel before thresholding p g Æ Typically add uniformly random amount from [-a,a] Æ Pure addition of noise to the image Æ Not good for black and white, but OK for more colors Æ Add a small random color to each pixel before finding the l t l i th t bl closest color in the table Ordered Dithering Ordered Dithering Ordered Dithering Ordered Dithering Æ Break the image into small blocks Æ Define a threshold matrix Æ Use a different threshold for each pixel of the block Æ Compare each pixel to its own threshold Æ The thresholds can be clustered, which looks like a (di it l) h lft i newspaper: (digital) halftoning Æ The thresholds can be “random” which looks better
- 6. Ordered Dithering Ordered Dithering Ordered Dithering Ordered Dithering Æ Bayer Ordered Dither Pattern (popular) y (p p ) Ordered Dithering Ordered Dithering Ordered Dithering Ordered Dithering
- 7. Error Diffusion Error Diffusion Error Diffusion Error Diffusion Æ Start at one corner and work through image pixel by pixel from left to right and from top from left to right and from top to bottom Æ The gray value of every pixel is compared to 50% of Æ The gray value of every pixel is compared to 50% of gray and either set to black or white Æ The error is propagated to neighbor pixels p p g g p Floyd Floyd- -Steinberg Diffusion Steinberg Diffusion Floyd Floyd Steinberg Diffusion Steinberg Diffusion
- 8. Error Diffusion Error Diffusion Error Diffusion Error Diffusion Color Image Color Image Color Image Color Image
- 9. Warping and Morphing Warping and Morphing Warping Warping Warping Warping Æ Æ Image warping Image warping Æ Æ Image warping Image warping Æ rearranging the pixels of a picture Æ Also called “image distortion” “geometric image Æ Also called image distortion , geometric image transformation” Æ We need a function that maps points between Æ We need a function that maps points between corresponding points in the source and destination images destination images Æ called “mapping” or “transformation” Æ Resampling (or interpolation) is required in Æ Resampling (or interpolation) is required in general
- 10. Mapping Mapping Mapping Mapping Æ Simple mappings Æ Affine mapping Æ Projective mapping Æ Bilinear mapping Æ These mappings can be applied to either the whole image or a part of the image Æ Other mappings Æ polynomial transformation Æ arbitrary function Æ Beier-Neely warping (used mostly in morphing) Affine Mapping Affine Mapping Affine Mapping Affine Mapping Æ The form of the affine mapping pp g or c by ax u + + = ⎥ ⎥ ⎤ ⎢ ⎢ ⎡ ⎥ ⎥ ⎤ ⎢ ⎢ ⎡ = ⎥ ⎥ ⎤ ⎢ ⎢ ⎡ y x f e d c b a v u f ey dx v + + = ⎥ ⎥ ⎦ ⎢ ⎢ ⎣ ⎥ ⎥ ⎦ ⎢ ⎢ ⎣ = ⎥ ⎥ ⎦ ⎢ ⎢ ⎣ 1 1 0 0 1 y f e d v Æ The combination of 2D scale, rotation, translation Æ A triangle maps to a triangle, and a rectangle maps to Æ A triangle maps to a triangle, and a rectangle maps to parallelogram Æ The inverse mapping is also an affine mapping pp g pp g Æ Three points can define an affine mapping (6 degree of freedom)
- 11. Projective Mapping Projective Mapping Projective Mapping Projective Mapping Æ It is also called Perspective mapping Æ Mapping form ) /( ) ( i hy gx c by ax u + + + + = ⎥ ⎤ ⎢ ⎡ ⎥ ⎤ ⎢ ⎡ ⎥ ⎤ ⎢ ⎡ x f d c b a qu or ) /( ) ( ) ( ) ( i hy gx f ey dx v y g y + + + + = ⎥ ⎥ ⎥ ⎦ ⎢ ⎢ ⎢ ⎣ ⎥ ⎥ ⎥ ⎦ ⎢ ⎢ ⎢ ⎣ = ⎥ ⎥ ⎥ ⎦ ⎢ ⎢ ⎢ ⎣ 1 y i h g f e d q qv Æ The affine mapping is a special case of the projective mapping when g=h=0 mapping when g h 0 Æ The mapping conserves a line Æ A line is mapped to a line Æ The inverse mapping is also a projective mapping Æ Four points can define a projective mapping (8 degree of freedom) Bilinear Mapping Bilinear Mapping Bilinear Mapping Bilinear Mapping Æ Mapping form h gy fx exy v d cy bx axy u + + + = + + + = Æ A square can be mapped to any shaped rectangles h gy fx exy v + + + = q pp y p g Æ A vertical or horizontal line can be mapped to a line, but other directional line is not mapped to a line Æ The inverse mapping requires the computation of square roots, and it may take long time Æ Four points can define a bilinear mapping (8 degree of freedom)
- 12. Mapping Mapping Mapping Mapping Æ Forward mapping Æ Forward mapping Æ Reverse(backward) mapping
- 17. Bilinear Interpolation Bilinear Interpolation Bilinear Interpolation Bilinear Interpolation Æ A B C D are intensity s ) 1 ( s A B E Æ A,B,C,D are intensity values t s ) 1 ( s − A B E sB A s E + − = ) 1 ( ) 1 ( t G sD C s F sB A s E + − = + ) 1 ( ) 1 ( ) 1 ( t − C D tF E t G + − = ) 1 ( [ ] [ ] sD C s t sB A s t + − + + − − = ) 1 ( ) 1 ( ) 1 ( C D F [ ] [ ] tsD C s t sB t A s t sD C s t sB A s t + − + − + − − = + + + = ) 1 ( ) 1 ( ) 1 )( 1 ( ) 1 ( ) 1 ( ) 1 (
- 20. Morphing Morphing Morphing Morphing Æ Morphing is an abbreviation for Æ Morphing is an abbreviation for Metamorphosis Æ It is a process of creating a smooth transition Æ It is a process of creating a smooth transition between two images Morph Morph = Warp the shape = Warp the shape + Cross + Cross dissolve the colors dissolve the colors + Cross + Cross- -dissolve the colors dissolve the colors Æ There are two kinds of morphing; Image Æ There are two kinds of morphing; Image based one and 3D model based one Morphing Demo Morphing Demo Morphing Demo Morphing Demo Vid Video W k f CMU t d t (htt // 2 d / h/) Work of CMU students (http://www-2.cs.cmu.edu/~ph/)
- 21. Image Morphing Techniques Image Morphing Techniques Image Morphing Techniques Image Morphing Techniques Æ Cross-dissolve Æ Cross dissolve Æ Feature-based morphing (Beier & Neely’s method) Æ Mesh morphing Æ Mesh morphing Æ View morphing Æ Others Cross Cross- -Dissolve Dissolve Cross Cross Dissolve Dissolve Æ Pixel-by-pixel color interpolation Æ Pixel by pixel color interpolation Æ Very primitive Æ Not smooth transitions
- 22. Feature Feature- -based Morphing based Morphing Feature Feature based Morphing based Morphing Feature Feature- -based Morphing(II) based Morphing(II) Feature Feature based Morphing(II) based Morphing(II) Æ Warping with multiple line pairs Æ Warping with multiple line pairs Æ The corresponding point is determined from the weighted average of points which from the weighted average of points which are determined from feature lines
- 23. Feature Feature- -based Morphing(III) based Morphing(III) Feature Feature based Morphing(III) based Morphing(III) Æ Warping with multiple line pairs Æ Warping with multiple line pairs Feature Feature- -based Morphing(IV based Morphing(IV) ) Feature Feature based Morphing(IV based Morphing(IV) ) Æ Weights Æ Weights
- 25. Mesh Morphing Mesh Morphing Mesh Morphing Mesh Morphing Æ Source and target images are meshed Æ Source and target images are meshed Æ The meshes for both images are i t l t d interpolated Æ The intermediate images are cross- Æ The intermediate images are cross dissolved Mesh Morphing Mesh Morphing Mesh Morphing Mesh Morphing
- 26. View Morphing View Morphing View Morphing View Morphing Æ 2-D image morphing does not necessarily Æ 2 D image morphing does not necessarily preserve shape of rigid bodies in intermediate images intermediate images View Morphing View Morphing View Morphing View Morphing Æ Makes use of camera location information to project images onto parallel planes
- 27. View Morphing Algorithm View Morphing Algorithm View Morphing Algorithm View Morphing Algorithm Æ Prewarp Æ Prewarp Æ apply projective transforms to the source images (H -1 and H -1) images (H0 -1 and H1 -1) Æ Morph Æ Use any image morphing technique Æ Postwarp Æ Postwarp Æ Apply Hs to obtain final image View Morphing View Morphing View Morphing View Morphing
- 28. View Morphing View Morphing View Morphing View Morphing View Morphing View Morphing View Morphing View Morphing
- 29. View Morphing View Morphing View Morphing View Morphing Vid Video