1. Tree-Structured Method for LUT Inverse Halftoning IEEE Transactions on Image Processing June 2002

2. Outline Introduction –Halftoning –Inverse halftoning Tree-Structured Method Result

3. Introduction Halftone –A technique to convert a continuous-toe image into a binary image

4. Introduction Halftone –Simple Thresholding –Ordered Dither

5. Introduciton Halftone –Error Diffusion

6. Introduction Inverse Halftone –Reconstructing a continuous-tone image from its halftoned version

7. Introduction Inverse Halftone –Low pass filter –LUT(Look Up Table) Depending upon the distribution of pixels in the template of the pixel

8. Tree-Structured LUT(TLUT) LUT: –Require large memory space 16-pix template: 2^16 = 64Kbytes TLUT: –Take advantage of nonexistent patterns and reduce storage –Compressed version of LUT

9. TLUT Small template will be used to get a crude inverse halftone Refined by adaptively adding pixels to the template Adaptive pixels will be placed in a tree structure

10. Tree Structure Each tree node is either split further or a leaf –Nodes are split to refine contone value –Leaf stores a contone value

11. Initial template … 32 個 (0,1) (1,1)

12. Designing the tree structure 1. the initial template of size a should be chosen from a neighborhood of the current pixel –Generate initial 2^a tree leaves

13. Template Selection –Assume that we have P images which have sizes x1*y1, x2*y2, …, xp*yp –Continuous tone images Di(n1, n2) and halftone images Hi(n1, n2), i=1, 2, …, P, (n1, n2) denote the cell location

16. Designing the tree structure 2.add leaf using MSE –2.1 for each leaf t and for each pixel p in N L do the following: assume that the leaf t is split into two nodes with the additional pixel p. calculate the MSE of this tree structure ( ) –2.2 find the leaf t 0 and additional pixel p 0 such that is minimum –2.3 update the tree structure by splitting the tree leaf t 0 with the additional pixel p 0

17. Assigning Contone Values to Tree Leaves Find the tree leaves for each pixel in the training set using the inverse halftoning algorithm Denote the set of contone values of pixels which have the same tree leaf t ans size a t the value of the leaf:

18. Inverse Halftone with Tree Structure 1.Find a pattern inside the initial template of size. 2. if node is a leaf, the contone value is stored in the node and assigned as the inverse halftone value 3. if node is split into two, the location (i, j) of the additional pixel is stored in the node. Get the halftone value of the pixel which is (i, j) away from the current pixel, if this value is 0(1), then the left(right) node is assigned as current node. Goto step 2.

19. Results: error diffused images

21. Results: clustered dot ordered dithered images

23. Results: dipersed dot ordered dithered images