Tree-Structured MTree-Structured Method for LUT Inveethod for LUT Inverse Halftoningrse HalftoningIEEE Transactions on Image IEEE Transactions on Image

ProcessingProcessingJune 2002 June 2002

OutlineOutline• Introduction

– Halftoning– Inverse halftoning

• Tree-Structured Method• Result

IntroductionIntroduction• Halftone

– A technique to convert a continuous-toe image into a binary image

IntroductionIntroduction• Halftone

– Simple Thresholding– Ordered Dither

IntroducitonIntroduciton• Halftone

– Error Diffusion

IntroductionIntroduction• Inverse Halftone

– Reconstructing a continuous-tone image from its halftoned version

IntroductionIntroduction• Inverse Halftone

– Low pass filter– LUT(Look Up Table)

• Depending upon the distribution of pixels in the template of the pixel

Tree-Structured LUT(TLUT)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

TLUTTLUT• 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

Tree StructureTree Structure• Each tree node is either split further or a leaf

– Nodes are split to refine contone value– Leaf stores a contone value

Initial template

…

32 個(0,1) (1,1)

Designing the tree structureDesigning 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

Template SelectionTemplate 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

Designing the tree structureDesigning the tree structure• 2.add leaf using MSE

– 2.1 for each leaf t and for each pixel p in NL 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 t0 and additional pixel p0 such that is minimum

– 2.3 update the tree structure by splitting the tree leaf t0 with the additional pixel p0

Assigning Contone Values to TrAssigning Contone Values to Tree Leavesee 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 at the value of the leaf:

Inverse Halftone with Tree Inverse Halftone with Tree StructureStructure

• 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.

Results: error diffused imagesResults: error diffused images

Results: clustered dot ordered Results: clustered dot ordered dithered imagesdithered images

Results: dipersed dot ordered dithResults: dipersed dot ordered dithered imagesered images