Tree-Structured MTree-Structured Method for LUT Inveethod for LUT Inve

rse Halftoningrse HalftoningIEEE Transactions on Image IEEE Transactions on Image

ProcessingProcessing

June 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 s

izes x1*y1, x2*y2, … , xp*yp– Continuous tone images Di(n1, n2) and halft

one 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 no

de and assigned as the inverse halftone value• 3. if node is split into two, the location (i , j) of the addi

tional 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