A Parallel Algorithm for Hardware Implementation of Inverse Halftoning

1
A Parallel Algorithm for Hardware Implementation
of Inverse Halftoning

• Umair F. Siddiqi1, Sadiq M. Sait1 Aamir A.
  Farooqui2
• 1Department of Computer Engineering
• King Fahd University of Petroleum Minerals,
  Dhahran 31261, Saudi Arabia
• 2Synopsys Inc.
• Synopsys Module Compiler, Mountain View
• California, USA

2
Analog halftoning

• The process of rendition of continuous tone
  pictures on media on which only two levels can be
  displayed.
• The size of dots are adjusted according to the
  local print intensity.
• When looked at a distance it gives the impression
  of the original picture.

3
Digital halftoning

• In digital halftoning the input of the system is
  a grey-level image having more than two levels
  for example, 256 levels and the resulting image
  has only two levels.
• The halftone image is comprised of zeros and ones
  but gives the impression of the original image
  from a distance.

4
Inverse halftoning

• Inverse halftoning is the reconstruction of
  continuous tone picture (e.g. 256 levels) from
  its halftoned version.
• The input to an inverse halftoning system in an
  image that consists of zeros and ones and output
  is an image in which each pixel have value from
  256 gray-levels.
• Inverse Halftoning finds application in image
  compression, printed image processing, scaling,
  enhancement, etc.
• Inverse halftoning can be for color images but we
  are concerned with gray-level images and their
  halftones.

5
Example of Inverse Halftoning
Halftone Image
Inverse Halftone or grey-level image
6
Demonstration of our Inverse halftoning algorithm

• The next few slides show how inverse halftone
  operation is performed in our algorithm.

7
Lookup Table (LUT) based Inverse Halftone
operation

• The Lookup Table (LUT) method proposed by Mese
  and Vaidyanathan is used for inverse halftone
  operation.
• The LUT method uses a template 19pels to select
  pixels from the neighborhood of the pixel that is
  going to be inverse halftone.
• This 19pels then goes into a LUT which compares
  the 19pels with its stored values and returns a
  gray-level for the input 19pels.

8
19pels Template
1 2 3 4 5
6 7 8 9 10
11 12 0 13 14
15 16 17
18
The pixel numbered 0 is the one going to be
inverse halftoned This pattern is associated with
each pixel that is to be inverse halftoned
9
Demonstration of LUT inverse halftoning
10
This is the first 19pels selected
11
This is the second 19pels selected
12
This is the third 19pels selected
13
This is the fourth 19pels selected
14
Our modification to LUT based Inverse Halftoning
15
Problem of parallel LUT inverse halftone operation

• The LUT method uses one Lookup table that
  contains inverse halftone values for all 19pels
  that are obtained through training set of
  halftones of standard images.
• To fetch parallel inverse halftone values of more
  than one 19pels we need to implement multiple
  copies of the LUT !

16
Our approach to parallel LUT inverse halftoning

• The single large LUT has been divided into many
  Smaller LUTs (SLUTs).
• Now more than one 19pels can fetch its inverse
  halftone value from a separate SLUT independent
  to other parallel 19pels.
• Next problem is to develop a method to send
  incoming 19pels to separate SLUTs.

17
Method to distinguish 19pels from each other

• The task to send many incoming 19pels to their
  separate SLUTs is accomplished by defining an
  operator over 19pels.
• This operator is called Relative XOR Change
  (RXC).
• When all incoming 19pels are operated through
  this operator they convert into distinguished
  values in the range of t to t, where t 19
  in our case, but it could be any random integer
  within a suitable range with respect to total
  number of SLUTs and hardware complexity.

18
Demonstration of RXC operation
19
RXC Operator for Pn

• Pn-1 19pels with the pixel 0 at position
  (row,col-1)
• Pn 19pels with pixel 0 at position (row,col)
• xor_1 XOR(Pn-1, Pn )
• Magnitude of RXC RXC Number of Ones(xor_1)
• Sign of RXC sgn(RXC) when Pn gt Pn-1
• -
  when Pn lt Pn-1
• Note pixel 0 is the one that is to be inverse
  halftoned

20
RXC over gray-level halftones I
Gray-level 230
Corresponding halftone obtained through Floyd and
Steinberg Error Diffusion Method
21
RXC over gray-level halftones II
Gray-level 130
Corresponding halftone obtained through Floyd and
Steinberg Error Diffusion Method
22
Magnified look at the halftones I
Gray-level 210
Gray-level 130
Halftone shows no column-wise periodicity among
dots over small 19pels regions
Halftone shows column-wise periodicity among dots
over small 19pels regions
23
Magnified look at the halftones II
Gray-level 120
Portion of the halftone from image Boat
Halftone shows no periodicity among dots over
small 1D 19pels regions
Halftone shows no periodicity among dots over
small 1D 19pels regions
24
NON Periodic Vibratory RXC Operator

• The operator RXC has been defined that is simple
  to implement in hardware as well as gives NON
  periodic vibratory response over most of the gray
  levels from 0 to 255.
• We have assumed that a gray level image is a
  composition of many gray levels and obtaining the
  performance of RXC over individual gray levels
  can give a clue about its performance on images.
  
• This assumption is found to be correct in
  simulation results.

25
Parallel application of RXC
26
Development of parallel table access algorithm
with RXC
The addition of Slut values from previous pixels
simplifies the hardware design
27
Formal Algorithm
28
Simulation

• The algorithm is implemented in MATLAB the
  performance and quality of inverse halftoning is
  estimated.
• We assumed LUT inverse halftone operation to be
  ideal.
• The simulation results show the quality loss with
  respect to original image that occurred in
  distribution of parallel 19pels to different
  SLUTs through RXC.
• This pixel loss is compensated through
  replicating gray level values from the neighbors.
  

29
Sample Image I
peppers
PSNR 34.7880
30
Sample Image II
lena
PSNR 32.5685
31
Sample Image III
mandrill
PSNR 28.1264
32
Hardware Implementation

• This section shows the hardware implementation of
  the proposed parallel algorithm in terms of block
  diagrams.
• The specification of the hardware design is
• Parallel Pixels to be inverse halftone n 15
• Number of SLUTs 19

33
Two Blocks of hardware Implementation

• The hardware system can be divided into two
  blocks
• RXC and modulus operators
• 19pels to gray-level decoders

34
RXC and modulus operators

• RXC and modulus operators components are
  responsible for the following tasks
• Input 19pels Output SLUT numbers Slut
• Accept 19pels from the halftone image and assign
  a sequence number to each entered 19pels.
• Perform RXC operation on all 19pels.
• Add the Slut value of the 19pels that has
  preceding sequence number to the current result.
• Then take mod of the current result with a fixed
  number i.e. 19 in our case to obtain Slut value
  for the current 19pels.
• The above three steps are pipelined so new 19pels
  are coming in while the current 19pels are in
  process.

35
RXC and modulus Block Diagram
RXC calculation for 19pels Pn
Pn-1 and Pn are two 19pels among all 19pels to be
inverse halftoned in parallel. Slut is the
Smaller LUT number where the concerned 19pels
should go to fetch its inverse halftone value.
36
Hardware Design of RXC and modulus Operator

• The next slides can show the hardware design of
  RXC operator for a 19pels pattern named Pn with
  the following parameters
• Parallel pixels to be inverse halftoned at a
  time 15
• Total number of SLUTs 19, therefore, Slut is
  from 0 to 19.

37
Determination of Slut from RXC
38
Block diagram showing gray-level decoding process
39
Routing of a 19pels to 5th SLUT
40
Routing of a 19pels to 16th SLUT
41
Routing of a 19pels to 3rd SLUT
42
Routing of a 19pels to 17th SLUT
43
SLUTi(i16)
44
Quality of inverse halftones
Image Halftone Algorithm pixel coverage w/o pixel compensation PSNR with pixel compensation
Boat FS ED 65.0864 30.3749
Clock FS ED 70.6667 30.1671
Peppers FS ED 68.9433 28.5484
Boat GN ED 63.7531 28.7139
Clock GN ED 69.8765 31.2554
Peppers GN ED 68.9509 29.0077
Boat EG ED 67.3086 32.1370
Clock EG ED 68.5926 29.9289
Peppers EG ED 69.9905 28.5483
45
Comparison to halftone 256256

• Algorithm in 7
  Proposed Algorithm
• Cycles/pixel 1 0.066
• LUT size 5.1 K entries 19 K entries
• Latency 4 clock cycles 17 clock cycles
• Time taken 691.3502 ms 45.6389 ms

46
Conclusion and Future Work

• A parallel implementation for inverse halftone
  has been presented.
• Results can be improved by improving the
  operators and training.
• Results obtained are encouraging.

47
Method to generate contents of SLUT

• The algorithm is applied on images in a training
  set and Sluts values are obtained.
• The 19pels then placed in the SLUT given by the
  corresponding Slut value.

48
Properties of SLUTs

• The SLUTs were developed using training set
  composed of FS ED halftone images of Boat and
  Peppers of size 256x256-pixels.
• The size of one SLUT is found to be 2.5K entries
  .
• The summation of entries in all 19 SLUTs comes to
  be 42.6K.
• The size of LUT in single LUT method is 9.86K
  entries, however, if the single LUT method is
  implemented multiple times for 15 parallel pixels
  the total size could become 148K entries.
• In this way, our method can provide 3.5 times
  decrease in lookup table size over single LUT
  based method.

49
Behavior of RXC over Grey-level halftones
Gray level 130
Gray level 210
NON Periodic Vibratory Response
Periodic Vibratory Response
Halftones obtained through Floyd Steinberg
Error Diffusion Method
50
Representation of RXC values on number line
Periodic Vibratory Values
RXC values to be used in SLUT access are
calculated by adding the RXC to the RXC of the
previous 19pels That is RXC for SLUT of Pn
(Slut) RXC of Pn-1 RXC of Pn-2(n)
From the number line we can see that adding RXC
over previous values gives zero or constant
result, therefore, we need NOT periodic vibratory
response from RXC operator.
51
Modified RXC I

• At present, RXC is a comparative operator that it
  gives values in comparison to the previous
  19pels.
• This behavior of RXC can give different Slut
  values if some 19pels are replaced from the
  image.
• Therefore, we are required to store same 19pels
  in more than one table.

52
Modified RXC II

• Let us define a standard value for RXC
• The value of 19pels at which the histogram of
  19pels present in training set images can be
  divided into two portions.
• We find Slut value of each 19pels with respect to
  this standard value.
• That way we can have almost uniform table size
  with no repetition of same value in different
  tables.

53
Example histogram
The mean 19pels 0111110100011100110