A MODIFIED TETROLET BASED IMAGE DE-NOISING FOR REAL TIME EDGE DETECTORS

AAiT, ECE 1

By: Eyob Teshome

Advisor :Prof. Bisrat Derebssa

Addis Ababa UniversityAddis Ababa Institute of Technology

Department of Electrical and Computer Engineering

Outline• Introduction

• Background

• Statement of the problem

• Objective

• Previous works

• Methodology

Tetrolet Image decomposition

Hardware realization

• Experiments and Results

• Conclusion

• Recommendation

AAiT, ECE 2

Introduction• Image de-noising algorithms:

Involves the manipulation of the image data to produce a high quality image.

• Tetrolet Transform image decomposition:

Based on the 2D-Haar wavelet transform, adapts the image characteristics automatically.

• Edge detection algorithm:

Used to finds the sharp intensity variation of an image.

• Edge detection is an initial step in object recognition.

AAiT, ECE 3

Background• Haar scaling(φ(t)) and main Wavelet functions(ψ(t)).

φ(t) . ψ(t) = 0 (i.e., Orthogonal)• Three major steps:

Figure 1: Basic steps in Wavelet based image de-noising algorithm

AAiT, ECE 4

5

Background(1)• In the Standard Tetrolet transform Image decomposition,

Images are sub-divided into 4x4 Pixels. Each 4x4 Pixels is partitioned using Tetrominoes.

The Haar transform is applied to generate 4 average coefficients and 12 detailed coefficients.

Figure 1: The five free tetrominoes. O-I-T-S-L-tetromino.

AAiT, ECE

6

Statement of the problem

AAiT, ECE

• [1],[2],[3] The standard tetrolet transform Selects 117 Tilings for covering of each 4 × 4 Pixels with four Tetrominoes. • [1],[2] Computationally costly and needs big Storage.

[1] After J levels: Store ) coeficient values. [1] For Complete decomposition (J = log2(N) − 1 ):

• The First order gradient based edge detection algorithms are susceptible to noise.

Objective• Improve the Tetrolet transform based image de-noising algorithm. • Use the improved image de-noising algorithm as a pre-processing step for other image processing algorithms.• To design and simulate a hardware realization of the Tetrolet based image de-noising algorithm using FPGA. • Compare the performance of the software as well as the hardware design with other benchmark techniques.• To compare the software and the FPGA implementation of the system via simulation.

AAiT, ECE 7

Previous Works• Tetrolet transform is first proposed by Jens Krommweh [1] for image compression.• In 2010, Singh [2] proposed a new approach to the de-noising problem based on the Tetrolet transform. • He achieves up to 2 dB better PSNR compared with other published Haar wavelet based methods.• Cai-lian Li [3] improves the Tetrolet based image de-noising algorithm using the Sure [5] thresholding method.• As a result, he achieved a better PSNR and visual quality.• For the software realization, this two methods takes a significant amount of computational time.

AAiT, ECE 8

Methodology

Figure 3: Overall system

• Linear Operation:

The addition or multiplication of the noise to the

image signal.

• An additive noise follows the rule:

w(x, y) = s(x, y) + n(x, y) ,

• While the multiplicative noise satisfies:

w(x, y) = s(x, y)× n(x, y) ,AAiT, ECE 9

• Tetrolet based de-noising involves three steps:

Tetrolet based image decomposition

Tetrolet Coefficient Thresholding

Tetrolet based image Reconstruction

Figure 4: Basic steps in Tetrolet based image de-noising algorithmAAiT, ECE 10

Tetrolet Based Image Decomposition

x x x … xx x x … x

… … .x x x . . . x

…

…

…

…

…

…

Note: averaging/differencingof detail coefficients shown

One level, vertical Haar decomposition:

detail

average

2D-Haar

Figure 5: 2D-Haar image decomposition

𝐿𝑜𝑤𝑝𝑎𝑠𝑠 : 𝑓 (𝑋 (𝑖 ) )=(𝑋 (𝑖 )+𝑋 (𝑖+1 ))√2

h𝐻𝑖𝑔 𝑝𝑎𝑠𝑠 :𝑔 (𝑋 (𝑖 ) )=(𝑋 (𝑖 )−𝑋 (𝑖+1 ))√2

AAiT, ECE 11

…

Tetrolet Based Image Decomposition(1)• The generalization of 2-D classical Haar wavelet transform.

Figure 6: The 5 free Tetrominoes: O - I - T - S - L.

Figure 7: The Tetrolet based image decomposition

x x x x … xx x x x … xx x x xx x x x

… … .x x x x . . . x

Tetrolet Partitions:…

…

…

…

…

… … .

…

AAiT, ECE 12

Tetrolet Based Image Decomposition(2)• 2D Haar DWT/DTT using filter banks(Analysis)

AAiT, ECE 13

Modify the Tetrolet Image de-composition• Only the 15 best Tilings are selected out of 117 Possible coverings.

Figure 8: The 15 selected Tetromino configurations.

Figure 9: The 22 fundamental forms tiling a 4 x 4 PixelsAAiT, ECE 14

Modify the Tetrolet Image de-composition(1)• An Improved Tetrolet based image de-noising algorithm flowchart.

15AAiT, ECE

Hardware Design• The whole design incorporates three stages.

Stage one is the Tetrolet based image decomposition with thresholding Stage two is the Tetrolet based image reconstruction The third stage is Sobel edge detection algorithm

• FDTT image decomposition is designed as a hierarchical scheme: Uses 1-D processing module twice to represent 2-D processing. The module can be used repeatedly on the same image for multilevel processing. Three of the first Tetrolet partitions are implemented. Figure 10: The first three Tetrolet partitions.

AAiT, ECE 16

Hardware Design(1)

• The proposed algorithm of the DFTT is divided into three phases:

Initializing phase, Horizontal Pixel phase and

Vertical Pixel phase.

Figure 11: Layout of the proposed architecture for the FDTT

• Memory: Modeled using non-synthesizable VHDL code for

simulation only.AAiT, ECE 17

Hardware Design(2)• The Low and High pass components for FTT image decomposition

[Low pass] [High pass]

• The original pixels values could be retrieved in IDTT process from the clean High and Low pas components.

• [7] The VHDL implementation of Sobel edge detection algorithm involves:

The convolution of the 3x3 masks with image pixels,

The gradient magnitude and the direction of the intensity variation,

The comparison of the magnitude value with the threshold value.

AAiT, ECE 18

Experimental Setup(Software)• The algorithms were tested in MATLAB (without C routines).

• Single level image decomposition.

• Performance Metrics: based on the execution time and the PSNR values.

[7]

Where x and y are the clean and estimated samples respectively.

• The Cameraman Test image, a size of 512x512,

• The Test image format used is the Gray Scale format.

• Processor: Intel Pentium Dual CPU T3400 @2.16GHz @2.17GHz

• Installed memory (RAM): 3.00GB

AAiT, ECE 19

20

Results

AAiT, ECE

5 10 15 20 25 30 35 40 450

5

10

15

20

25

30

35

40

De-noising Algorithms for Cameraman Image

TetroletMtetroletR.haarBayesThre.SoftThre.Noisy

Noise Standard Deviation(Sigma)

PSN

R in

dB

Image Noisy VisuHard

VisuSoft

Sure Bayes R-haar Tetrom Modified Tetrolet

Avg. Exec. Time(in sec)

- ≈0.32506

≈0.34547

≈0.34222

≈0.33863

≈0.94957

≈20min

≈7.3693

21

Result(1)

Noisy Image

Hard Soft Sure Bayes R.Haar Tetrolet Mod. Tetrolet

0

5

10

15

20

25

σ=10σ=20σ=30

De-noising Methods with Sobel

PS

NR

in d

B

AAiT, ECE

Noisy Image

Hard Soft Sure Bayes R.Haar Tetrolet Mod. Tetrolet

0

5

10

15

20

25

σ=10σ=20σ=30

De-noising methods with Roberts

PS

NR

in

dB

Experimental Setup(Hardware)• The design is synthesized using Xilinx XST Synthesis tool

• Simulated using ModelSim SE Simulation Tool Environment.

• Hardware Platform:

Xilinx Virtex®-4 FPGA (XC4VSX Series).

• Input image:

White Gaussian noise corrupted 128x128 Cameraman

image.

• Picture data are 8-bit pixels.

• A Text file is used as input for test bench configurations for

simulation.

• Data Converter application accompanies this thesis:

Read an image in ‘jpg’ format and store its contents in

‘txt’ format, AAiT, ECE 22

Device utilization FDTT

Table 3: Device utilization FDTT for different Tetrolet Partitions

Device Utilization Summary

Logic Utilization

Available

2D-HAAR 2TETROLET. 3TETROLET15TETR.

Used

Utilization

Used

Utilization

Used

Utilization

Utilization

Number of Slices 10240 383 3% 522 5% 797 7% ≈ 31%

Number of Slice Flip Flops

20480 279 1% 365 1% 542 2% ≈ 15%

Number of 4 input LUTs 20480 716 3% 976 4% 145

4 7% ≈ 31%

Number of bonded IOBs 320 36 11% 36 11% 36 11% ≈ 11%

Number of GCLKs 32 1 3% 1 3% 1 3% ≈ 3%

AAiT, ECE 23

REAL-TIME PERFORMANCE

• FDTT has the maximum frequency (168.297MHz). No.

Table 4: Review of No. of clock cycle and Timing for FDTT and 2D Haar image decomposition

AAiT, ECE 24

Stage of

design

No. Tetrolet

partitions

Execution

time(ns)

No. of

Clock

cycles

Maximum

Frequency(M

Hz)

Time duration

of Clock

period (ns)

1D-Haar 6102625 122053 203.934 50

One (2D-

Haar)

9157075 183142 189.418 50

Two 1221152

5

244231 195.409 50

Three 2137487

5

427984 168.297 50

Fifteen ≈

9163350

0

≈

1832670

≈ 50

Conclusion• Tetrolet based de-noising is much more computationally intensive

while providing a better result.

• The modified image de-noising algorithm has comparably as equal

quality as the previous Tetrolet based image de-noising algorithm.

• The FPGA design of the Tetrolet image decomposition algorithm is

running at a maximum frequency of 168.297MHz targeting Virtex-4

FPGA.

• In addition, the entire VHDL utilized only 9% of the total logic

elements available on this FPGA.

• FPGA based implementation of Tetrolet based image de-noising results

in significant improvement in terms of speed over the Software

realization. AAiT, ECE 25

Recommendation• With Tetrolet transform, a good result can be brought for Poisson

noise and Speckle noise.

• For the software realization, if the vectoring of loops further

exploited, the execution time can be improved more.

• It is recommended to realize and check the performance of the full

Tetrolet transform based de-noising on FPGA.

• The Sobel edge detection is synthesized for only 64x64 image

sizes due to the fact that Xilinx ISE only support loops with 64

maximum iterations.

• This issue is not solved for this thesis. It is left as a future work.AAiT, ECE 26

Main References[1] J. Krommweh, ”Tetrolet transform: A new adaptive Haar wavelet algorithm for sparse image representation ”, Journal of Visual Communication and Image Representation, Vol. 21, no. 4, pp. 364–374, 2010.

 

[2] Singh, Manish Kumar, "de-noising of natural images using the wavelet transform" (2010). Master's Theses, Paper 3895.

[3] Cai-lian Li, Ji-xiang Sun and Yao-hong Kang, "A new algorithm for image denoising based on Tetrolet transform", International Conference on Image Processing and Pattern Recognition in Industrial Engineering, Volume 7820, pp. 78201L-78201L-7 (2010).

[4] M. Korn, Geometric and algebraic properties of polyomino tilings, PhD thesis, Massachusetts Institute of Technology (2004).

 

[5] David L. Donoho and Iain M. Johnstone. “Adapting to Unknown Smoothness via Wavelet Shrinkage.” Journal of the American Statistical Association, Vol. 90, No. 432, pp. 1200-1224, Dec. 1995.

 

[6] An improved Sobel edge detection, Computer Science and Information Technology (ICCSIT), 2010 3rd IEEE International Conference on 9-11 July 2010.

[7] CNRS, CEREMADE, University Paris-Dauphine.

Internet: http://www.ceremade.dauphine.fr/~peyre/

[8] VHDL Design Representation and Synthesis (2nd Edition), James R. Armstrong, F. Gail Gray . Prentice Hall, April 9, 2000.AAiT, ECE 27

THANK YOU!

AAiT, ECE 28