interpolation techniques; simulation & analysis

Interpolation Techniques; Simulation & Analysis

Asmar Azar Khan 2005-06-0003

CS 584 Multimedia Communication

Objective◘ Study and analyze different interpolation

techniques

◘ Performance analysis of these techniques on different performance metrics

◘ To propose a hardware based approach for Interpolation

Agenda ◘ Introduction

◘ Transcoding◘ Image Scaling

◘ Literature Review◘ Interpolation Techniques

◘ Linear◘ Nearest◘ Cubic◘ Spline

◘ Proposed Algorithm ◘ Filtering

◘ Design Implementation ◘ Memory Requirement◘ Delay Requirement

◘ Future Proposals ◘ Questions

Introduction◘ Interoperability of multimedia devices

◘ Each device has different encoder and hence decoding schemes ◘ Broadband TV and Video on demand ◘ PDA and Mobile◘ Online Gaming ◘ Internet Telephony

◘ Role of Transcoders and Image Scaling

Transcoding ◘ A steer demand of multimedia on network have

given rise to challenges ◘ Heterogonous Encoders and Decoders◘ Bit Rate ( video) ◘ Delay ( voice and video) ◘ Quality ( multimedia)

◘ A technique where we change the encoded bit stream on the fly according to receiver compatibility◘ Encoded scheme ◘ Error Correction Techniques ◘ Spatial and Temporal Resolution

Image Scaling ◘ Spatial Resolution of Image and Video

◘ HDTV ( 1620 x 1200) etc… ◘ PC Monitors ( 1280 x 800) XVGA◘ PDA (640 x 480) VGA◘ Mobile (176 x 144) QCIF

Literature Review ◘ Software based approaches

◘ Interpolation Techniques ◘ Nearest Neighbor ◘ Linear ◘ Cubic Spline ◘ Bicubic Spline

◘ Hardware based Nearest Neighbor ◘ Simulations results for Advanced Techniques◘ Recently DCT domain Interpolation has been

presented

Interpolation◘ Whenever an image is desired to be re-

sampled ◘ It is first interpolated to continuous image◘ Then the image is sampled

Interpolator Original Image

Sampler Scaled Image

Interpolation Methods◘ Nearest Neighbor ◘ Linear ◘ Quadratic◘ Cubic B Spline◘ Normal

Nearest Neighbor ◘ Nearest Pixel Value

◘ Less Complex ◘ Low Quality◘ Edge handling

h(x) = 1 ,

0 ,

0 < | x | < 0.5

else

Courtesy: Thomas M. Lehmann , Survey: Interpolation Methods in Medical Image Processing IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. 18, NO. 11, NOVEMBER 1999

Linear Interpolation:

h(x) = 1 - | x | ,

0 ,

0 < | x | < 1

else


Quadratic Interpolation

h(x) = A1|x|2 + B1|x| + C1 , 0 < |x| <0.5A2|x|2 + B2|x| + C2 , 0.5 < |x| <1.50 , else


B-Spline Interpolation

h(x) = 1/2|x|3 -|x|2 + 2/3 , 0< |x| <1-(1/6)|x|3 + | x|2 -2|x| +4/3, 1< |x| <2

0 , else


Simulation • An image of 512 x 512 was taken

• It was reduced to 256 x 256

• Then interpolated using different techniques

512 x 512 256 x 256 512 x 512Down sampling Interpolation

Preprocessing; Low Pass Filter◘ A 7-tap filter used for CCIR-601 to SIF conversion

[ -29 0 88 138 88 0 -29] * 1/256

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Simulation; Test Image

SNR Calculation

Interpolation SNR (dbs)Linear 13.0467

Nearest 12.9016

Bi-Cubic 13.0013

Spline 12.9886

Histogram Analysis

0 100 200 300 400 500 6000

10

20

30

40

50

60

70Histogram of Original Filtered Image

Nearest Neighbor

0 100 200 300 400 500 6000

10

20

30

40

50

60Histogram of Nearest Interpolation twice scaling

Linear Interpolation

0 100 200 300 400 500 6000

10

20

30

40

50

60

70Histogram of Linear Interpolation twice scaling

Bicubic Interpolation

0 100 200 300 400 500 6000

10

20

30

40

50

60Histogram of Cubic Interpolation twice scaling

Spline Interpolation

0 100 200 300 400 500 6000

10

20

30

40

50

60 Histogram of Spline Interpolation twice scaling

Nearest Neighbor Nearest Interpolation twice scaling

Linear Interpolation Linear Interpolation twice scaling

Bicubic Interpolation Cubic Interpolation twice scaling

Spline Interpolation Spline Interpolation twice scaling

Fourier Transform of Original Image

0 100 200 300 400 500 600-5

0

5

10

15

20Fourier Transform of Original Filtered Image

Fourier Transform of Nearest Neighbor

0 100 200 300 400 500 6000

2

4

6

8

10

12

14

16Fourier Transform of Nearest Interpolation twice scaling

Fourier Transform of Linear

0 100 200 300 400 500 600-2

0

2

4

6

8

10

12

14

16Fourier Transform of Linear Interpolation twice scaling

Fourier Transform of Bicubic

0 100 200 300 400 500 600-2

0

2

4

6

8

10

12

14

16 Fourier Transform of Cubic Interpolation twice scaling

Fourier Transform of Spline

0 100 200 300 400 500 600-4

-2

0

2

4

6

8

10

12

14

16 Fourier Transform of Spline Interpolation twice scaling

Re sampling Algorithm◘ Low pass filter is applied to avoid aliasing

◘ Up sampling is done first in horizontal direction means column wise and then vertical direction i.e. row wise.

◘ 40/11 is non integer factor ◘ Up sample by 40 ◘ Down sample by 11

◘ Similarly 10/3 factor

Mapping onto scaled image

11

3

40

10

176

14 4

48 0

640

There will be 768 blocks/slices of original and scaled image

Post Processing◘ A 7-tap filter used to convert SIF to CCIR-

601

[-12 0 140 256 140 0 -12] * 1/256

◘ Removes the blocking effects from the interpolated image by introducing blurring

◘ As nearest neighbor techniques introduces sudden changes due to boundary value problems

Controller based approach◘ Distributed memory architecture

◘ State Machine based hardware

◘ Pre processing filtering

◘ Post processing filtering

◘ Memory Read and Write

Distributed Memory Architecture

Mem inMem out

Mem in

Mem in

Mem in

Mem out

Mem out

Mem out

Input Image Output Image

11 to 40 Mapping

a b c d e f g h i j k

a a a b b b b c c c d d d d e e e e f f f g g g g h h h h i i i j j j j k k k k

3 to 10 Mapping

a b c

a a a b b b b c c c

System Block Diagram

I/P RAM(176 x 8)

Hardware O/P RAM(640 x 8)

Data from Memory

8 bit data In

port A address

8 bit data out

Data to Memorystart

7-tap FIR

ROM

Statemachinecontroller

CLK B

Test bench

CLK

reset

CLK C

Future Proposals◘ Advanced Interpolation methods

◘ Cubic Spline◘ Normal Spline

◘ Generic Conversion ◘ Generic scaling ratio

Questions !

I thank you for your time..

interpolation techniques; simulation & analysis

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