1. Least-Squares Warped Distance for Adaptive Linear Image Interpolation

2. Presentation Outline
Introduction
Basic Concept of Interpolation
Conventional Interpolation
Previous Adaptive Linear Interpolation
Proposed Method
Example of Proposed Method
Simulation Results
Conclusions

3. Introduction
Image interpolation plays a key role in the image processing literature
Image resizing/rotation/warping/morphing
Image/video compression
Mosaicking color filter array in DSC
De-interlacing in DTV
Lifting-based wavelet transform
Timing recovery in a digital modem
Sample rate converter
Adaptive image interpolation can provide a substantial gain in image quality.
Especially, warped distance (WaDi) approach

4. Basic Concept of Interpolation
With given discrete samples f (xk), generating continuous function as follows
The ideal kernel is the sinc function
Interpolation Kernel

5. Conventional Interpolation
Linear -1 1

6. Conventional Interpolation
Keys’ Cubic Convolution Interpolation -2 -1 1 2

7. Previous Adaptive Linear Interpolation
Warped Distance Linear Interpolation
Definition of warped distance as follows
Note that
The variable A is a pixel-based parameter
The variable k is an image-based parameter (k = 8 fixed for the Lena image)

8. New WaDi a for a given distance s
Proposed Method
New WaDi a for a given distance s
Use distance s as a pixel-based parameter
Introduce a system to calculate s
Including low pass filter and MMSE

9. Proposed Method
Generic diagram

10. Proposed Method
Systematic approach to employ the least-squares technique

11. Example of Proposed Method
Low complexity version
Apply 3-tap low pass filter gi = 1/2{s, 1, 1-s}
Define cost function as follows

12. Example of Proposed Method
Get a to minimize the cost as follows
We have
where

13. Two scenarios to evaluate the methods
Simulation
Two scenarios to evaluate the methods
One is a decimation-interpolation simulation
Filtered followed by down-sampler with a factor of two
Interpolate decimated image with a factor of two
The other is a rotation test
Fifteen rotations performed successively
Rotate by 24 degree for each rotation

14. Simulation Results for DI Test
PSNR resulting from the decimation-interpolation test
Images
Linear
CCI
WaDi-Linear
WaDi-
LSWaDi-
Lena
33.28
34.25
34.09
34.21
34.62
Peppers
31.57
31.96
31.61
31.63
32.00
Baboon
23.28
23.59
23.42
23.35
23.66
Airplane
30.33
31.08
30.48
30.50
31.15
Goldhill
31.01
31.49
31.45
31.37
31.64
Barbara
25.25
25.40
25.34
25.31
25.38

15. Simulation Results (DI Test)

16. Simulation Results (Rotation Test)

17. A Pixel-based adaptive linear interpolation has been presented
Conclusions
A Pixel-based adaptive linear interpolation has been presented
A generic system, formulation, and its low complexity version have been proposed
Simulation results show that the proposed method
Give better visual quality
Give better objective quality in terms of PSNR
than previous methods such as conventional linear, cubic convolution, and previous warped distance-based methods