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Least-Squares Warped Distance for Adaptive Linear Image Interpolation

Least-Squares Warped Distance for Adaptive Linear Image Interpolation. Presentation Outline. Introduction Basic Concept of Interpolation Conventional Interpolation Previous Adaptive Linear Interpolation Proposed Method Example of Proposed Method Simulation Results Conclusions.

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Least-Squares Warped Distance for Adaptive Linear Image Interpolation

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  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 -1 1 • Linear

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

  15. Simulation Results (DI Test)

  16. Simulation Results (Rotation Test)

  17. 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

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