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

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

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

Conventional Interpolation Linear -1 1

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

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)

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

Proposed Method Generic diagram

Proposed Method Systematic approach to employ the least-squares technique

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

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

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

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

Simulation Results (DI Test)

Simulation Results (Rotation Test)

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