Retinex Algorithm Combined with Denoising Methods Hae Jong, Seo Multi Dimensional Signal Processing Group University of California at Santa Cruz

UCSC EE Dept Hae Jong Background New Approaches Experimental Results SSR, MSR, MSRCR Retinex Algorithm by two Bilateral filters Retinex Algorithm by two higher order Bilateral filters Summary Overview

UCSC EE Dept Hae Jong Background on Retinex Algorithm Part 1

UCSC EE Dept Hae Jong Retinex Algorithm Flow Chart Kimmel et.al “A variational Framework for Retinex”

UCSC EE Dept Hae Jong Retinex Algorithms Single Scale Retinex Multi Scale Retinex Multi Scale Retinex With Color restoration Retinex Image Enhancement : Daniel J. Jonson et.al Gaussian function The weighted average version of different scale SSR Different weight factor for different color bands Given image Reflectance

UCSC EE Dept Hae Jong Retinex Algorithm Dynamic range compression Sharpening Color constancy Daniel J. Jonson et.al Retinex Image Enhancement :

UCSC EE Dept Hae Jong Shortcoming? Amplify the noise

UCSC EE Dept Hae Jong Retinex by Two Bilateral Filters Part 2 Michael Elad “Retinex by Two Bilateral Filters”

UCSC EE Dept Hae Jong Since the reflectance is passive, 0≤R≤1, we require S≤L and s≤. The illumination is supposed to be piecewise smooth. Things to consider Trivial solution (L=255) should be avoided - The illumination should be forced to be close to s. Michael Elad “Retinex by Two Bilateral Filters”

UCSC EE Dept Hae Jong Noise is magnified in dark areas. Forcing works against noise suppression. smooth illumination envelope smooth reflectance The Overall Model - shortcoming Requires an iterative solver! Promotes hallows on the boundaries of the illumination. Michael Elad “Retinex by Two Bilateral Filters”

UCSC EE Dept Hae Jong The bilateral filter is a weighted average smoothing, with weights inversely proportional to the radiometric distance and spatial distance between the center pixel and the neighbor [Tomasi and Manduchi, 1998] The first Jacobi iteration that minimizes the above function leads to the bilateral filter [Elad, 2002] Bilateral Filter

UCSC EE Dept Hae Jong The Formulation with Bilateral Filter With this new formulation: Non-iterative solver can be deployed, Both the illumination and the reflectance are forced to be piece-wise smooth, thus preventing hallows, Noise is treated appropriately. Michael Elad “Retinex by Two Bilateral Filters” Smooth illuminationSmooth Reflectance

UCSC EE Dept Hae Jong Numerical Solution Part 1: Find by assuming r=0 Part 2: Given, find r by Bilateral filter on s in an envelope mode Bilateral filter on s- in a regular mode Part 1: Find by assuming r=0 Part 2: Given, find r by Michael Elad “Retinex by Two Bilateral Filters” illuminationReflectance

UCSC EE Dept Hae Jong Higher order Bilateral filter on z- in a regular mode New Suggestion – Higher order Bilateral Part 1: Find by assuming r=0 Part 2: Given, find r i by Higher order Bilateral filter on z in an envelope mode

UCSC EE Dept Hae Jong Returning Some Illumination Kimmel et.al “A Variational Framework for Retinex”

UCSC EE Dept Hae Jong Experiment Results Part 3 Michael Elad “Retinex by Two Bilateral Filters”

UCSC EE Dept Hae Jong Example 1 OriginalResult (γ=3) Parameter : Regular mode Envelope mode

UCSC EE Dept Hae Jong Example 2 OriginalResult (γ=3) Parameter : Regular mode Envelope mode

UCSC EE Dept Hae Jong Example 3 OriginalResult (γ=3) Parameter : Regular mode Envelope mode

UCSC EE Dept Hae Jong Example 4 ( Hallow Effect ) OriginalResult (γ=3) Parameter : Regular mode Envelope mode

UCSC EE Dept Hae Jong Parameter : Bilater Filter VS Kernel Regression Bilater Filter VS Kernel Regression OriginalBilateral Filtered Result Kernel Regression Filtered Result Regular mode Envelope mode

UCSC EE Dept Hae Jong Conclusion & Future work Kimmel et.al “A Variational Framework for Retinex” Implemented Retinex by two bilateral filters It overcomes hallows, the need for iterations, and handles noise well. Kernel regression method can do better using higher order. Apply Iterative Steering Kernel Regression this frame work

UCSC EE Dept Hae Jong Conclusion & Future work Kimmel et.al “A Variational Framework for Retinex” Implemented Retinex by two bilateral filters It overcomes hallows, the need for iterations, and handles noise well. Kernel regression method can do better using higher order. Apply Iterative Steering Kernel Regression this frame work

UCSC EE Dept Hae Jong Main References [1] Elad.M, “Retinex by Two Bilateral Filters”, Scale-Space 2005, LNCS 3459, pp , (2005). [2] Rahman.Z, Jobson.D.J, Woodell.G.A : “Retinex processing for automatic image enhancement”. Journal of Electronic imaging, January (2004) [3] Takeda.H, S.Farsiu, and P.Milanfar, “Kernel Regression for Image Processing and Reconstruction”, IEEE Trans. on Image Processing, vol. 16, no. 2, pp , Feb. (2007) 2, 8

UCSC EE Dept Hae Jong Thanks Hae Jong, Seo Website :

UCSC EE Dept Hae Jong Back up Michael Elad “Retinex by Two Bilateral Filters”

UCSC EE Dept Hae Jong s SmallLarge llumination as an Upper Envelope            d s Minimize 2 2 s Michael Elad “Retinex by Two Bilateral Filters” smooth illumination being close to s