Analysis and extensions of the Frankle-McCann

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1 Analysis and extensions of the Frankle-McCann Retinex algorithm Jounal of Electronic Image, vol.13(1), pp , January School of Electrical Engineering and Computer Science Kyungpook National Univ.

2 2/ 2 Flowchart Input image Log scale Ratio-product-reset-average Retinex Post-LUT Averaging Normalizing Per-pixel weighting Post-Retinex

3 3/ 2 Abstract Retinex Algorithm Process of estimating the per-pixel gains necessary to achieve dynamic range compression in the original image Extension Suppress artifacts Reduce the number of iterations

4 4/ 2 Introduction High Dynamic Range More accurate rendition of the original image Realistically converted to a low resolution Retinex theory Illuminant estimation, gamut mapping and HDR imaging ratio-product-reset-average operation From a maximum brightness default state to a final image that has dark region in the input image

5 5/ 2 Proposed method Distance-weighting function Out-to-in spatial comparisons Soft reset operation

6 6/ 2 Preliminaries Notation The values ranging between 0 and 65,535 Convert input image into log scale Easy to use Multiplication and division operater g [ m, n ] log( f [ m, n ]) inp = input (1)

7 7/ 2 Raw image Acquisition Using the Nikon D1 digital camera with 12 bit output value Combine the 12 bit image to form a 16 bit high dynamic range raw image Applying no gamma function to any of the image shown

8 8/ 2 Fig.3. Sensitivity of the Nikon D1 digital still camera, measured with a spectroradiometer.

9 9/ 2 Formulation and extensions of retinex Comparison of a destination pixel to other source pixel Square spiral structure From long distance to short distance Out to in direction, inward spiral Each step perform by ratio-product-reset-average operation Initial spacing S between comparison pixels p 2 log 2 min( M, N) 1 where is rounding P =,

10 10 / 2 Halving and changing the direction For image ( p = 7) The set of comparison pixels Ω = { g[ m, n 128], g[ m 64, n], g[ m, n + 32], (2) g[ m + 16, n],..., g[ m, n + 2], g[ m + 1, n]} Assume that Q comparison pixels in the image, final state of the image is g inp g 0 g ip g q Input image Image containing the initial value of the ratio-products, maximum brightness in the image Image containing the intermediate ratio-products

11 11 / 2 Compute the ratio-product-reset-average at q stage g Initial set of Intermediate products Updating g ip ip g ip g = q 1 [ m] R{ g 1[ m s] + ( g [ m] g [ m s]) w} = q inp inp where m = [ m, n] w = the distance-weighting s = vector depicting the distance of the source pixel from the destination pixel R( ) = reset function (3)

12 12 / 2 Geometric mean of the previous ratio products and new intermediate products g q 1 + g ip g q = 2 Distance-weighting function in equation (3) Control of bright transition by distance Lessen the impact of far way sources on the propagation of ratio products Destination pixel to have a brightness greater than 1.0 Need to renormalization during post processing (4)

13 13 / 2 Hard reset function RP, RP 1 R( RP) = 1, otherwise (5) Soft reset function R( RP) = RP, 1 + log( RP) / 8, RP 1 otherwise (6) Smooth contrast transition between closely spaced dark to light transitions

14 14 / 2 Post-Retinex processing Direct inverse of the input step Antilogof image and normalization Averagingthe image obtained after retinex with the initial image to reduce the number of iteration before normalization f Retinex, the image in linear space obtained by the retinex algorithm and, the initial image f 0

15 15 / 2 Normalization f f avg norm f [ ] [ ] [ ] Re m f0 m m tinex + = (7) 2 favg[ m] + min( favg ) [ m ] = (8) min( f ) avg The brightest point goes to white and the darkest point goes to black

16 16 / 2 Per-pixel weighting computing the median of the 3 3 neighborhood of the per-pixel brightness ratio of an normalized retinex image and the initial image Y [ m + k] w[ m ] = median, k [-1,0,1] Y 0 [ m + k] norm 2 (9) where brightness Y=0.3R+0.6G+0.1B and 2 [ 1,0,1] denotes the Cartesian product of [ 1,0,1]

17 17 / 2 The final image f final [ m] = w[ m] f0[ m] (10)

18 18 / 2 Experimental results Chromatic response of retinex Independently applied to each color channel Recombine in the post-retinex operation After first iteration, maximum chromatic desaturation For subsequent iteration, becoming more uniform across the image

19 19 / 2 Fig.2. (a) 16-bit synthetic image modified in Photoshop so that detail can be observed in an 8-bit image. The saturated colors have a value of 32,767 out of a maximum 65,535. Fig.2. (b) Image obtained, left to right, after Retinex for one and eight.

20 20 / 2 Dual spiral versus single spial Using dual spiral to reduce artifacts and number of iterations (a) (b) Fig.3. The set of comparison pixels for a single spiral and a dual spiral. Black pixels are source pixels. The gray line depicts the pseudo-spiral path.

21 21 / 2 (a) (b) Fig.4. Dual spiral versus single spiral, (a) Raw image from 16-bit per primary color image, and its 8-bit per primary rendition obtained (b) single square spiral path with two Iterations, and (c) dual square spiral path with one iteration (c)

22 22 / 2 Distance weighting Distance weighting factor in Eq. (3) Experimenting with and w 1/ log10( s power ) s 0.1 s provided better contrast without affecting detail in the highlight regions

23 23 / 2 (a) (b) (c) Fig.5. Effect of weighting functions. (a) Raw image from 16-bit per primary color 0.1 image, and its 8-bit per primary rendition obtained. (b) 1/ log10( s ) and (c) s

24 24 / 2 Out-to-in versus in-to-out spatial comparisons In-to-out method Significant computational savings by reverse the order of computing spatial comparisons Remove the negligible effect due to the distanceweighting function Out-to-in method Preventing from objectionable artifacts

25 25 / 2 (a) (b) (c) Fig.6. (a) the saturated red, green, gray, blue, and white colors have a value of 65,535. (b) out-to-in, (c) in-to-out

26 26 / 2 Median filtering of channel gains To mitigate pixel-to-pixel variations 3 3 neighborhood Much more accurate rendition of the image Present the true color rather than make the brightest object appear white

27 27 / 2 Fig.7. Applying median filtered channel gains to the church image in Fig. 4(a) the pixel gains are determined from dual spiral retinex processing and applied to the original RGB values.

28 28 / 2 (a) (b) (c) Fig.8. (a) raw image, (b) dual spiral retinex processing and (c) applying per-pixel gains to the raw image

29 29 / 2 Conclusion Frankle-McCann Retinex algorithm Adding Dual spiral pixel paths Distance-weighting spatial multiplier Soft reset mechanism Advantage Better rendition with single iteration More true color with per-pixel gains

Basic relations between pixels (Chapter 2)

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