School of Electrical and Color Halftoning Jan Allebach School of Electrical and Computer Engineering Purdue University West Lafayette, IN 47907-2035 allebach@purdue.edu

Outline 1. Description of NPAC-DBS 2. Experimental results showing effect of different color spaces and HVS models on halftone quality. 3. Example color images halftoned using NPAC-DBS and color PARAWACS based on a DBS screen (a) A color ramp (b) The Ruiyi image (c) The church image

Description of NPAC-DBS Imaging pipeline TRC for target output device (Indigo Press) Selection matrix/ random selection Unlinearized NPAC image set Linearize with TRC Linearized NPAC image set (For printing purpose) Initial NP images Unlinearized NPAC image set (For display purpose) NPAC image sets and NP DBS Halftoned NP images NP image in CMYK/sRGB Initial NP images (CMYK image is for print sRGB is gamma corrected for display)

Description of NPAC-DBS High level description For display purposes: sRGB halftone image & CMY halftone description NPAC image set (non-linearized) NPAC-DBS (Does not account for dot gain) NPAC image set (linearized) For printing purposes: CMYK halftone image (Account for dot gain) (These halftones are not the same)

Description of NPAC-DBS Block Diagram Random selection NP YyCxCz Initial NP image (GNP ) NPAC image set eYy ~ GYy eYy GYyCxCz - ~ GCx eCx eCx ~ eYyCxCz GNP GNP’ - E GCz eCz ~ eCz - Accept or reject the swap Linear trasfor-mation FYy FYyCxCz Here, FCx where FsRGB is the autocorrelation of HVS point spread function for the i th component of the opponent color space. , (original image in linear sRGB color space) FCz

NPAC-DBS block diagram cont’d After obtaining the final NP halftone, replace NP in each pixel with the corresponding sRGB values to get final halftoned image for display, or replace with the corresponding CMYK values to get halftoned image for printing. Replace NP on each pixel with sRGB Halftone in sRGB (with gamma correct) Final NP halftone (generated from non-linearized NPAC image set) Replace NP on each pixel with CMYK Final NP halftone Halftone in CMYK (generated from linearized NPAC image set)

NPAC image set to initial NP image Let be the area coverage of the Neugebauer Primaries in an NPAC image, where k denotes the Neugebauer Primary, , and is the location of pixel on the NPAC image, where , and M is the height, N is the width of the image. Also, let a randomly generated number be , and the Neugebauer Primary being selected for pixel is denoted , where , and satisfy the following condition: Note: In theory, can be a very large number, here, can be as large as 255.

Delta E calculation First, calculate the continuous tone image represented in YyCxCz color space according to the halftone image and error. Where Next, calculate autocorrelation of point spread function: Then, calculate correlation between point spread function and perceived error: Finally, normalize

Outline 1. Description of NPAC-DBS 2. Experimental results showing effect of different color spaces and HVS models on halftone quality. 3. Description of how PARAWACS works 4. Example color images halftoned using NPAC-DBS and color PARAWACS based on a DBS screen (a) A color ramp (b) The Ruiyi image (c) The church image 5. Screens and example images for the CMYK halftones

Effect of different color spaces and HVS models on halftone quality HVS models investigated: 1. Nasenan’s luminance channel HVS model 2. Mullen’s chrominance channel HVS models 3. Wandell’s HVS model 4. Daly’s luminance channel HVS model

Nasenan’s Frequency domain Filter For filtering luminance channel, we chose HVS Nasanen Model, which is given as where a = 131.6, b = 0.3188, c = 0.525, d = 3.91, Γ is the average luminance of the light reflected from the print in cd/m2, usually set to 11, and and are the spatial frequency coordinates in cycles/degree subtended at the retina.

Nasenan’s spatial domain Filter Generate HVS point spread function Windowing p(r) : Circular window size is 6 ( the spread of h(r) ) Where Normalize p(r) ~ In 2D, , where corresponds to pixel coordinates. Lee, C. (2008). Hybrid screen design and automatic portrait image enhancement. (Doctoral dissertation)

Blue-yellow channel contrast sensitivity function cycles/degree Approximation by Kolpatzik and Bouman to experimental data collected by Mullen, which is given as: where and are the spatial frequency coordinates in cycles/degree subtended at the retina. Mullen, K T, (1985), The contrast sensitivity of human colour vision to red-green and blue-yellow chromatic gratings.. The Journal of Physiology, 359 doi: 10.1113/jphysiol.1985.sp015591.

Red-green channel contrast sensitivity function cycles/degree Approximation for Red-Green channel contrast sensitivity based on data collected by Mullen: where and are the spatial frequency coordinates in cycles/degree subtended at the retina.

Mullen’s filters in spatial domain Red-Green and Blue-Yellow channel filters are generated in similar way as Nasenan’s filter. Generate HVS point spread function Windowing p(r) : Circular window size is 6 ( the spread of h(r) ) Normalize p(r) ~ Where , for Red-Green channel. for Blue-Yellow channel. In 2D,

Wandell’s HVS filters Wandell’s spatial kernel is: where The scale factor is chosen so that sums to 1, the scale factor is chosen so that for each color plane, its two-dimensional kernel sums to one. The parameters for the three color planes are: Where spread is in degrees of visual angle. Plane Weights ωi Spreads σi Luminance 0.921 0.0283 0.105 0.133 -0.108 4.336 Red-Green 0.531 0.0392 0.330 0.494 Blue-Yellow 0.488 0.0536 0.371 0.386 Zhang & Wandell (1997). A spatial extension of CIELAB for digital color image reproduction, SID Journal.

Daly’s HVS model Daly HVS model: Where spatial frequency has unit of cycles/degree, a = 2.2, b = 0.192, c = 0.114, d = 1.1, = 6.6 Daly’s HVS model with respect to spatial frequency in cycles/inch: Where is 37.8152

Comparison between Wandell, Daly and Nasenan frequency domain models

Comparison between Wandell, Daly and Nasenan spatial domain filters

YyCxCz and Wandell Color Space halftone results comparison Luminance: Nasenan’s Chrominance: Single Mullen chrominance channel filter Luminance: Daly’s filter Chrominance: Single chrominance channel filter Wandell O1O2O3 filter ✔ Color Space: YyCxCz Color Space: Wandell Color Space: YyCxCz Normalized Error: 1.6061 Normalized Error: 1.7787 Normalized Error: 13.0332 NPAC set: 40% Yellow, 20% Magenta, 0% Cyan-Magenta, 40% White Image size: 512 x 512 Filter parameter: S=3000

YyCxCz and Wandell Color Space halftone results comparison Luminance: Nasenan’s Chrominance: Single Mullen chrominance channel filter Luminance: Daly’s filter Chrominance: Single chrominance channel filter Wandell O1O2O3 filter ✔ Color Space: YyCxCz Color Space: Wandell Color Space: YyCxCz Normalized Error: 1.4263 Normalized Error: 5.2454 Normalized Error: 12.6397 NPAC set: 40% Cyan, 20% Magenta, 0% Cyan-Magenta, 40% White Image size: 512 x 512 Filter parameter: S=3000

YyCxCz and L*a*b* Color Space halftone results comparison Luminance: Nasenan’s filter Chrominance: Single chrominance channel filter Very similar Color Space: YyCxCz Color Space: L*a*b* Normalized Error: 1.6061 Normalized Error: 1.6274 NPAC set: 40% Yellow, 20% Magenta, 0% Cyan-Magenta, 40% White Image size: 512 x 512 Filter parameter: S=3000

YyCxCz and L*a*b* Color Space halftone results comparison Luminance: Nasenan’s filter Chrominance: Single chrominance channel filter Very similar Color Space: YyCxCz Color Space: L*a*b* Normalized Error: 1.4263 Normalized Error: 1.4433 NPAC set: 40% Cyan, 20% Magenta, 0% Cyan-Magenta, 40% White Image size: 512 x 512 Filter parameter: S=3000

Outline 1. Description of NPAC-DBS 2. Experimental results showing effect of different color spaces and HVS models on halftone quality. 4. Example color images halftoned using NPAC-DBS and color PARAWACS based on a DBS screen (a) A color ramp (b) The Ruiyi image (c) The church image

Example halftone images NPAC-DBS Parawacs selection matrix Original image

Example halftone images NPAC-DBS Parawacs selection matrix Original image

Example halftone images NPAC-DBS Parawacs selection matrix Original image

Thank you !