DIGITAL HALFTONING Sasan Gooran

Digital Images Pixel based They consist of a number of square image elements, which are called pixels. Each pixel has a position in the image and a value that describes its tone value in that position. The number of pixels per inch is called resolution. (ppi = pixels / inch) Another way of mentioning resolution is to say how many pixels an image totally consists of. Ex. 1024 x 768 pixels. 28/11/2018 Digital Halftoning

Digital Images Pixel based Bit depth: Number of bits that are used in order to represent the tone value in computer. Commonly we use 256 levels of tone, i.e. Bit depth = 8. 28/11/2018 Digital Halftoning

Digital Images How much memory? bit/pixel Line 1 2 tones Grayscale 8 256 tones Indexed color 8 256 colors RGB 3*8=24 256^3=16.7 millions colors CMYK 4*8=32 256^4=4.3 billions colors 28/11/2018 Digital Halftoning

Halftoning Because printing is generally not able to reproduce different tones of a color, the original image has to be transformed to a binary image. This is called halftoning. 28/11/2018 Digital Halftoning

Halftoning Prepress Halftoning Print Con-tone Image Halftoned 28/11/2018 Digital Halftoning

Halftone cell Halftone cell Halftone dot The fractional area of the cell covered with ink is decided by the pixel value. (Or by the mean of the pixel values if the small square shown in the image to the left consists of more than one pixel). 28/11/2018 Digital Halftoning

Line screen frequency In conventional halftoning the distance between the centers of two neighboring dots is constant. Number of halftone dots per inch is called line screen frequency. It is denoted by lpi (lines per inch). 28/11/2018 Digital Halftoning

Line screen frequency & Resolution Micro dot Resolution: number of micro dots per inch (dpi) Halftone cell In this case: 17 levels of gray 28/11/2018 Digital Halftoning

Levels of gray Ex, 600 dpi and 100 lpi gives 37 levels of gray Which one to choose???? 28/11/2018 Digital Halftoning

lpi & ppi When scanning an image, for practical reasons and for better reproduction, you normally choose a ppi that is twice as high as lpi. A sampling factor of 1.5 is acceptable in most cases. A sampling factor higher than 2 is unnecessary. 28/11/2018 Digital Halftoning

Lpi & ppi Ex. If your original image is (24 x 36 mm) and you want the printed image to be (80 x 120) mm when lpi = 133, you should choose a ppi around 887 lines/inch. 28/11/2018 Digital Halftoning

AM and FM Halftoning AM (Amplitude Modulated) Halftoning The size of the dots varies while their frequency is kept constant. The darker the gray tone the bigger the dot. FM (Frequency Modulated) Halftoning The size of the dots is constant. Their frequency (number) is changed. The darker the gray tone the more the number of micro dots. 28/11/2018 Digital Halftoning

AM and FM Halftoning 28/11/2018 Digital Halftoning

AM and FM Halftoning 28/11/2018 Digital Halftoning

AM and FM Halftoning AM FM 28/11/2018 Digital Halftoning

Thresholding This threshold matrix represents 10 levels of gray. 0.6 1 0.1 0.3 0.2 Original Image Threshold matrix Halftoned Image This threshold matrix represents 10 levels of gray. 28/11/2018 Digital Halftoning

Threshold matrix Example: Line 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 28/11/2018 Digital Halftoning

Threshold Matrix Example: spiral 1 2 3 4 12 13 14 5 11 16 15 6 10 9 8 7 28/11/2018 Digital Halftoning

Threshold Matrix Example: spiral Line Spiral 28/11/2018 Digital Halftoning

Error Diffusion FM Original Image Halftoned Image 0.3 Threshold 0.5 0.7 Threshold 0.5 Original Image Halftoned Image 0.3 Error Filter 7 (*1/16) 3 5 1 28/11/2018 Digital Halftoning

Error Diffusion FM 28/11/2018 Digital Halftoning

Hybrid Halftoning Example 1 AM+FM Homogeneous parts by AM Details by FM 28/11/2018 Digital Halftoning

Hybrid Halftoning Example 1 28/11/2018 Digital Halftoning

Hybrid Halftoning Example 2 Some printing methods are not able to produce the dots sufficiently small. Ex. Flexography. 5.2% 28/11/2018 Digital Halftoning

Hybrid Halftoning Example 2 Utilize a FM method for the highlights and shadows using the smallest possible dot. Use an AM method for the rest of the image. 28/11/2018 Digital Halftoning

Hybrid halftoning Example 2 28/11/2018 Digital Halftoning

Hybrid Halftoning Example 2 28/11/2018 Digital Halftoning

Hybrid Halftoning AM Hybrid 28/11/2018 Digital Halftoning

Hybrid Halftoning Hybrid, The FM method is Error diffusion 28/11/2018 Digital Halftoning

Color Mixing (Additive) 28/11/2018 Digital Halftoning

Color Mixing (Subtractive) 28/11/2018 Digital Halftoning

Color Mixing Three primary colors CYAN (C) MAGENTA (M) YELLOW (Y) 28/11/2018 Digital Halftoning

Color Mixing Three secondary colors RED (R, MY) GREEN (G, CY) BLUE (B, CM) 28/11/2018 Digital Halftoning

Color Mixing And Black BLACK (K, CMY) 28/11/2018 Digital Halftoning

3-Color Print Original 28/11/2018 Digital Halftoning

Konventionellt raster AM Halftone Konventionellt raster 28/11/2018 Digital Halftoning

FM Halftone FM- raster 28/11/2018 Digital Halftoning

AM Halftone, same angle for C, M, Y & K 28/11/2018 Digital Halftoning

AM Halftone, same angle for C & M Miss-registration Correct registration Position error 28/11/2018 Digital Halftoning

AM Halftone, same angle for C & M Miss-registration Correct registration Angle error Moiré pattern 28/11/2018 Digital Halftoning

AM Halftone, different angles for C, M,Y & K 15, 75, 0 and 45 degrees 28/11/2018 Digital Halftoning

Rosette Pattern 28/11/2018 Digital Halftoning

Rosette Pattern 28/11/2018 Digital Halftoning

FM (Stochastic) Halftone, 4-color print “Moiré pattern” and “Rosette pattern” disappear 28/11/2018 Digital Halftoning

NUEGEBAUER’S Equations X, Y, Z are the tristimulus values for the average color of a surface ai is the fractional area covered by color Xi, Yi, Zi 28/11/2018 Digital Halftoning

Demichel’s Equations (3-color print) Aw =(1-ac)(1-am)(1-ay) Ac =ac(1-am)(1-ay) Am =am(1-ac)(1-ay) Ay =ay(1-ac)(1-am) Ar =amay(1-ac) Ag =acay(1-am) Ab =acam(1-ay) Ak=acamay 28/11/2018 Digital Halftoning