Grafisk produktion och Tryckkvalitet

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1 Grafisk produktion och Tryckkvalitet Rastrering och objektiva kvalitetsmått Sasan Gooran (VT 2007) Why halftoning? Original Halftoned Prepress Halftoning Print Digital Image Image Conventional Halftoning Halftone cell Original Image Halftoned image lpi: Number of halftone cells per inch Conventional, AM 1

2 Micro dot Halftone cell lpi: Number of halftone cells per inch dpi: Number of micro dots per inch AM & FM (1st & 2nd Generation) Halftone AM FM, 1st FM, 2nd AM & FM Halftone AM FM 2

3 FM Halftone, 1st and 2nd generation First Second Halftoning, thresholding Original Image Threshold Matrix Halftoned Image Halftoning, thresholding Threshold Matrices Clustered Line Spiral Dispersed

4 FM Halftone, Error Diffusion Threshold 0.5 Original Image Error Filter 7 (*1/16) Halftoned Image Error Diffusion The threshold value is 0.5 Suffers from artifacts, See specially the highlights and shadows and also the mid-tone regions Error Diffusion The threshold value is a random number between 0.25 and 0.75 Better? 4

5 Models of Visual Perception { (0.114 ) 1.1 } H ( f ) = 2.6( f )exp f f is the frequency in cycles/degree The spacing between the dots is given by: = τ = 2arctan( ) = degrees f 2Rd Rd π R is the printer resolution and d is the viewing distance. Models of Visual Perception Viewing distance, d = 30 inches Printer resolution, R = 300 dpi A simple Printer Model (Dot overlap Model) β γ T α β α α 2β α β β 2α γ 1 1 2α 1 α α 1 2α γ α 2β α β β α β b(j) b p(j) 1 p( j) = f α + f2β f3γ if b( j) = 1 b( ) = 0 1 if j 5

6 Least Square Model Based Algorithm g(original) EYE MODEL z b(binary) PRINTER MODEL EYE MODEL w 2, j j ) ε = ( z i w i j The squared error One way: Start with an initial binary image b. For each pixel (j) find the binary Value b(j) that minimizes ε. Iterative Method Controlling Dot Placement (IMCDP) Assumptions: The original continuous-tone image is scaled between 0 and 1 0 and 1 represent white and black respectively The binary/halftoned image is totally white to begin with IMCDP The mean of the density values of the original image corresponds to the area of the inked regions Original Image Binary Image The first dot is placed where the original image has its largest density value 6

7 IMCDP The impact of the placed dot is fed back to the original image by a filter Original Image Binary Image The next dot is placed where the modified image has its largest density value Iterative Halftoning, IMCDP Original IMCDP IMCDP(filter) A Gaussian filter is used Experiments show that an 11 x 11 Gaussian filter leads to satisfactory results in most cases The size of the filter should be changing for the light and dark parts of the original image 7

8 IMCDP(filter) For halftoning of a constant image with a coverage of p% the size of the filter is decided by: a = 100/ p The size of the filter is (2a + 1) x (2a + 1) rounded IMCDP(filter) 11 x 11 filter 21 x 21 filter IMCDP 8

9 Objektiva kvalitetsmått Objective Quality Measure (Halftone Images) Why difficult? A method that works well for certain kinds of images, might produce results of low quality for other images The definition of a good halftoning method may vary from application to application There might be a number of requests that cannot be formulated by a simple objective measure And so on Objective Quality Measure (Halftone Images) A number of criteria The original grayscale image and the binary image should be as similar as possible (How to define this similarity?) The black dots in the highlights (and the white dots in the shadows) should be placed homogeneously. In color case, the color should also be reproduced as accurate as possible And so on 9

10 A simple measure e = ( b( j) g( j)) j g is the original image and b is the resulting binary image 2 Which image b gives the lowest error e? SNR (Signal-to-Noise ratio) SNR( db) = 10log 10 ( j j g( j) ( g( j) b( j)) 2 2 ) SNR These kinds of measures are very easy to apply but they assume that the distortion is only caused by additive noise. These measures don t correlate well with our perceived visual quality 10

11 Quantization Noise Spectrum (QNS) The quantization noise is defined as: q( j) = g( j) b( j) The quantization noise spectrum (QNS) is defined as: Q( k, l) 2 Q is the 2-dimensional Fourier transform of q The smaller the quantization noise spectrum, the more similar b and g are. Similarity By similarity we mean the perceptual similarity. Since the eye acts as a low-pass filter it is desirable that the QNS is is small in the low pass region, that means: e = Ω Q( k, l) 2 is small Ω denotes a low-pass region. QNS (Example) g = 1/32 Error diffusion IMCDP 11

12 QNS The error e has been calculated for the images shown in previous slide when W is a circular low-pass region that occupy 12.5% of the image. The error is slightly smaller for the image halftoned by ED than the one by IMCDP!!!! Therefore: It is not only the magnitude of the QNS in the low-pass region that is important. The shape of QNS also plays a significant role. Desirable: A more or less circularly symmetric QNS with small magnitude in the low pass region QNS (Example) Error diffusion IMCDP QNS (Example) Error diffusion IMCDP 12

13 Homogeneousness One way of studying the characteristic of a halftoning method is to study the halftone patterns (tints) produced by the method. By a halftone pattern we mean the result of halftoning a constant image. We want the dots in the halftone pattern to be placed as homogeneously as possible over the entire image The set of distances from each dot to its closest dot gives a good picture of how close/far the dots in the halftone pattern are placed. The couple mean value and standard deviation of the data in this set can be used as a measure for homogeneousness of the pattern. (NOTE: Useful for very light and dark tones only) Desirable: Big mean value and small standard deviation Homogeneousness 11 x 11 filter 21 x 21 filter (Mean value, standard deviation)=(7.28, 1.19) for the image to the left and (8.76, 0.82) for the image to the right Frequency Response Original ED (Floyd & Steinberg filter) ED (Jarvis-Judice-Ninke filter) IMCDP The frequency is increased from left to right 13

14 Frequency Gain Use the original image in the previous page as the input image and Compute the frequency gain: G ( f ) = I I out in I out and I in are the Fourier transform of the output and the input Image, respectively. Desirable: G(f) is close to 1 at low frequencies. Frequency Gain ED (F & S) ED (J & J & N) IMCDP Frequency Gain From the previous diagrams we see that error diffusion methods have a tendency of high-pass filtering (edge enhancement) the original image The frequency gain for the image halftoned by IMCDP is very close to 1 at low frequencies The gain at higher frequencies are not of any particular interest because the eye is less sensitive there 14

15 Halftone Image Quality A method that works well for certain images, might produce results of low quality for other images. An image with two gray levels (0.49 in the left half and 0.5 in the right half) is halftoned by Floyd-Steinberg error diffusion Original image Error diffusion While the border between these two gray levels are hardly detected by the eye, it is emphasized by error diffusion because of a sudden change of pattern structure Color Halftoning NUEGEBAUER S Equations X X Y = a Y i i i Z Z i i a i i =1 X, Y, Z are the tristimulus values for the average color of a surface a i is the fractional area covered by color X i, Y i, Z i 15

16 DEMICHEL s Equations A w =(1-a c )(1-a m )(1-a y ) A c =a c (1-a m )(1-a y ) A m =a m (1-a c )(1-a y ) A y =a y (1-a c )(1-a m ) A r =a m a y (1-a c ) A g =a c a y (1-a m ) A b =a c a m (1-a y ) A k =a c a m a y Conventional Color Halftoning Same raster angle Error in position can cause color shift Conventional Color Halftoning Same raster angle Error in raster angle can cause Moiré 16

17 Conventional Color Halftoning Different raster angle, 0, 15, 75 and 45 degrees AM different angles Rosette patterns FM Color Halftoning A color image is normally halftoned by halftoning its color channels (separations) independently Since the color perception is very much dependent on how the separations behave in relation to each other, having a good structure of dot placement in each channel doesn t guarantee a good perception of the halftone color image, see the images in the next slide Color Halftoning, FM The color channels are halftoned independently in the image to the left while being halftoned dependently in the image to the right. Independent Dependent 17

18 IMCDP Color Halftoning C C M M Y Y IMCDP Color Halftoning 50% Cyan, 50% magenta 50% Cyan, 50% magenta Independent Dependent Dot-off-Dot Color Halftoning Dot-off-dot causes color shifts. This color shifts have to be compensated by using measurement data. The compensation is dependent on the printing system (printer, paper etc.) used to print the colors. 18

19 Color Compensation We look back at the example with 50% cyan, and 50% magenta. Our aim is to have the same color in both cases, i.e. Independent and dependent halftoning (dot-off-dot) In the independent case the dots are placed independently, hence Demichel s equations could be utilized, which meanse that in the image to the left we have 25% paper, 25% cyan, 25% magenta and 25% blue Knowing the tristimulus values (XYZ) for the white paper, primary and secondary colors we can find the color (XYZ values) of the image to the left, which we call the target color and denote by (Xt, Yt, Zt) The goal is now to find the coverage for cyan and magenta (denoted by cd and md respectively) in such a way that the image to the right has the same color as the one to the left Color Compensation The following equation system should be solved to find cd and md. X t = cd X c + md X m + (1 cd md ) X Yt = cdyc + mdym + (1 cd md ) Yp Zt = cd Zc + md Zm + (1 cd md ) Z p p Notice that it is assumed that cd+md is less than or equalt to 100% (or 1). Otherwise the expression to the right hand side of the above equation system is not valid Notice also that the above equation system has three equations And two unknowns. Color Halftoning 50% Cyan, 50% magenta 50.82% Cyan, 36.51% magenta Independent Dependent Notice! Compensation is done for Ink-Jet. For correct color reproductions the images should be printed using the same Ink-Jet. 19

20 Dependent Halftoning (dot-off-dot) The yellow channel can be halftoned independent of the two others (?!) c och m denote the coverage for cyan and magenta. c + m <= 1, dot-on-dot can be avoided c + m > 1, Blue dots occur Dependent Halftoning (dot-off-dot) c + m >1, Blue dots occur b= c+m-1 (Coverage of blue) c =c-b=1-m och m =m-b=1-c => c +m <1 Halftone c and m as before Replace the white dots with blue Dependent Halftoning vs. Independent 20

21 Independent Dependent Homogeneousness in color patterns The dots should be placed homogenously over the entire halftoned color image To use the homogeneousness measure for grayscale halftone patterns perform a logical OR (if the dots are represented by 1) or a logical AND (if the dots are represented by 0) between the color channels By doing that you get a black and white halftone pattern for which you can use the measure defined previously 21

22 Homogeneousness in color patterns (Mean value, Standard deviation) (2.69, 1.06) (3.95, 0.37) 22