1. Background |
| Reflective uniformity is what printers and paper manufacturers both strive to achieve. When that goal is missed, one of the resulting visual appearances may be mottle. Mottle is very complex in its many causes and difficult to describe from observation because of its many variations. |
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The term mottle is not limited to use in the printing and paper industries. Furniture manufacturers use mottle to describe the many grains of wood. Biologists have used mottle to describe the patterns found in butterfly wings. Botanists use mottle to describe cell structures in leaves. Mottle even has one definition for papermakers and another for printers; however, the end user makes no distinction between the two.
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Mottle has been described as, "an unwanted laterally varying reflectivity in homogeneous tone areas that expresses itself as stochastic 'cloudiness' or 'graininess' or sometimes in more ordered patterns. It is not visible in text areas, hardly visible in 'busy' images rich in detail, but may be clearly visible in calmer image parts like skies or homogeneous background tone plates" (Johansson, 1992).
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| Figure 1 - A Mottled Print Example |
| In response to a need in the market place to be able to quantify mottle, Apogee Systems, Inc. is developing an image analysis system that uses a flatbed scanner to capture images and measure mottle. This article provides an overview of mottle, establishes a framework for quantifying mottle and describes how the method measures an image and calculates mottle. |
2. Types and Causes of Mottle
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While the description of mottle as non-uniform reflection seems simple, it belies the complexity of the processes in light reflectance and human perception of uniformity of reflection. First, consider the reflection of light from a printed surface. When a printed sample is perceived as being flat and solid, the light is thought of as being totally reflected from the surface, but this is not true. All surfaces, metal, plastic, or paper are rough, with pits and holes. Coatings such as clay and ink partially fill some of these pits while laying on top of other features. Light waves penetrate into the sample's surface. Some are absorbed by the substrate, and converted into heat, while others are reflected once or many times before exiting the surface. Some waves may pass entirely through the sheet. Light waves can also pass through the ink, the substrate, bouncing off whatever lies behind the sheet, and pass back through the sheet and ink before reaching our eyes. Any variation in the ink density, the substrate density, the reflectance of either, or the background can cause apparent mottling of the image.
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The geometry and physics of light reflection from a sheet can have a dramatic influence on apparent mottling. While we normally think of paper and printed surfaces as diffuse reflectors, that is, they scatter light equally in all directions, regardless of the angle of the incident light, no surface is perfectly diffuse. Paper and printed areas both scatter incident light and also have a specular reflection like that of a mirror. Some portions of light are reflected at a predictable angle, usually an angle equal and opposite to the angle of incidence. Small waves, wrinkles, cockling or surface textures in the sheet can cause the specular reflections to appear as variations in the reflection. Surface textures can even create "corner reflectors," highly specular areas where the light intensity appears to be magnified.
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Limiting the discussion to only those effects that are truly variations in the reflection of a printed surface still leaves a wide variety of print related processes which can create a mottled appearance. Mottling of print can be caused by paper, ink, converting, and press-related problems, and is most often a result of several of these factors interacting simultaneously. Numerous sources and types of mottle have been described in the literature.
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Paper formation and surface characteristics cause the most basic set of mottle types. Variations in the density, surface smoothness, fiber content, fines, filler content, sizing, surface pH, and specific energy of the paper can have a dramatic influence on the ability of an ink to transfer onto the surface, its absorbency, wicking, penetration, and drying characteristics. Uneven fiber distribution within the sheet (formation) is often at the root of these effects since the formation also influences the retention of fines and additives. A poor mass distribution also has a negative influence on the light scattering coefficient of the paper as well as its opacity (Norman, 1973). |
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Backtrap Mottle - The ink's inability to transfer from the print blanket to the paper. Typically caused when the ink is unstable or the solvent/oil is lost too quickly, any non-uniformity in the ink transfer rate can create a mottled appearance. Backtrap mottle usually appears in first down inks, and is sometimes a result of improper ink pH or viscosity for the paper being used. Low viscosity inks sometimes produce an appearance called "orange peel," named for the pattern that the ink creates (Sandreuter, 1994). |
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Water Interference Mottle (WIM) - paper does not absorb the fountain solution reducing the ink's ability to transfer to paper. Typically, WIM is caused by excessive water, improper ink formulation, inadequately mixed solutions, or excessive alcohol (Sandreuter, 1994). |
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Wet Ink Trap Mottle - an incorrect ink tack or pH sequence. Usually a second down ink appears mottled when it is printed over a first down ink, but appears unmottled when printed alone on the substrate (Sandreuter, 1994). |
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Density Mottle - uneven pressures between metal type, gravure cylinder or offset blanket and paper. Not as common in lithography, but can be seen as a result of a smashed blanket (The Mead Corporation [Mead], 1992). |
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Gloss Mottle - an uneven ink surface characteristic not immediately evident at printing. Caused by paper's non-uniform absorption resulting in portions of the ink to appear glossy and others matte. Ink improperly formulated for a particular paper is also a contributor to gloss mottle (Mead, 1992). |
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Dry Trap Mottle - called crystallization, this occurs because of excessive dry time between runs of a multicolor job on a single color press or improper wax content in a set of ink. As ink dries, wax migrates to the top surface. Excessive wax migration to a dried ink surface can make the adhesion of subsequent inks difficult because the surface becomes slippery, hard and smooth (Williams, 1985). |
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Finally, variations in impression caused by incorrectly mounted plates, press bounce, drive gear marks, fluting, etc. can cause the print surface to appear mottled. Mottle from paper surface characteristics is normally a stochastic process and usually effects all inks equally, while the ink transfer functions are random but tend to effect some inks more than others. Impression-caused variations are often regular and predictable from sheet to sheet and lend themselves to isolation in a frequency domain.
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3. Quantification of Mottle
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| From an image analysis perspective, the phenomena we refer to as mottle is composed of at least two independent effects. The two processes act together, most likely in a non-linear way, to create the sensation we refer to as mottling. Based on our definition for mottle, if we segregate the areas of the printed image into areas which are darker (less reflection than the median), and areas that are lighter (greater reflection), mottle is then the variation between these two groups. For purposes of clarity, we will refer to the areas of a sample which are lighter or darker than the median gray tone as "patches." They are also sometimes called blotches, clumps, flocs (of fiber) or light-weight areas (LWA). Regardless of the name, these patches can be described in two ways, their size and their variation from the median. Figure 2 depicts some of these terms. We perceive both light and dark patches on a sample because the patches are different from the area around them. The size and contrast between these patches cause the "graininess" of a mottled sample. |
 Figure 2 - Mottling patches and Perimeters |
| The differences between apparent mottle conditions and the effect of size and contrast are shown in Figure 3. Nine conceptual examples of mottling are shown in the synthetic image. Each sample is exactly 100 pixels in each dimension with the squares representing lighter and darker mottle patches. The size and contrast variations are shown in the nine patches as follows: |
Figure 3 - A conceptual example of mottle |
| • Size of the patches varies from left to right in the three sets of images, from 25 to 10 to 5 pixels per patch |
| • Contrast between the patches varies from top to bottom across the sets, from a contrast of 128, to 64, to 32 grayscale values. |
| Note that as we progress to the lower right, the sensation or severity of the mottling is reduced. If we extend this trend, it is clear that if the contrast between the light and dark patches is reduced far enough or if we reduce the size of the patches far enough, we will no longer perceive them as mottled. Likewise, if the patches become large enough to encompass the entire printed area in one patch or so that the eye does not perceive the area as broken into parts, we will not think of them as mottled. In reality, this is exactly what happens. All print areas are mottled to some degree, but if the patch areas are small, and/or the contrast between them is small, we are less likely to perceive them as mottled. |
Thus, if there is little contrast between the light areas and dark areas, the size of the patches is unimportant. On the other hand, if the patches are small, the contrast becomes unimportant since the eye integrates the patches and perceives a solid print area. Small patches with large contrast is very similar to screen tinting process colors creating the illusion of a solid color.
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| 4. Acquiring a digital image of the sample |
| In our method, a desktop scanner is used to acquire an image of the sample, and a desktop PC then applies a series of image analysis algorithms to produce quantitative measures of various aspects of the print quality. The digitized image is simply a two dimensional matrix of picture elements or pixels. The scanner generates a numerical measurement of the reflectance for each pixel. The reflectance is represented as a number between 0 and 255, where 0 indicates black or very little light is reflected (an optical density of about 3.0), while 255 is a 100% diffuse reflector (an optical density of 0.0). This measure of reflection is referred to as gray scale values (gsv). |
| Mottling can come from a wide variety of causes, many of which are not directly related to the printability of the substrate or the ink. The scanner's 45/0 geometry tightly controls the angle and intensity of the light and the background behind the sample so that mottle measurements from the scanner correctly reflect the printability of substrate and ink. |
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The size of the pixels are defined by the resolution of the image, 100 dpi (dots per inch) implies 100 pixels per inch in each direction. The gray scale value of each pixel, measuring the reflectance in that area, is stored as a byte in the computer, thus an 8 1/2 x 11-inch sheet, digitized at 300dpi becomes a 8.4MB file on the computer.
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Figure 4 - A digital image of a print sample |
| Often the image is scanned as a color image rather than as a gray scale image. Color scanning is based on the RGB system. Each pixel scanned in color is described by three numbers, one for the red light reflecting from the surface, one for the green reflection, and one for the blue reflection. Each of the values are represented as a number between 0 and 255 and are converted to gray scale before analysis. The most common scheme for converting RGB values to gray scale uses the equation, gsv = A*red+B*green+c*blue (red, green, and blue are the reflective values in each channel, and A=0.30, B=0.60, C=0.10), from the parameters set by the National Television Standards Committee (NTSC). |
Our method defaults to these values, but they may be modified to favor one color over another. Once the image is acquired, we must then measure the size of the mottle patches and their relative contrasts.
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| 5. Specific Perimeter: measuring patch size |
| Several algorithms or schemes have been proposed for measuring the size or texture of the patches, including: |
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Specific Perimeter defined by Jordan and Nguyen (1986) measures the size of the patches directly by counting the pixel lengths that constitute the perimeters of the patches. |
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Co-occurrence matrices defined by Ness and Göttshing (1993) is a pixel-to-pixel correlation calculation that measures the likelihood that a pixel is similar to the pixels around it |
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Autocorrelation, Fourier, and Band-pass filter analysis has been proposed by several authors, including Johansson (1992). This technique captures the frequency or wavelength of the variations in the sheet. |
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| Specific perimeter tends to be entirely independent of the range of density variations and measures only the sizes of the patches, while most other methods include at least some degree of density variation dependence. For that reason, specific perimeter is used in our method. |
| The specific perimeter (SP) of an image is the length of the outline of the features of an image when it is bisected at its median gray scale value (Jordan and Nguyen, 1986). Figures 5a, 5b, and 5c illustrate this concept. First, the gray scale histogram of the image pixels is created and the median value is determined. The median is defined as the gray scale value at which the gray scale values of half of the pixels are less than this value and half are greater. |
| Note that the median value is used rather than the mathematical average, because the median is not influenced by widely scattered variations in the gray scale density values. Figure 5a is a gray scale image that is exactly 10 pixels square, and Figure 5b is the gray scale histogram of the 100 pixels. The median value is exactly 127.5 because half of the pixels have grayscale values greater than 127.5 and half have a gsv less than 127.5. |
Figure 5a - A small gray scale image |
Figure 5b - Histogram of the gray values in the small gray scale image |
Figure 5c - Image after binary detection at the median value of the small gray scale image |
| Detecting Figure 5a at the median results in the binary image Figure 5c. From Figure 5c, it is an easy matter to add the pixel lengths to compute the perimeter. The patches in Figure 5c have a total perimeter of 84. Note that we include half of the perimeter of the image to account for the remainder of the patches outside the image. To calculate specific perimeter, we normalize the perimeter by the area of the sample, i.e. 100, so in this case, the specific perimeter becomes 0.84. |
Figure 6 - Specific perimeter equation |
| Ix and Iy are the width and length of a pixel and the summations in the numerator are along the boundaries of the perimeter of the patches. Lx and Ly are the length and width of the image and by multiplying them together, in the denominator, creates a measure of the image area. |
| Note that the above calculation was done in pixels; however, in reality, the calculation should include the resolution of the image pixels, see Figure 7. |
Figure 7 - Specific perimeter equation including resolution |
| Dx and Dy are the pixel dimension, e.g. mm. per pixel. |
| Assuming that the x and y pixel dimensions are the same, then the equation can be simplified, Figure 8. |
Figure 8 - Simplified specific perimeter equation |
| R is the resolution in pixels per mm (i.e. R=1/D). |
| If the pixel dimensions are measured in millimeters per pixel, then the specific perimeter will be in units of mm-1. |
| It should be clear at this point that as the patches get smaller, the number of patches will grow as well as the total perimeter. As the patches become smaller, the specific perimeter approaches a theoretical limit of 2/D or 2R. |
| Referring back to Figure 3, we can easily compute the perimeter of the patches as 800, 2000, and 4000 pixels for each of the three columns of images. Dividing by the area of the image (100x100 = 10000 pixels), yields 800/10000, 2000/10000, and 4000/10000, or 0.08, 0.20, and 0.40. As expected, the specific perimeter is larger for finer grained (smaller) patches. Also note that the SP is independent of the gray values and the medians of the three rows in Figure 3; the specific perimeter values remain unchanged with gray scale. Assuming that Figure 3 was created at 50dpi (.508 mm/pixel), the specific perimeters become 0.157 (0.08/0.508), 0.394, and 0.787 respectively. |
Figure 9 - Estimating the average area of the patches |
| This equation is important in that it demonstrates the close relationship between specific perimeter and patch area, and allows us to estimate the average patch area in square millimeters from the specific perimeter. Of course, in a real sample, the patches would not be a checkerboard pattern as shown in Figure 3, but the equation in Figure 9 is still a reasonable estimate of the patch sizes. Using the equation in Figure 9 to estimate the area of the upper left patch in Figure 3 produces the following result. |
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| When Figure 3 was created, each patch was 25 pixels in each dimension or 625 pixels. Converting the above estimated area to pixels, assuming a scanner resolution of 50dpi, demonstrates the accuracy of the estimate: |
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The slight error in the above calculation is due to round off in computing the specific perimeter.
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6. Coefficient of Variance: measuring contrast
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Numerous techniques could be used to estimate the differences in gray density between the dark and light patches; however, the statistical coefficient of variance is the most common and statistically valid. Simply, it is the standard deviation divided by the mean of the gray values
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Figure 10 - A typical gray scale histogram |
| The standard deviation (designated s) is defined as the square root of the squares of the distances of each pixel's gray value from the mean gray value. The standard deviation is in units of gray value, and effectively measures the width of the histogram such that 68% of the pixels are between the range of ±1s gray values from the mean, see Figure 11. |
Figure 11 - Standard Deviation |
| Dividing the standard deviation by the mean normalizes it from variations in the mean. The coefficient of variation is by equation in Figure 12. |
Figure 12 - Coefficient of Variation |
The coefficient of variation thus unitless and is sometimes treated as percent deviation, i.e. cov*100%.
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| 7. Gray Span: another measure of contrast |
| Coefficient of variation is hard to visualize. Hence, we also measure the gray span. When we compute the specific perimeter, we divide the gray scale histogram around the median value. If we simply average the gray values of all of the pixels whose gray values are less than the median, we produce a measure of the average dark patch. Likewise, averaging all of the pixels whose gray values are greater than the median produces a measure of the lightness of the average light pixel. The difference between these is the gray span and is similar to the COV as a measure of the width of the gray scale distribution. If the distribution is Gaussian, the gray span is approximately 1.6*s. |
| 8. Mottle Index: combines size and contrast measures |
| Following the suggestions of Neb (1992), our method computes a mottle index which combines both the specific perimeter and the gray scale coefficient of variation. See Figure 13 |
Figure 13 - Mottle index (MI) |
| As the distribution of gray values gets wider, that is, there is more contrast between the light patches and the dark patches, the COV gets larger as does the MI. As the patches get larger, the specific perimeter gets smaller, and again the mottle index increases. The mottle index thus is smaller for samples with little mottle and larger for samples showing significant mottle. Table 1 may make these relationships clearer. |
| Finally in an attempt to put the mottle index in context, we return to Figure 3. As described before, the three columns vary the size of the patches, while the three rows of images vary the contrast. The image is repeated here with the COV, SP, and MI values inserted below each patch, including the assumption that the image was digitized at 50dpi (0.508 mm/pixel). |
| Table 1 – Expected Mottle Values |
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COV
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SP
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MI
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Good Print
Little Mottle
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Small
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Large
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Small
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Fair Print
Large Patches
Little Contrast
Some Mottle
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Small
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Small
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Moderate
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Fair Print
Small Patches
Large Contrast
Some Mottle
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Large
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Large
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Moderate
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Poor Print
Large Patches
Large Contrast
Severe Mottle
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Large
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Small
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Large
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Figure 14 - Sample Mottle Values |
| 9. Conclusion |
| The method we have described seems to capture the pertinent variables in quantifying mottle and has the beauty of being conceptually simple to understand. Tests on numerous printed samples and on evaluations of coated board finishes have demonstrated that the Mottle Index described above is highly correlated to the perceptions of human judges. |
Apogee Systems has implemented this method into commercially available software product called Spec*Print. This product is a collection of several analytic tools that measure various aspects of the print quality of samples, including mottle, color, cross/down-machine analysis, barcodes, wicking, bleed, and trap analysis.
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| References |
| Johansson, Per-Åke (1992). Print mottle evaluation by band-pass image analysis. STFI Swedish Pulp and Paper Research Institute. Stockholm, Sweden. |
| Jordan, B. D. and Nguyen, N. G. (1986). Specific perimeter - a graininess parameter for formation and print-mottle textures. Paperi ja Puu 6-7. 476-482. |
| Ness, C. and Göttsching, L. (1993). Formation of Paper and Mottling of Solid Prints. Institut für Papierfabrikation, Darmstadt Germany |
| Neß, C. Praast, H., Renner, U., Göttsching, L., Papp, J. (1992). Formation von Graphischen Papieren und Gleighmaßighejt der Druckwiedergabe (Mottling). Das Papier 46:11. 641-651. |
| Norman, B. and Wahren, D. (1973). Mass distributions and sheet properties of paper. In Bolam, F. (Ed.) The fundemental properties of paper related to its users. Translations of the Symposium held at Cambridge. (1973). 7-73. |
| Sandreuter, N. P. (1994). Predicting print mottle: a method of differentiating between three types of mottle. Tappi Journal, 77:7, 173-184. |
| The Mead Corporation. (1992). Printed mottle: Density mottle, gloss mottle, back trap mottle, trapping mottle. Paper and the graphic arts: A bulletin from the graphic arts technology department. Dayton, Ohio: Author. |
Williams, R. L. (1985). Paper & ink relationships. Manhattan, Kansas: Roger L. Williams.
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