Verity IA - Stochastic Frequency Distribution Analysis Stochastic Frequency Distribution Analysis Created by Roy R. Rosenberger, Verity IA LLC [email protected].

Verity IA - Stochastic Frequency Distribution Analysis

Stochastic Frequency Distribution Analysis

Created by Roy R. Rosenberger, Verity IA LLC

[email protected]

Pattern Measurement


The Stochastic Frequency Distribution Analysis measurement algorithm has been applied to:

Patterns are pervasive!

Formation Transmitted Light

Formation X-rayPrufbau Strips

IGT Strips

Calender Blackening


Measurement Apparatus

Verity IA Pattern analysis software

Scanner with axially symmetric illumination

White faced specimen weight

Fast computer with 512 RAM

Scanner transmission tray with glass

specimen weight overlay

Scanners with axially symmetric illumination have proven to be the best for acquiring the large RGB digital images necessary to measure spatially distributed mottle.


Pattern MeasurementThe underlying algorithm for all applications is the stochastic Frequency Distribution Analysis (SFDA) developed by Verity IA. It is employed with different operation constants for the wide variety of patterns to which it is applied.

What is Stochastic Analysis?


Stochastic: Derives from the Greek, stochas, for target.

Imagine a target shoot with nine (9) marksmen.

Each marksman has the same number of shots: nine (9).

In this match, the marksman’s skill is determined by theStandard Deviation ( or Error) of the distance the marksman’s nine shots are from the center of the target.

10-8-6-4-2-0-2-4-6-8-10

Stochas


Statistically, the marksman’s skill is determined by the Standard Deviation (or Error) of the distance the marksman’s nine shots are from the center of the target.

The or Error for each target arranged as a 2D data array:

4, 6, 58, 4, 23, 3, 3

Each target score , 1 to n , is used to calculate the Standard Deviation , SD, and the Mean, X, ( or team score) for the group of targets.


In a digital image the target has 256 imaginary rings determined by the 8 bit luminance value for each picture point, where Black = 0 & White = 255.

As each arrow hits this target it strikes one of 256 rings and the score is recorded as a luminance value.

145145 120120 170170

180180 100100 145145

145145 170170 175175


Stochastic Distribution

Formation Magnified 15 x

1 - The square target area is moved across the image in a regular pattern of rows and columns to form a uniform 2D matrix.

3 - The Std. Dev. and Average of the target Differences are two of the three terms used compute the Pattern Measurement Number.

2 - The Differences among the picture point luminance values (LV) within each target is calculated and saved in a 2 D vector.


Stochastic Distribution

Statistical data from each target are saved in a 2D array for subsequent computation of overall Pattern Number.

Formation Magnified 15 x

The Area of Interest is covered with contiguous targets

The 2d array can also used to extract the horizontal (CD) and vertical (MD) variations

Directional orientation


Applying Stochastic Frequency Distribution Analysis

to Pattern Measurement


A, B & C have exactly the same number of each target luminance values (LV), but they are distributed differently within the inspection area.

ISO 13660 Mottle (A) = ISO 13660 Mottle (B) = ISO 13660 Mottle (C)

ISO 13660 provides the same number for each pattern.

Which image has the most distinctive pattern?

A B C


Y P

ixe

ls

X Pixels

Verity IA SFDA based Pattern Measurementworks on a digital image of any size and recognizes each pixel as a separate measurement unit.

Luminance Value (LV) is the digital value of the measurement element on a scale of 0 to 255

220

20

150

100

Tile, always 2 x 2


What characteristic differentiates these images?The transition in shade within a 2 x 2 target

Compute: Absolute Difference Among the area LV’s

* Absolute difference

{ *Abs (A – B) + Abs (A – C) + Abs (A – D) + Abs (B – C) + Abs (B – D) + Abs (C – D) }

Diff =

1 2 3

Each image has the same number of areas with the same LV.Count = 144

Compute: Gray Scale Luminance Value (LV) for each area in the 2 x 2 tile

D = 220

B = 120

C = 20

A = 160

D = 160

B = 20

C = 120

A = 220

D = 20

B = 20

C = 120

A = 220AD = The Absolute Pixel LV Difference, is proportional to the rate of change or transition from light to dark among the four (4) LV.

1 Diff = 640

2 Diff = 640

3 Diff = 700


Pattern Measurement

Calculate two properties of the 2 x 2 target

Each image has the same number of areas with the same LV.Count = 144

Absolute Pixel LV Difference (AD) & Average Pixel LV (M)

AD1 to 36

& M1 to 36

Use image #3 as example

Create two Data Files ¼ the size of source

AD AD AD AD AD AD

AD AD AD AD AD AD

AD AD AD AD AD AD

AD AD AD AD AD AD

AD AD AD AD AD AD

AD AD AD AD AD AD

Populate with results from each tile


Pattern Measurement – Basic Premise 2

AD1 to 36

& M1 to 36

AD AD AD AD AD AD

AD AD AD AD AD AD

AD AD AD AD AD AD

AD AD AD AD AD AD

AD AD AD AD AD AD

AD AD AD AD AD AD

Standard Deviation among the Differences:

AD

Average Difference:AveAD

Standard Deviation among the Averages:

M)

Populate data files with results from each tileWhere: AD = Absolute Difference among LV

M = Average of LV

(A Measure of transitions)

(Similar to ISO 13660 Mottle)

Layer X = AveAD X AD X M


Transitions within the Image:

The absolute difference in the luminance values among the four (4) picture elements within a 2 element x 2 element target is an index of the three dimensional rate of change. The standard deviation of these indices and their average are two terms in the Pattern Number calculation.

Spatial Luminance Variance (LV):

The average LV for these same four (4) picture elements is used to create a new element stored in a new data base ¼ the size of the original image. The standard deviation among these new elements is the spatial distribution component in the Pattern Number calculation.


Building the Target Size Layer

The four (4) elements within the tile are averaged together. These averages are then used to create a new virtual image or layer dedicated to the target size.

Each target in the new layer is twice the physical width & height of the original but remains 2 elements x 2 elements.


Spatial Distribution – Tile Physical Size – Limited by ImageY

Pix

els

X Pixels

Each Target is 2 Elements x 2 Elements based on the average of the previous layer 2 Element x 2 Element tile.

Based upon a digital image of any size, the method recognizes each pixel as a separate sensor.

Four target of this size will not fit in the image. The spatial measurement will be limited to the first four.

The target physical dimensions in each layer follow a binary progression. When overlaid on the original pixel image the tile sizes progress from:

2 pixels x 2 pixels in layer 1 to

1024 pixels by 1024 pixels in layer 10.The actual tile dimensions are resolved based upon the sensor calibration

or camera resolution, ppi, ppi.


Spatial Perception – Spatial Distribution 3 – Data Source Layers

Averaging the four data cells in the previous layer to create the new layer data cell suppresses the higher frequency variations present in the previous layer.

Original Pixel Image Layer 1 Layer 2

No more layers can be formed from this small image.Larger targets will not fit.


Building the Layers - Spatial Distribution

AD1 to 36

& M1 to 36

AD AD AD AD AD AD

AD AD AD AD AD AD

AD AD AD AD AD AD

AD AD AD AD AD AD

AD AD AD AD AD AD

AD AD AD AD AD AD

AD1 to 6

& M1 to 6

AD AD AD

AD AD AD

AD AD AD

MAveAD

xAD

x = Mottle# Tile X+1

AveAD x AD xM = Mottle# Tile Size X

The tile averages become the basis of the next layer (x+1) mottle measurement

Spatial Mottle Analysis

Layer X + 1(Original Scale)


Layer X(Original Scale)


Layer X - 1(Original Scale)

To Max of 10 Target Sizes


Spatial Distribution – Each Layer Dedicated to a Target Size

Layer 0 = Individual pixels of any size, resolution, or calibration

Layer 1 = Pixels grouped, 2 x 2 (2 pixels x 2 pixels)

Layer 2 = Layer 1 Averages grouped, 2 x 2 (4 p x 4 p)

Layer 3 = Layer 2 Averages grouped, 2 x 2 (8p x 8p)

Layer 4 = Layer 3 Ave. grouped, 2 x 2 (16p x 16p)

Layer 5 = Layer 4 Ave. grouped, 2 x 2 (32p x 32p)

Layers 6, 7, 8, 9, & 10 each grouped 2 x 2 to a maximum of 1024 pixels x 1024 pixels in the underlying image

To maximum of 10 layers with minimum of four (4) grouped data per layer. The last layer is the one that will allow a minimum of four (4) data cells to be created.

The target physical dimensions in each layer follow a binary progression. When overlaid on the original pixel image the tile sizes progress from:

2 pixels x 2 pixels in layer 1 to

1024 pixels by 1024 pixels in layer 10.The actual tile dimensions are resolved based upon the sensor calibration

or camera resolution, ppi, ppi.


Can we see the smallest 2 x 2 target?

Mottle is a function of viewing distance.

The digital image can contain patterns that are sub-visible as well those that are visible at normal viewing distance and those that are apparent only at a long distance.

• Sub-visible• Normal -Visible• Macro


Pattern Number CalculationPattern Number for the FULL range of tile sizes that will fit in a

typical digital image.

Sub-Visible

Normal Visible

Macro


Why disagreement with visual perception?

The human eye can visibly inspect a large image at various viewing distances and recognize a pattern. To do this we examine the frequency of luminance changes in all directions and form opinions as to their severity, spatial distribution, and physical size of recognizable objects.

The viewing distance directly influences our ability to identify some patterns. One cannot see the detail at 1 meter that one can see at 50 cm. But one can see at 50 cm all the detail that is visible at 1 meter. It is difficult for most viewers to compare one large area to another one unless they are contiguous.

In monochromatic images the human eye cannot see luminance variations as well as the sensors in the scanner’s camera. The SFDA algorithm is sensitive to the three dimensional variations in the spatial distribution.


Color Band (Channel) Analysis


Color – Digital Image - Basic component blends

Blue

Green

Red

Cyan

Magenta

Yellow

BlacK

White

The Variation Source - Diagnostics


Diagnostics - CMY Extraction

Reflected

Absorbed

Individually examine the effects of Cyan, Magenta, and Yellow Ink as:

–Reflected Components

–Absorbed Components

Camera and Scanner CCD array of sensors produce an RGB image.


Average of AllMottle: 34.87

Color BandExtracted

(Absorbed by:)

Red (Cyan)Mottle: 54.18

Green (Magenta)Mottle: 50.69

Blue (Yellow)Mottle: 74.04

Average of AllMottle: 19.15

Color BandExtracted

(Absorbed by:)

Red (Cyan)Mottle: 44.25

Green (Magenta)Mottle: 29.31

Blue (Yellow)Mottle: 39.63

Specimen #1 from Test 1 Specimen #1 from Test 2

Images enhanced: Interpolation = 12, Brightness gain = 85.


Pattern Measurement Theory

Stochastic Frequency Distribution Analysis

Created by Roy R. Rosenberger, Verity IA LLC

[email protected]


IGT A5 Wet Trap Test

An application of the method


IGT A5 Wet Trap Test Description – No Time Delay

The IGT A5 has two print heads. Each applies ink to the same print test strip in different but overlapping positions. The interval between each head application can be precisely controlled.

No Time Delay Wet Trap.First print head stops at ¾ point and with no time delay the second head starts at ¼ point. The second head finishes at full length while the first stops at the ¾ point.

Step 2 - 2nd Print Head - No Delay Wet Trap -

Step 1 - 1st Print Head Print Area

IGT Printed Paper Test Strip


IGT A5 Wet Trap Test Description –Time Delay

The IGT A5 has two print heads. Each applies ink to the same print test strip in different but overlapping positions. The interval between each head application can be precisely controlled.

Time Delay wet trap vs. No Delay Wet Trap.Print with time delay causes first print head to stop at mid-point and after a time delay the second head starts at ¼ point at the same time as the first head begins again at the mid-point. The second head finishes at full length while the first stops at ¾.

Step 1 - 1st Print Head Print Area

IGT Printed Paper Test Strip

Step 2 - Time Delay (Example: 6 Seconds)

Step 3 -B1st Head Restarted with 2nd Head- No Delay Wet Trap -

Step 3 –A 2nd Print Head - Time Delay Wet Trap -



Run a series of different time delays on a single paper specimen.

Arrange the test strips to for visual inspection and to acquire a digital image of the time delay areas.

Inspect and then acquire the digital image in full RGB color

9 Sec. Delay

6 Sec. Delay

3 Sec. Delay

No Delay

Example A5 Strip


IGT A5 Wet Trap Test Description –Time DelayVisual Inspection

Time delay over-print test run on same paper specimen at four (4) different time delays between first print and second print (over-print).

Three inspectors visually ranked results:

9 Sec. Delay

6 Sec. Delay

3 Sec. Delay

No Delay

Test For: …………………….. Date 7/17/02IGT A5 Test Cyan Ink Paper Grade: xxxxxx

Rank by Degree of MottleInspector #

1 2 3No Delay 1 1 1

3 Sec 2 2 26 sec 4 3 49 sec 3 4 3

Rank 1 : Best - Lowest Mottle: Rank 4 Worst - Highest Mottle



The inspectors do not agree on the rank of the two worst.

9 Sec. Delay

6 Sec. Delay

3 Sec. Delay

No Delay

Test For: …………………….. Date 7/17/02IGT A5 Test Cyan Ink Paper Grade: xxxxxx

Rank by Degree of MottleInspector #

1 2 3No Delay 1 1 1

3 Sec 2 2 26 sec 4 3 49 sec 3 4 3

Rank 1 : Best - Lowest Mottle: Rank 4 Worst - Highest Mottle

All inspectors agree that 6 & 9 are the worst.


Wet Trap – Variable time delay

9 Sec. Delay

6 Sec. Delay

3 Sec. Delay

No Delay

IGT A5 at RIT, Wet Trap Analysis: Overprinted sections of printed stripsscanned as single image at 300 ppi

Time delay –seconds 0 3 6 9

Mean Luminance

105

100

95

90

40

30

20

10Time delay –seconds 0 3 6 9

New Mottle #

Mottle = 13.3

Mottle = 19.6

Mottle = 33.5

Mottle = 27.4

Mean: 92.9 Mode: 92

Mean: 97.3 Mode: 97

Mean: 95.8 Mode: 95

The pixel luminance value statistical mode* for the 9 second is greater than the 6 second, thus more ink was transferred and it is possible the mottle level IS higher.* most populous luminance value

Mean: 102.4 Mode: 103


Wet Trap – Variable time delay

9 Sec. Delay

6 Sec. Delay

3 Sec. Delay

No Delay

IGT A5 at RIT, Wet Trap Analysis: Overprinted sections of printed stripsscanned as single image at 300 ppi

Mottle = 13.3

Mottle = 19.6

Mottle = 33.5

Mottle = 27.4


A typical mottle digital image example from a Back Trap / Water Interference Test

The image was acquired at 300 ppi and is 200 mm x 200 mm.

Zooming shows the individual pixels that make up the image.

The new mottle measurement is used in the measurement of back trap / water interference measurement at RIT.

2nd unit Cyan 6th unit Cyan

Side by side images of the 2nd unit and 6th unit cyan offset print made at the Rochester Institute of Technology, Rochester, NY.

For effective mottle measurement the digital image must be large enough and have only enough resolution to visibly demonstrate the mottle to be measured.


The process begins with a CMY extraction

300 ppi, RGB, side by side images of the 2nd unit and 6th unit cyan offset print made at the Rochester Institute of Technology, Rochester, NY.

Digital resolution need only be sufficient to visually replicate the mottle. As will be demonstrated, 300 ppi has been found to be good working resolution.

2nd unit Cyan 6th unit Cyan2nd unit Cyan 6th unit Cyan

Convert result to gray scale image

Original RGB image

RGB Band split

Cyan extraction


Diagnostics - CMY Extraction

• Example:

• Produce a solid blue by: – Print Solid Cyan– Overprint with Magenta

• Acquire full color (RGB) digital image of blue area

• Split digital image into individual RGB color images

• Recombine reflected components– Green + Blue = Cyan– Red + Blue = Magenta

+ =


The image tile concept: ISO 13660 5.2.3.1 & 5.2.4

ISO 13660 Mottle = ( M 1 to n )

[Standard deviation of the average pixel luminance values within each tile]

Minimum Rectangular Inspection Area >= 161 mm2 with a minimum Height and Width >= 12.7 mmand divided into (n) >= 100 non-overlapping square tiles

Each tile >= 1.61 mm2 with Height and Width >= 1.27 mm 600 spi H x W = 30 x 30: 300 spi H x W = 15 x 15

1.27 mm

1.27

mm

For each tile, compute the average (M)pixel luminance value (LV) of the pixels within it:

n = Total number of tiles

M 1 to n = Average Pixel Luminance Value(0 to 255)


Mottle Measurement Set-up Tile Size Range

Best : Mottle = 16.4 Worst: Mottle = 21.5

Before Clipping 10.8 mm tileBest : Mottle = 19.2 Worst: Mottle = 25.5

After Clipping 10.8 mm tileThe measurement is sensitized for the conditions in this test series


Spatial Distribution – Sub-Visible vs. Visible TilesThis method is based entirely upon the digital image resolution, calibration, spi, ppi.

When applied to its full range, the first tile is 2 pixels x 2 pixels regardless of resolution.

The division between visible and sub-visible tile dimensions is arbitrarily set at about 0.2 mm x 0.2 mm. On close inspection the eye can perceive a high contrast change in shade within this small square.

Typical tile dimensions at various resolutions:

The physical dimensions of the tiles in each layer determine if the tile is visible.

Tile Number & Width in MillimetersResolution

spi (ppi)Sensor Spacing 1 2 3 4 5 6 7 8 9 10

150 0.169 0.34 0.68 1.35 2.71 5.42 10.84 21.67 43.35 86.70 173.40300 0.085 0.17 0.34 0.68 1.35 2.71 5.42 10.84 21.67 43.35 86.70600 0.042 0.08 0.17 0.34 0.68 1.35 2.71 5.42 10.84 21.67 43.35

1000 0.025 0.05 0.10 0.20 0.41 0.81 1.63 3.25 6.50 13.00 26.012000 0.013 0.03 0.05 0.10 0.20 0.41 0.81 1.63 3.25 6.50 13.00

The method allows the division between visible and sub-visible to be selected.


Full Tile Size Range - Mottle – Cyan 2nd unit

300 spi (ppi) image with a selected area of the 2nd unit cyan, 85 mm x 195 mm

The full range of tile sizes applied to the 2nd unit cyan.

The tile size range that fits inside the selected area within the image

Full Range Average Mottle = 62.3

Mottle numbers for each tile size.



Application – Full Range Mottle – Cyan 2nd unit


The full range of tile sizes applied to the 2nd unit cyan.


Sub-Visible

Sub-Visible

Full Range Average Mottle = 62.3




Does the largest tile sense mottle?

Clipping the upper layers to constrain the measurement to sensitize measurement.


Application – Visible Range Mottle – Cyan 2nd unit


Visible range of tile sizes applied to the 2nd unit cyan


Visible Range Average Mottle = 16.2


The largest tile makes no contribution to mottle measurement in this image.

It could be eliminated from the mottle calculation to make it more responsive.

Eliminating 21.7 mm tile: Mottle = 19.3

Verity IA - Stochastic Frequency Distribution Analysis Stochastic Frequency Distribution Analysis Created by Roy R. Rosenberger, Verity IA LLC [email protected].

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