day 2 - unibas.ch · plan day 1 - 'look at the data' • scale, calibrate, re-size,...

plan

DAY 1 - 'look at the data'• scale, calibrate, re-size, visualize• histograms, profiles, LUTs• morphological operations• from element maps to phase maps• volume estimates

DAY 2 - 'image analysis basics'• segmentation image → bitmap

POP, NOP, edge detectors• image analysis of segments, best fit ellipses• re-direct sampling• property mapping• texture mapping

DAY 3 - 'all about grain size'• 2D grain size / grain size distribution• 3D grain size / grain size distribution• fractal grain size distribution

DAY 4 - 'all about shape'• paror - orientation of particles• surfor - orientation of surface• ishapes - shapedescriptors

DAY 5 - 'spatial aspects'• FFT - spatial frequencies• ACF - neighbourhood relations• spatial distributions

segmentation

steps in image analysis

recording

analysis

1

23

4

etc.


recording

analysis

1

2

34 etc.

segmentation

recording

analysis


pre-processing

segmentation

post-processing

image models

models

images

thresholding

segmentation based on image model

grey levelslicing

edgedetection

post-processingranking filters

structural filtering

segmentation: point operation

step 1segmentationbasis = grey value (Z)⇒ bitmap

step 2 structural filtering

Z X

Y

segmentation: neighboorhood operation

high

low

step 1 segmentationbasis = neighboorhood (X,Y)⇒ grey scale image

step 2 thresholding - structural filtering

Z X

Y

ranking filters I

original

minimum median maximum

0 0 0 1 1 1 1 1 1


ranked grey values of 3x3 neighbourhood

original


0 0 0 0 0 0 0 0 1



ranking filters I

original

0 1 1 1 1 1 1 1 1




ranking filters I

original

ranking filters I

median minimum maximum

40 25 23

25 10 15

13 1 5

original

ranking filters I for gray scale images


1 5 10 13 15 23 25 25 40



original median minimum maximum

ranking filters I for gray scale images

original set count:1 - erode if 1 is white2 - erode if 2 are whiteetc.

set count:1 - dilate if 1 is black2 - dilate if 2 are blacketc.


ranking filters II

definition of neighbouring pixels

original

Set Count:1 - erode if 1 of 9 is white2 - erode if 2 of 9 are white....8 - erode if 8 of 9 are white

Set Count:1 - dilate if 1 of 9 is black2 - dilate if 2 of 9 are black....8 - dilate if 8 of 9 are black

strength of operation:

WEAK

STRONG

ranking filters II


original

erode 7 erode 5 erode 3 erode 1

erosion

ranking filters II

original

dilate 7 dilate 5 dilate 3 dilate 1

dilation

ranking filters II

original

= opening = closing

1. erode2. dilate

1. dilate2. erode

morphological operations

original ultimate points

distance map watershed

morphological operations

logical operations

Logical operations on bitmaps

AND1 0

1 1 00 0 0

1 01 1 10 1 0

1 01 0 10 1 0

1 01 1 00 1 0

image 1

image 1 image 2

imag

e 2

OR

XOR

COPY

(1∪2)

(1∩2)

(1|2)

image addition

1 + 2

1 to 2

COPY 1 to 2

1 AND 2 1 OR 2 1 XOR 2

image 1

- copy & paste control- Image Math...

image 2

Adding two images

shifted copy of 1

shift copy:Δx=+2 Δy=-2

image 1

Adding image and copy of image

1 AND 1 1 OR 1 1 XOR 1

exerciseerode dilate...

exercise

1. open Truzzo2. pre-process (noise) - background - re-size - crop3. background correction4. save

5. Lazy LUT: perform contiguous segmentation 6. make stack of 6 phases7. start pots-processing: morphological filtering

Lazy erodedilate

Macro: Jazy erodilate (imageJ)

post-processingclean up

segmentation

manual cleaning

phase map

invert: phase mask

original

increase brightness

cleaning in stack using phase masks

phase mask + brightness

added OR

continue manualcorrections

thresholdinvert

merge mask and light version

grain maps

z-project/average: 1-5

procedure 1: separate grains ...

4

2 3

6

1

5

yields grain boundaries

grain maps

... derive grain boundaries

4

2 3

6

1

5

using colored grain maps

minimum filter

phase map: no grain boundaries

grain map: grain boundaries = 'phase'

derive phase map from grain map

phase maps

average all(incl. holes & unidentified)

procedure 2: separate phases ...

4

2 3

6

1

5

phase maps

erode phasesaverage

... derive phase boundaries

4

2 3

6

1

5

phase mapgrain map

segmentation based on Z

25 78 106 158 200

originalDensity Slicing = contiguous grey values

Z X

Y

Segments and segment boundaryContiguous areas = spatially contiguous

phase map

10 63 18187 150

255

250 10 63 18187 150

255

250

grain mapphase map

post-processing yields:

compare segmentations

qtz = 26.8%qtz = 28.8%qtz = 29.7%

phase- grain- grain boundary maps

phase phase map6 phases (%)

grain + gb map 7 phases (%)

grain map 5 phases (%)

number of grains

biotite 7.7 6.6 7.3 15

K-feldspar 20.8 18.9 20.7 32

muscovite 2.4 2.0 2.2 7

plagioclase 40.1 36.9 40.4 66

quartz 28.8 26.8 29.4 47

rest 0.13 0.08

grain b 8.7

sum 100.0 100.0 100.0 167

biotite K-feldspar muscovite

plagioclase quartz unidentified

phase boundaries

phase vs. grain boundary maps

all boundaries phase boundaries only

grain boundaries sensu strictu

neighbourhood operations

(NOP)

i-1 / j-1 i / j-1 i+1 / j-1

i-1 / j i / j i+1 / j

i-1 / j+1 i / j+1 i+1 / j+1

3 x 3 neighborhood

introductory example: moving average166 89 72 89 79 82 139 84 22 44 99 131 156 183 193 168

102 49 39 51 62 70 72 31 22 56 124 161 180 205 212 190

70 34 31 62 65 107 114 70 56 72 114 143 180 205 207 171

44 29 24 44 124 92 67 70 56 46 60 151 226 188 141 99

31 29 7 14 84 39 14 27 24 44 114 126 236 219 107 67

24 39 22 9 12 27 19 29 19 54 109 89 183 255 193 97

24 27 24 17 17 39 75 102 82 94 126 141 168 231 231 178

22 22 27 36 19 29 114 121 121 141 168 168 193 207 200 166

19 22 36 41 17 22 60 75 116 107 87 161 193 188 156 129

17 24 56 54 17 14 94 158 97 79 82 89 126 134 119 111

14 27 27 9 12 19 84 156 77 75 102 60 79 104 97 84

12 17 9 2 19 29 54 114 87 89 109 79 79 67 72 94

14 17 14 41 77 99 131 178 151 153 168 139 121 75 65 82

27 36 72 129 156 158 163 200 180 175 195 180 136 49 17 17

29 54 134 180 188 180 158 168 195 190 183 146 107 22 0 2

24 36 97 148 163 175 171 161 168 173 143 99 67 12 7 7

101 86 64 65 72 84 79 61 43 61 102 141 169 188 191 190

85 72 57 61 74 87 85 67 50 67 104 143 171 191 192 190

54 46 40 55 75 85 77 62 53 67 103 148 182 193 179 170

39 33 30 50 70 78 66 55 51 65 96 150 186 189 156 132

32 27 24 37 49 53 42 36 41 58 88 143 185 194 151 117

29 25 20 22 28 36 41 43 52 74 99 143 183 202 175 145

26 25 24 20 22 39 61 75 84 101 121 149 181 206 195 177

22 24 28 26 26 43 70 96 106 115 132 156 183 196 187 176

21 27 35 33 27 42 76 106 112 110 120 140 162 168 156 146

20 26 32 29 22 37 75 101 104 91 93 108 126 132 124 116

18 22 25 22 19 38 80 102 103 88 84 89 90 97 98 96

16 16 18 23 34 58 96 114 120 112 108 104 89 84 82 82

20 24 37 57 78 98 125 139 147 145 143 134 102 75 59 57

29 44 75 110 134 145 159 169 176 176 169 152 108 65 36 30

34 56 98 140 164 168 170 173 178 178 164 139 90 46 14 8

35 62 108 151 172 172 168 170 175 175 155 124 75 35 8 4

30 25 23

25 10 15

13 1 5

10 15

1/9 1/9 1/9

1/9 1/9 1/9

1/9 1/9 1/9

= 1/9· [30 + 25 + ... 5] = 15

1 1 1

1 1 1

1 1 1

·1/9· =

30 25 23

25 10 15

13 1 5

example: moving average

neighborhood operations

averaging filters

3 by 3 moving average

1 1 11 1 11 1 1

≠ median

moving average

0 1 0

1 1 1

0 1 0

1 0 1

0 1 0

1 0 1

influence of shape

1 1 1 1 1 1 1

1 1 1 1 1 1 11 1 1 1 1 1 1

1 1 1 1 1 1 1

1 1 1 1 1 1 1

1 1 1 1 1 1 1

1 1 1 1 1 1 1

influence of size

Gaussian

1 1 2 1 1

1 2 4 2 1

2 4 8 4 2

1 2 4 2 1

1 1 2 1 1

2 2 3 4 5 5 6 6 6 5 5 4 3 2 2

2 3 4 5 7 7 8 8 8 7 7 5 4 3 2

3 4 6 7 9 10 10 11 10 10 9 7 6 4 3

4 5 7 9 10 12 13 13 13 12 10 9 7 5 4

5 7 9 11 13 14 15 16 15 14 13 11 9 7 5

5 7 10 12 14 16 17 18 17 16 14 12 10 7 5

6 8 10 13 15 17 19 19 19 17 15 13 10 8 6

6 8 11 13 16 18 19 20 19 18 16 13 11 8 6

6 8 10 13 15 17 19 19 19 17 15 13 10 8 6

5 7 10 12 14 16 17 18 17 16 14 12 10 7 5

5 7 9 11 13 14 15 16 15 14 13 11 9 7 5

4 5 7 9 10 12 13 13 13 12 10 9 7 5 4

3 4 6 7 9 10 10 11 10 10 9 7 6 4 3

2 3 4 5 7 7 8 8 8 7 7 5 4 3 2

2 2 3 4 5 5 6 6 6 5 5 4 3 2 2

(5x5)

(15x15)

linear filters

5.2 Linear Filters 107

L

L

M

N

KK

H

I

u

v

no coverage

full coverage

Figure 5.7 Border geometry. The filter can be applied only at locations (u, v) where thefilter matrix H of size (2K+1) × (2L+1) is fully contained in the image (inner rectangle).

0

0

0

1

0

1

1

0

1

1

0

0

0

0

0 0 0 0

0 1 1 1 0

0 1

0

1

0

3

1

9

5

2

5

3

1

2

1

0

1 2 1 0

1 3 5 3 1

2 5

0

0

0

-1

0

16

-2

-1

-2

-1

0

-1

0

0

0 -1 0 0

0 -1 -2 -1 0

-1 -2

(a) (b) (c)

Figure 5.8 Typical examples of linear filters, illustrated as 3D plots (top), profiles (center),and approximations by discrete filter matrices (bottom). The “box” filter (a) and the Gaussfilter (b) are both smoothing filters with all-positive coefficients. The “Laplace” or “Mexicanhat” filter (c) is a difference filter. It computes the weighted difference between the centerpixel and the surrounding pixels and thus reacts most strongly to local intensity peaks.

gradient filters

gradient filters

0 -.5 0

0 0 0

0 .5 0

0 0 0

-0.5 0 0.5

0 0 0

0 0 0

0.5 0 -0.5

0 0 0

0 .5 0

0 0 0

0 -.5 0

maxim

um o

f 4

(average of 4)

0 0 00 1 -10 0 0

0 0 01 0 -10 0 0

influence of separation

E-W difference

-1 0 1-1 0 1-1 0 1

-1 -1 -10 0 01 1 1

influence of direction

Shadows

0 0 -10 1 00 0 0

0 -1 00 0 10 0 0

Robert's cross 2 x 2 (gradient / 1st derivative)

- maximum of 4 gradient images- thresholding

Robert's cross 2 x 2 (gradient / 1st derivative)

maximum of 8 directions

Sobel operator

1 2 10 0 0-1 -2 -1

1 0 -12 0 -21 0 -1

-1 -2 -10 0 01 2 1

-1 0 1-2 0 2-1 0 1

-2 -1 0-1 0 10 1 2

0 1 2-1 0 1-2 -1 0

2 1 01 0 -10 -1 -2

0 -1 -21 0 -12 1 0

(1st derivative)

Sobel 3x3

hand-made Sobel

Find edges 5x5

Roberts Cross

0 1 0

1 -4 1

0 1 0

1 1 1

1 -8 1

1 1 1

Laplace operator (2nd derivative)

1 1 1 1 11 1 1 1 1

1 1 -24 1 11 1 1 1 1

1 1 1 1 1

original

-1 -1 -1 -1 -1-1 -1 -1 -1 -1-1 -1 40 -1 -1-1 -1 -1 -1 -1-1 -1 -1 -1 -1

Laplace 5· 5

-1 -1 -1

-1 12 -1

-1 -1 -1

Laplace 3· 3

Laplace for sharpening

1 1 2 1 11 2 4 2 12 4 8 4 21 2 4 2 11 1 2 1 1

-1 -1 -2 -1 -1-1 -2 -4 -2 -1-2 -4 44 -4 -2-1 -2 -4 -2 -1-1 -1 -2 -1 -1

Gauss 5x5

Laplace 5x5

-1 -1 -2 -1 -1-1 -2 -4 -2 -1-2 -4 88 -4 -2-1 -2 -4 -2 -1-1 -1 -2 -1 -1

-1 -1 -1 -1 -1-1 -1 -1 -1 -1-1 -1 24 -1 -1-1 -1 -1 -1 -1-1 -1 -1 -1 -1

-1 -1 -1 -1 -1-1 -1 -1 -1 -1-1 -1 48 -1 -1-1 -1 -1 -1 -1-1 -1 -1 -1 -1

Laplace for sharpening

Laplace for edge detection

-1 -1 -1-1 8 -1-1 -1 -1

-1 -1 -1-1 8 -1-1 -1 -1Laplace 3· 3

Laplace 3· 3

Difference: Gaussian - Original

original

Gauss 15 x 15

difference, equalized

original

Gauss 15X15

difference

image horizontal traverse

Difference: Gaussian - Original

exerciseConvolve...

exercise

1. open Parrot_P_64.tif and parrot_test.tif2. enlarge window to 200%3. convolve with filter kernels4. watch little test figure5. watch histogram

Lazy grainboundaries

Lazy grain boundaries input

RGB colour image

Lazy grain boundariesearth.unibas.ch/micro

Uses different versions of same image.Originally written to analyze a • stack of misorientation images or• differently polarized imagesbut can also be used for any• multichannel image e.g. RGB stack

Image SXM and Fiji / imageJ

'orientation' images (5 types)

crosspol crosspolcirpol

azi / inc misoredge

Lazy grain boundaries: input images

use stack

set of misorientation images

Lazy grain boundaries

cuo


cuog-z-m


cuog-z-m-ji-tji-tji


cuog-z-m-ji-tji-tji-t5y


typical artefactsof segmentation:

• corner of 4• oversegmentation• 45° diagonals

→ 2000_RH_Lazygbd_JSG.pdf


exerciseLazy

grainboundaries

exercise

1. open RubyGap image2. try Lazy grainboundaries

3. open stack of misorientation images (2w920misor)4. try Lazy grainboundaries

Image SXMAnalyze

Analyze

define measurements

Area- no. of pixels- scaled area

Image SXM Analyze

X-Y centercenter of gravity

Image SXM Analyze

Perimeter/Lengthlength of perimeter

Image SXM Analyze

Ellipse Major AxisEllipse Minor Axis

Image SXM Analyze

AngleAngle of Major Axisw/r to horizontal

Image SXM Analyze

A

A! ! = Arequ! (equivalent radius)! = √ (A / π)dequ! (equivalent diameter)! = 2· √ (A / π)Pequ! (equivalent perimeter)! = 2· √ (π· A)

A

requ

dequ

Pequ derived measures

a (major diameter)

b (minor diameter)

P (perimeter length)

A (area)

"Len"

"Minr"

"Majr"

"Area"

φ (orientation of a)

positive x = 0°CCLW = positive

"Angle"

φ

best fit ellipse

requ, a, b,! size (linear)

b / a ≤ 1! axial ratio, flattening, ..

a / b ≥ 1! aspect ratio, elongation, ...

P / Pequ ≥ 1! circularity, sphericity, ...! lobateness, angularity, convexity, ...! ("fractal dimension")

shape descriptors - shape factors

Image SXMAnalyze

Analyze

define measurements

ImageJ Analyze

Fiji - Set Measurements

Area, Gray value distributionArea:Area of selection in square pixels or in calibrated units.

Mean (= Mean Gray Value):Average gray value within the selection (0-255) or calibrated units.

StdDev (= Standard Deviation):Standard deviation of the gray values used to generate the mean gray value.

Mode (= Modal Gray Value):Most frequently occurring gray value within the selection (highest peak in the histogram).

Min, Max (= Minium and Maximum Gray Level):Minimum and maximum gray values within the selection.

1 32

Shape & x-y coordinates of segmentsX, Y (= Centroid):Average of the x and y coordinates of all of the pixels in the image or selection.

XM, YM (= Center of Mass):Brightness-weighted average of the x and y coordinates all pixels in the image or selection.

Perim. (= Perimeter):The length of the outside boundary of the selection.

BY, BM, Width, Height (= Bounding Rectangle):The smallest rectangle enclosing the selection: BX and BY are the coordinates of the upper left corner of the rectangle.

1 32

1 32

Best fit ellipseMajor, Minor, Angle (= Best Fit Ellipse):

Major is long diameter (2a)Minor is short diameter (2b)

Angle (0° - 180°) is the angle between the major axis and the x-axis (0°) counting counterclockwise.

The coordinates of the center of the ellipse are X and Y (= Centroid)

2

Edit>Selection>Fit Ellipse:

1 32

Shape descriptorsCirc. (= Circularity): area / area of perimeter-equivalent circle.

AR (= Aspect ratio): major_axis / minor_axis.

Round (= Roundness): 4*area / (π*major_axis^2) = the inverse of the aspect ratio.

Solidity: area / convex area.

1

Edit>Selection>Convex Hull:

1 32

Caliper diametersFeret (= Feret's Diameter) (= maximum caliper):The longest distance between any two points along the selection boundary.

FeretAngle (0°-180°):The angle between the Feret's diameter and the x-axis.

FeretX, FeretY:The starting coordinates of the Feret's diameter.

MinFeret (= minimum caliper):The minimum caliper diameter

Density measuresIntDen, RawIntDen (= Integrated Density):"IntDen" = the product of Area and Mean Gray Value"RawIntDen" = the sum of the values of the pixels in the image or selection

Median:The median value of the pixels in the image or selection.

Skewness, KurtosisThe third order moment about the mean.The fourth order moment about the mean.

Area FractionThe percentage of pixels in the image or selection that have been highlighted in red using Image>Adjust>Threshold. For non-thresholded images, the percentage of non-zero pixels.

Kaleidagraph plotting results

deriving shape descriptors

1:1

shape descriptors: axial ratio b/a

mean of b/a: 0.62565

c8=c7/c6

slope of b vs. a: 0.63447

shape descriptors: axial ratio b/a

c2=sqrt(c1/pi)

shape descriptor: b/a as f(requ)

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 45 90 135 180

TruzzoHighMagNoSc100

a/b

Angle

Rf - φ diagram

shape descriptor

fractal dimension: 1.2156

shape descriptor: P / Pequ

b/a

comparison: quartz - plagioclase

b/a(requ)


Rf-φ


P/Pequ


exerciseimage analysis

exercise

1. open Meluzina M32. perform image analysis type 2 and 33. plot results

4. open TOSsedi EPI and TRANS5. make bitmap of TRANS6. perform image analysis type 2 and 3 using re-direct

TOS sediMOTIVATION:

Use two scans of same sand:! transmission mode - for bitmap! incident light - color, grey values

Use Re-direct sampling to analyze all aspects of shape and surface texture (color)

1.! Open images!! RGB opens as stack and Index image

2.! Check scale!scale if necessary

3.! Extract Green Channel!! Stacks > Stack to Windows! keep 002 (G = green channel)! discard Index image! discard 001 (R) and 003 (B)

4.! Analyze > Options!check all ...!

5.! Analyze > Analyze Particles...

6.! Analyze > Show Results! File > Save As...

TOS_2_bit TOS_2_epiG (green channel of RGB)

TOS sedi7.! Kaleidagraph! if applicable, delete last particle ( = scale bar)

7.1! Functions > Bin Data...!! make histogram of "Majr" (=long axis of best fit ellipse)

7.2! calculate Pequ ! Data > Insert Column after "Len" (=measured perimeter)! !! ⌘F = Formula Entry

7.3! plot Pequ against Len!! Gallery > Scatter Plot

7.4! make line fit! Curve Fit > Linear Plot! !7.5! force through zero! Curve Fit > Curve Fit Options...

Plot

TOS sedi8.! Map Properties!! Macros > Load Macros: Lazy Grain Mapping!! if applicable, turn OFF Re-direct Sampling!! in Analyze > Options...!! Select area (ROI) without scale!! ⌘D Duplicate! File > Save As... TOS_2_bit_crop.tif

8.1! [B] Size Map! Max radius = 1.19 mm

8.2! [F] Shape factor Map! Max shape factor = 1.55

(Detail of TOS_2_bit_cropB)

(Detail of TOS_2_bit_cropF)

TOS sedi8.3! Threshold maps! [B] Size Map at requ > 0.5mm (dequ > 1mm)! [F] Shape factor Map at SF1 > 1.25

8.4! Interesect! TOS_2_bit cropF>1.25.tif! TOS_2_bit crop B>05.tif

! =>! r > 0.5 mm AND P/Pequ > 1.25

SF1 > 1.25 requ > 0.5 mm

day 2 - unibas.ch · plan day 1 - 'look at the data' • scale, calibrate, re-size,...

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