MorphCol supplement #20 ­ Tilting (Roll) Experiments in AMOR 3.17. Finding a solution for the "G. miocenica problem"

Michael Knappertsbusch, 13.5.2011
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Introduction
Until AMOR 3.17 automated orientation (AutoTilt) of menardiforms into keel position was programmed under the assumption of symmetrical biconvex profiles in keel view. The keel-view area increases as the tilt (Roll) angle deviates from the horizontal position of the slide and attains a minimum if the shell stands upright in perfect keel-position. If the geometry of the shells shows asymmetry in keel-view, such as in G. miocenica (umbilico-convex shells, i.e. flat on spiral side, convex on umbilical side, see Figure 1), the implemented algorithm leads to oblique positioning of the shell. Equally difficult is the automatic positioning if the shells are spiro-convex in keel view (as was often experienced with shells of G. multicamerata). Automatic orientation into keel-position with AMOR degrades as asymmetry of the shells increases in keel view. These difficulties were coined the "G. miocenica problem", see initial experiments described in Knappertsbusch (2011). In the following report these problems are investigated in more detail using a specimen of G. menardii (symmetric, biconvex), a specimen of G. miocenica (asymmetric, weakly umbilico-convex), and a specimen of G. truncatulinoides (asymmetric, extremely umbilico-convex).

Figure 1 - "Symmetric"biconvex profile (G. menardii, left), asymmetric spiroconvex profile (R. contusa, middle), and extremely asymmetric umbilico-convex profiles (G. truncatulinoides, right). Image courtesy from Bolli et al. (1957), Text Figure 2.

 

Definitions
The following keel view measurements were performed as a function of the tilt (Roll) position: Spiral area, umbilical area, spiral length a, umbilical length b, and total area (see Figure 2 for G. miocenica).

Figure 2 ­ Definitions, illustrated for the case of G. miocenica. The spiral area (orange) is separated from the umbilical area (blue) by a vertical line, that passes centrally through the extreme points of the upper and lower keel region. Line a is the width of the spiral area, line b is the width of the umbilical area. The spiral area is the partial area on the spiral side, the umbilical area is the area on the umbilical side, both together totalling to the total area. Length a is the width of the spiral area, length b is the width of the umbilical area. The spiral area is separated from the umbilical area by a vertical line, which passes through the mean of the X-coordinates of the uppermost and lowermost point of the periphery of the shell (see Figure 2).

 

Experimental settings in AMOR
Image series were captured in the manual mode of AMOR 3.17. Tilting (Roll) increments were 1 mouse click at normal sensitivity (1 mouse click at normal sensitivity corresponds to a tilting angle of 1.5°, see MorphCol Suppl. #18, and Tests in AMOR 3 and AMOR 3.1 from 17 March 2009).

Sequence of operations in the manual mode:

AutoCenter
Tilt (Roll)
Autofocus, reading of the Roll position in the AMOR window
Capture image
Tilt (Roll, 1 mouse click)
Repeat sequence

Tilting to the right side (slide inclined to the right side) gives negative steps of the Roll position (images R0001, R0002, . . ., R0022). Tilting to the left side (slide is inclined to the left side) gives positive steps of the Roll position (images L0001, L0002, . . ., L0022). At the horizontal position the Roll position is 0 (Image N0000).

 

Magnifications used:

2.49x for G. menardii (reading at AMOR).
3.89x for G. miocenica (reading at AMOR).
3.89x for G. truncatulinoides (reading at AMOR).

 

 

Materials
The following samples were used in this test series:

G. menardii: DSDP 502A-1H-1, 15-20cm, 100-500 micrometers, 2/128 split, "menardiforms keep". Specimen
now mounted in slide "Specimens to image, 1.3.2004", Field 32.
G. miocenica: ODP 925B-9-5, 92.5-93.5cm, Slide a, Specimen 4301.
G. truncatulinoides: VICOMED 1 (Mediterranean Sea), Ki04, 90-1.5cm. ". Specimen
now mounted in slide "Specimens to image, 1.3.2004", Field 31.

 

 

Image processing and measurements
After collection of images, they were transferred to Macintosh, where they were processed using Wayne Rasband's freeware software Nih-Image 1.60. Morphometric measurements of the keel views were done in two ways and are illustrated in Figures 3 and 4 below: The first applied Manual Outlining of the areas of interest using the polygon-tool in Ni-Image (designated with MO in the graphs below). The second method is more towards semi-automation and applied the Density Slicing tool in Nih-Image (labelled with DS in the graphs shown below). While MO was initially applied to G. miocenica and G. truncatulinoides, the DS method was applied to G. menardii as this second method is much faster.

 

The sequence of image processing operations in Nih-Image were the following ones:

Manual Outlining (MO) method:

Open image
Smooth
Using the rubber band: Locate the lowest point (coordinates XL,YL) in the lower keel region, then
locate the highest point (coordinates XH,YH) in the upper keel region, estimate the the arithmetic mean
XM from XL and XH).
Draw vertical line through XM, giving the spiral and the umbilical areas of the keel view.
Save image
Using the polygon tool: manually outline spiral area
measure (area), save to Excel sheet
Determine length a (using rubber band), save to Excel sheet
Revert to saved
Using the polygon tool: manually outline umbilical area
measure (area), save to Excel sheet
Determine length b (using rubber band), save to Excel sheet
Close image
Repeat sequence with next image

 

Density Slicing (DS) method:

Open image
Smooth
Using the rubber band: Locate the lowest point (coordinates XL,YL) in the lower keel region, then
locate the highest point (coordinates XH,YH) in the upper keel region, estimate the the arithmetic mean
XM from XL and XH).
Draw vertical line through XM, giving the spiral and the umbilical areas of the keel view.
Save image
Make ROI with area on umbilical side, Fill with black, deselect.
Density Slice spiral area
measure (area), save to Excel sheet
Determine length a (using rubber band), save to Excel sheet
Revert to saved
Make ROI with area on spiral side, Fill with black, deselect.
Density Slice umbilical area
measure (area), save to Excel sheet
Determine length b (using rubber band), save to Excel sheet
Close image
Repeat sequence with next image

 

Results
Measurements of the spiral and umbilical partial areas as well as spiral and umbilical length a and b depend on the position of the vertical separation line. A gif animation to illustrate how the separation line varies while tilting the specimen is shown for the specimen of G. truncatulinoides in Figure 3.


Figure 3 ­ Animated sequence of G. truncatulinoides and the vertical line separating the spiral from the umbilical area while tilting (Click into image to launch animation). The line remains considerably stable.

Measurements were then plotted and composed in Figures 4 and 5. In Figure 4 images of G. miocenica (in the middle row) were outlined using the Manual Outlinig method, while in Figure 5 images of G. miocenica were outlined using the Density Slicing method. The data (areas in square pixels, lengths a and b in pixels) are given in the Appendix in Tables 1 and 2 (G. miocenica, using MO and DS, respectively), Table 3 (G. truncatulinoides, using MO), and Table 4 (G. menardii, using DS).

Figure 4 - Matrix of diagrams showing the results of the Roll-Experiment for G. menardii (symmetric-biconvex; left column), G. miocenica (asymmetric & weakly umbilico-convex; middle column), and G. truncatulinoides (asymmetric & strongly umbilico-convex; right column). All measurements are in function of the Roll position. Roll positions are negative when the slide is inclined to the right side. Roll position is zero if the slide is in horizontal position, and positive, when the slide is inclined to the left side. Measurements include the spiral area & spiral length a (first row); umbilical area & umbilical length b (second row); spiral & umbilical areas cumulating to the total area (third row); spiral area & total area (fourth row); and Spiral area & umbilical area (lowermost row). Labels in the lower right corner of each graph indicate the method of area determination, i.e. DS indicates Density Slicing, while MO indicates Manual Outlining using the polygon tool in Nih-Image. The black pictograms indicate the direction of inclination of the slide.

 

 

Figure 5 - Matrix of diagrams showing the results of the Roll-Experiment for G. menardii (symmetric-biconvex; left column), G. miocenica (asymmetric & weakly umbilico-convex; middle column), and G. truncatulinoides (asymmetric & strongly umbilico-convex; right column). All measurements are in function of the Roll position. Roll positions are negative when the slide is inclined to the right side. Roll position is zero if the slide is in horizontal position, and positive, when the slide is inclined to the left side. Measurements are the spiral area & spiral length a (first row); umbilical area & umbilical length b (second row); spiral & umbilical areas cumulating to the total area (third row); spiral area & total area (fourth row); and Spiral area & umbilical area (lowermost row). Labels in the lower right corner of each graph indicate the method of area determination, i.e. DS indicates Density Slicing, while MO indicates Manual Outlining using the polygon tool in Nih-Image. The black pictograms indicate the direction of inclination of the slide.

 

 

Figure 6 ­ Illustration of morphological parameters that are compared in the diagrams of Figures 4 and 5: Spiral area & spiral length a (first row in Figures 4 and 5); umbilical area & umbilical Length b (second row in Figures 4 and 5); Spiral & umbilical areas (third row in Figures 4 and 5); Total area (fourth row in Figures 4 and 5), and Spiral & umbilical areas, again, (in last row of Figures 4 and 5).

 

Conclusions

  • Spiral area and the spiral length a are always well correlated to each other and display minimum functions in all three types of profiles (symmetrical biconvex, asymmetric weakly umbilico-convex, and asymmetric strongly umbilico-convex.
  • Umbilical area and umbilical length b show also good correlation to each other within each profile type, however parameters show changing characteristics depending on the profile type: In case of G. menardii (symmetric biconvex) the curves show a minimum function. In case of G. miocenica (asymmetric, weakly umbilico-convex) values do not follow a minimum function; while in G. truncatulinoides both curves show a maximum function behaviour.
  • Summing the spiral area and umbilical area up to give the total area all three profile types give a minimum function, however with changing degree of contributions from each of the two portions.
  • The minima positions between the spiral area and the total area differ from each other, depending on the profile type.
  • In conclusion, for finding a good minimum function not the total area should be used for automated keel orientation but rather the spiral area.
  • There might be a threshold (depending on the ratio of a to b) where each of the characteristic profile type might be applied.
  • No tests have yet been made with asymmetric umbilico-convex profiles.

    •

     

    References
    Bolli., H.M., Loeblich, A.R. Jr. and Tappan, H. (1957)    . Planktonic foraminiferal families Hantkeninidae, Orbulinidae, Globorotaliidae and Globotruncanidae. In: Loeblich, A.R., Tappan, H., Beckmann, J.P., Bolli, H.M., Montanaro Gallitelli, E., and Troelsen, J.C. (eds.). Studies in Foraminifera. United States National Museum Bulletin 215, pp. 3-60.

    Knappertsbusch, M. (2009). MorphCol supplement #18. Vertical correction for the Auto-Focus in AMOR 3.5. 10 p. http://pages.unibas.ch/museum/microfossils/Research/MORPHCOL/Start.html

    Knappertsbusch, M. (2011). Lösung des "G. miocenica"-Problems. MorphCol Supplement #19, URL http://pages.unibas.ch/museum/microfossils/Research/MORPHCOL/Start.html

     

     

     

     

    Appendix - Raw data

     

     

    Table 1 ­ Measurements for G. miocenica, using MO for determination of spiral and umbilical areas.

    Roll position, steps Roll (normal clicks) Image Spiral area (square pixels) Umbilical area (square pixels) Length a (spiral, pixel) Length b (umbilical, pixel) Area (thresholding), square pix Sp_Area+Um_Area
    -2200 -22 R0022 27396 30111 82 99 55609 57507
    -2100 -21 R0021 26211 30006 79 100 55858 56217
    -2000 -20 R0020 25198 29612 76 100 53865 54810
    -1900 -19 R0019 23664 30323 72 102 53355 53987
    -1800 -18 R0018 22416 30531 69 103 51677 52947
    -1700 -17 R0017 20609 30728 63 105 50706 51337
    -1600 -16 R0016 19979 30838 60 104 49584 50817
    -1500 -15 R0015 18660 30203 56 104 48579 48863
    -1400 -14 R0014 18006 30172 52 104 47644 48178
    -1300 -13 R0013 15927 30597 48 105 46159 46524
    -1200 -12 R0012 16044 29317 48 103 44887 45361
    -1100 -11 R0011 14278 29980 45 104 44023 44258
    -1000 -10 R0010 13724 29738 44 104 42685 43462
    -900 -9 R0009 12684 29775 41 104 42725 42459
    -800 -8 R0008 11344 30975 39 106 41854 42319
    -700 -7 R0007 11405 29767 38 103 41309 41172
    -600 -6 R0006 11093 30374 38 104 40837 41467
    -500 -5 R0005 10873 30201 37 103 40850 41074
    -400 -4 R0004 10599 30645 37 104 40847 41244
    -300 -3 R0003 10317 30885 36 104 41283 41202
    -200 -2 R0002 10225 31729 36 106 41733 41954
    -100 -1 R0001 10002 31683 36 106 41408 41685
    0 0 N000 11123 31101 37 107 41611 42224
    100 1 L001 10972 31714 37 106 41997 42686
    200 2 L002 10748 32416 37 110 42063 43164
    300 3 L003 13120 30893 42 105 43116 44013
    400 4 L004 12082 32376 40 109 43404 44458
    500 5 L005 13474 31788 45 106 44513 45262
    600 6 L006 13439 32185 45 110 45118 45624
    700 7 L007 14920 32028 48 108 46407 46948
    800 8 L008 15660 32261 51 109 47853 47921
    900 9 L009 15837 32604 53 109 48481 48441
    1000 10 L010 16741 33273 54 111 49305 50014
    1100 11 L011 16579 33886 53 113 50591 50465
    1200 12 L012 18427 33188 59 111 51639 51615
    1300 13 L013 19954 32475 62 111 52228 52429
    1400 14 L014 19572 34130 62 114 53399 53702
    1500 15 L015 22145 32676 69 111 54384 54821
    1600 16 L016 22420 33594 70 113 54677 56014
    1700 17 L017 25208 31452 78 108 56393 56660
    1800 18 L018 24099 34057 75 116 56673 58156
    1900 19 L019
    2000 20 L020 24970 35339 79 118 59377 60309
    2100 21 L021 25227 35849 81 121 60277 61076
    2200 22 L022 23836 38190 78 125 60735 62026

     

     

     

     

     

    Table 2 ­ Measurements for G. miocenica, using DS for determination of spiral and umbilical areas.

    Roll position, steps Roll (normal clicks) Image Spiral area (square pixels) Umbilical area (square pixels) Length a (spiral, pixel) Length b (umbilical, pixel) Total area (spiral+umbilical)
    -2200 -22 R022 25994 31007 81 104 57290
    -2100 -21 R021 24492 31162 77 106 57298
    -2000 -20 R020 22900 31883 72 108 55844
    -1900 -19 R019 22643 30877 70 105 54375
    -1800 -18 R018 20571 31369 64 108 53177
    -1700 -17 R017 19922 31230 63 108 51927
    -1600 -16 R016 18526 31279 58 109 50285
    -1500 -15 R015 17414 30924 54 108 48448
    -1400 -14 R014 16871 30574 53 107 47759
    -1300 -13 R013 17028 28806 54 104 46253
    -1200 -12 R012 14528 30082 48 108 44787
    -1100 -11 R011 13855 29983 46 109 43770
    -1000 -10 R010 13640 29422 46 107 43172
    -900 -9 R009 11590 30453 41 109 42895
    -800 -8 R008 11652 29567 41 108 41929
    -700 -7 R007 10531 30398 38 108 41134
    -600 -6 R006 10213 30422 37 109 41166
    -500 -5 R005 10793 29806 38 106 41095
    -400 -4 R004 10240 30325 37 106 41297
    -300 -3 R003 9879 30912 37 108 41235
    -200 -2 R002 10244 30575 38 106 41270
    -100 -1 R001 10235 30965 38 107 41395
    0 0 N000 10111 31074 38 108 42007
    100 1 L001 9924 31646 37 110 41946
    200 2 L002 11512 30640 41 108 42677
    300 3 L003 11407 31315 40 110 43455
    400 4 L004 11049 32386 40 112 44196
    500 5 L005 13032 31420 46 109 45174
    600 6 L006 13285 31984 47 111 45020
    700 7 L007 14129 32331 50 112 46815
    800 8 L008 14394 32771 49 113 48182
    900 9 L009 16893 31355 56 110 48876
    1000 10 L010 16222 33020 55 114 49840
    1100 11 L011 15917 34274 53 117 50964
    1200 12 L012 18107 33106 58 115 52069
    1300 13 L013 17561 34446 59 118 52810
    1400 14 L014 19143 33992 63 117 54135
    1500 15 L015 20055 33963 65 118 54509
    1600 16 L016 21710 33765 71 116 55251
    1700 17 L017 21530 35079 71 121 57034
    1800 18 L018 21761 35285 73 122 57949
    1900 19 L019
    2000 20 L020 23256 36209 77 124 59492
    2100 21 L021 23323 37268 78 127 60904
    2200 22 L022 24714 36261 81 124 62070

     

     

    Table 3 ­ Measurements for G. truncatulinoides, using MO for determination of spiral and umbilical areas.

    Roll position, steps Roll (normal clicks) Image Spiral area (square pixels) Umbilical area (square pixels) Length a (spiral, pixel) Length b (umbilical, pixel) Total area (spiral+umbilical)
    -2200 -22 R0022 34316 40964 100 166 75280
    -2100 -21 R0021 32828 42024 96 169 74852
    -2000 -20 R0020 32923 40961 96 167 73884
    -1900 -19 R0019 31595 41944 91 168 73539
    -1800 -18 R0018 29227 43727 85 174 72954
    -1700 -17 R0017 28005 43852 83 175 71857
    -1600 -16 R0016 27609 43774 82 175 71383
    -1500 -15 R0015 27627 44295 81 174 71922
    -1400 -14 R0014 25935 44127 79 176 70062
    -1300 -13 R0013 23972 45366 73 178 69338
    -1200 -12 R0012 21956 46681 68 181 68637
    -1100 -11 R0011 21325 46446 68 180 67771
    -1000 -10 R0010 19889 46905 64 181 66794
    -900 -9 R0009 19361 46834 63 181 66195
    -800 -8 R0008 18067 47718 59 183 65785
    -700 -7 R0007 18312 47236 59 182 65548
    -600 -6 R0006 16086 48463 54 184 64549
    -500 -5 R0005 16317 48001 54 183 64318
    -400 -4 R0004 16207 47939 56 183 64146
    -300 -3 R0003 14820 49132 53 185 63952
    -200 -2 R0002 15630 48632 54 184 64262
    -100 -1 R0001 13795 50837 49 189 64632
    0 0 N000 13639 51008 48 187 64647
    100 1 L001 13375 52405 47 190 65780
    200 2 L002 13564 52159 48 189 65723
    300 3 L003 13393 53352 46 192 66745
    400 4 L004 13852 53548 50 192 67400
    500 5 L005 15909 52355 54 189 68264
    600 6 L006 19202 49489 63 182 68691
    700 7 L007 18963 50431 62 183 69394
    800 8 L008 19490 50588 63 184 70078
    900 9 L009 20721 50089 67 181 70810
    1000 10 L010 21654 49913 69 181 71567
    1100 11 L011 22952 49155 71 179 72107
    1200 12 L012 22559 50127 71 181 72686
    1300 13 L013 23672 49636 74 179 73308
    1400 14 L014 24340 49122 76 178 73462
    1500 15 L015 25579 48417 79 176 73996
    1600 16 L016 25526 48828 78 176 74354
    1700 17 L017 27197 48111 82 172 75308
    1800 18 L018 29355 46156 89 167 75511
    1900 19 L019 29003 47234 88 169 76237
    2000 20 L020 27635 48700 85 172 76335
    2100 21 L021 30591 46226 93 165 76817
    2200 22 L022 31648 45958 96 163 77606

     

     

     

    Table 4 ­ Measurements for G. menardii, using DS for determination of spiral and umbilical areas.

    Roll position, steps Roll (normal clicks) Image Spiral area (square pixels) Umbilical area (square pixels) Length a (spiral, pixel) Length b (umbilical, pixel) Total area (spiral+umbilical)
    -2200 -22 R022 18571 15043 72 61 33614
    -2100 -21 R021 18252 14708 70 60 32960
    -2000 -20 R020 18252 14651 70 59 32903
    -1900 -19 R019 17996 13767 68 56 31763
    -1800 -18 R018 16694 13427 64 55 30121
    -1700 -17 R017 17226 12023 65 50 29249
    -1600 -16 R016 15642 12584 59 51 28226
    -1500 -15 R015 14738 12319 57 50 27057
    -1400 -14 R014 14266 12252 57 49 26518
    -1300 -13 R013 13990 11442 57 46 25432
    -1200 -12 R012 13894 10616 57 42 24510
    -1100 -11 R011 13325 10606 56 41 23931
    -1000 -10 R010 13556 9830 57 39 23386
    -900 -9 R009 12804 9914 55 40 22718
    -800 -8 R008 12574 9723 55 39 22297
    -700 -7 R007 12722 9081 55 38 21803
    -600 -6 R006 12171 9426 54 40 21597
    -500 -5 R005 11963 9597 54 40 21560
    -400 -4 R004 12587 8592 57 37 21179
    -300 -3 R003 12557 8602 58 37 21159
    -200 -2 R002 12071 8764 57 38 20835
    -100 -1 R001 12472 8454 59 37 20926
    0 0 N000 12659 9079 60 39 21738
    100 1 L001 14098 7868 64 35 21966
    200 2 L002 13468 9191 61 38 22659
    300 3 L003 13548 9621 62 40 23169
    400 4 L004 14445 9065 64 38 23510
    500 5 L005 14968 9237 65 39 24205
    600 6 L006 14629 10251 62 43 24880
    700 7 L007 14910 10797 63 43 25707
    800 8 L008 15895 11839 62 46 27734
    900 9 L009 16213 11374 66 44 27587
    1000 10 L010 16515 12272 66 47 28787
    1100 11 L011 17096 12720 68 50 29816
    1200 12 L012 17607 13367 69 52 30974
    1300 13 L013 17162 14843 68 57 32005
    1400 14 L014 18399 14911 72 58 33310
    1500 15 L015 18882 14496 74 59 33378
    1600 16 L016 18847 15945 75 64 34792
    1700 17 L017 19656 16512 78 66 36168
    1800 18 L018 20308 16984 80 67 37292
    1900 19 L019 21409 16823 84 67 38232
    2000 20 L020 22380 17088 86 70 39468
    2100 21 L021 21914 19000 85 78 40914
    2200 22 L022 22649 18696 87 77 41345