MATLAB Mandible Tracing

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MATLAB Mandible Tracing Calculations Program

• Documentation by Antonis Vakis
• Supplemental Material for
• PHYLOGENY, SCALING, AND THE GENERATION OF EXTREME
  FORCES IN TRAP-JAW ANTS
• JOSEPH C. SPAGNA, ANTONIS I. VAKIS, CHRIS A.
  SCHMIDT, SHEILA N. PATEK,
• XUDONG ZHANG, and ANDREW V. SUAREZ

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The images, within their original folders (e.g.
093004as4), need to be placed in a directory
called 'Images,' located in the current working
directory
So far, all captures have been saved as
sequential TIFF files
First, run the tracing program
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The folder name is saved as a parameter called
filename
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Specify the number of frames per second (fps)
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Specify the width of video in pixels (width)
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Specify the height of video in pixels (height)
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Specify the image resolution in dots per inch
(dpi)
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Viewing the image thumbnails, select the range of
images over which the full motion of the
mandibles is captured
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Viewing the image thumbnails, select the range of
images over which the full motion of the
mandibles is captured
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Viewing the image thumbnails, select the range of
images over which the full motion of the
mandibles is captured
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Specify whether the strike involves both or just
one of the mandibles
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First, select the approximate location of the
mandible base
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Then, sequentially select the left and right
mandible tips over the selected frames of interest
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Finally, reselect the approximate location of the
mandible base an average mandible position will
be used for the calculations
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In the case where it is unknown, the
magnification can be calculated from the average
recorded mandible length for each species
Magnification parameter zoom Default value 10x
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Finally, run the calculations program
The name of the folder must be specified this is
the same name as the .mat file to be used
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Calculations Rcrude
Mandible base, A (x1, y1)
Rcrude
Closed position B (x2, y2)
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Calculations Grid

• Select number of grid points/ possible positions
  of centers of rotation
• e.g. 40 intervals, 41 x 41 1,681 grid points
• Create grid centered around the calculated
  mandible base location
• cor_values_min_x base_coords(1,1) Rcrude
• cor_values_max_x base_coords(1,1) Rcrude
• cor_values_min_y base_coords(1,2) Rcrude
• cor_values_max_y base_coords(1,2) Rcrude

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Calculations Grid

• Create a matrix with grid coordinates using
  values calculated for the minima and maxima in
  the x and y directions, as well as the interval
• Reshape the resulting 41 x 41 x 2 matrix to a
  matrix of size 1681 x 2 (cor_values matrix)

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Calculations Rvalues

• Having established the number of iterations for
  the left and right centers of rotation locations,
  specify the number of iterations for each
  mandible radius (values, e.g. 200)
• Specify
• Rmin Rcrude Rcrude/2 (50 smaller)
• Rmax Rcrude Rcrude/2 (50 larger)
• Rvalues linspace(Rmin,Rmax,values)

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Calculations Iterations

• Using nested for loops, iterate the values of x,
  y and R for the left and right mandibles
• for of possible radius values (values) (p)
• for of elements (41 x 41 1,681) (k)
• for of frames (e.g. 8) (i)
• to get the RMS_error for each mandible

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Calculations RMSerror

• The RMS (Root Mean Square) error is calculated
  from the formula
• where radius is defined as
• and 3 is the number of free parameters (x, y, R)
  for each mandible
• Methodology of circle fitting using RMS error
  adapted from Amara Graps of Stanford Universitys
  Solar Oscillation Investigations
  (http//www.mathcom.com/corpdir/techinfo.mdir/scif
  aq/q230.html)

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Calculations Minimum RMSerror

• The resulting matrices of the left and right
  mandible RMS_error values are reshaped into two
  new matrices of size 336,200 x 1, where 336,200
  41 x 41 x 200
• Using a simple algorithm (min command), the
  minimum values of the RMS_error are found
  (RMSleft_min RMSright_min)
• These are used to extract the values of x, y and
  R where the error is minimum for each mandible

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Calculations RMSerror plots
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Calculations Radii c.o.r.
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Calculations ? and a

• To calculate the angular velocities and
  accelerations use the following formulae, based
  on the difference of the slopes in each frame
• ?(i) atan coords(i,2) x0y0(1,2)
• coords(i,1) x0y0(1,1)
• ?(i) ?(i1) ?(i)fps (rad/s)
• a(j) ?(j1) ?(j)fps (rad/s/s)
• where ?(i) is the slope of each frame, ?(i) is
  the ang. velocity, a(j) is the ang. acceleration,
  and fps are the frames per sec. For n frames,
  there are n-1 velocity and n-2 acceleration values

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Calculations u and a

• In order to convert the angular velocities and
  accelerations into their linear counterparts, the
  radius of each mandible is needed in meters
• Rnew (R/ dpi/ zoom)0.0254 (m)
• Then, the linear velocities and accelerations
  are
• u(i) ?(i)Rnew (m/s)
• a(j) a(j)Rnew (m/s/s)

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Calculations Velocity Plots
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Calculations Acceleration Plots
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Output of Calculations Program