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<HTML><HEAD><TITLE>GPIV</TITLE>
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<A href="index.html"> Contents </A>  <br>
<A href="intro.html"> Previous </A>  <br>
<A href="piv_intro.html"> Next </A> 
<P>
<A NAME="gpiv.html"> <H1>2 GPIV</H1></A>

<A NAME="sect2.1"><H2>2.1 Starting up</H2></A>

Gpiv may be started up in different ways. In case it needs to trigger
the lasers and camera, the RTAI and gpivtrig Linux kernel modules will
have to be loaded (and unloaded after closing Gpiv). The gpiv_control
script (from the gpivtrig package, which also includes the gpivtrig
module) might be used: "gpiv_control <b>"</b>gpiv key1
...<b>"</b>". Gpiv_control has to be run with root privileges. In case
no trigering is used or if the modules have already been loaded in the
kernel, starting the application is straightforward with: "gpiv". If
the modules have not been loaded in the kernel, a warning message will
be displayed and the trigger services will be disabled.
<br>

The Gpiv console will be launched that consists a menu bar, a
tool-bar, process toggle-buttons, a tabulator and a data buffer list
(<a href="#fig2.1">Figure 2.1</A>). At the bottom of the console you can
find an application bar that displays information of the highlighted
item as well as a progress bar that displays the progress of the
running process.
<br>

Gpiv reads its default program parameters from ~/.gnome2/gpiv following
the GNOME mechanism. These parameters may be overruled by command line
keys for the current session (invoke "gpiv --help" or "man gpiv" for
information about the command line options) or by the
Settings->Preferences from the console menu's. There are also
additional Gpiv variables that can not be defined by command line
keys. These variables are stored from previous sessions (like the last
displayed tabulator, image Base-names for recording or image name used
for loading with File->Open). The process variables that are used for
recording, interrogation, validation and post-processing are read from
~/.gpivrc or from the system-wide available gpiv.conf (mostly installed
at /etc/ under Unix/Linux) respectively. These process variables
are shared with the programs from the Gpivtools package.
<br>

<P>
<IMG SRC = "figures/gpiv-fig_console_record.png"><br>
<A NAME="fig2.1" id="fig2.1">Figure 2.1 Gpiv console with image recording
tabulator</A>
<P>
<P>

<A NAME="sect2.2"><H2>2.2 Menu and toolbar</H2></A>

The menu bar consists general tasks for Gpiv, like file-handling,
preferences and help menus. Underlined characters represent the ALT
short-hand key for launching the menus.
<P>

The "File" menu contains "open", "save", "save as", "print", "close"
for reading, storing, printing (not working, yet!), and closing
data and "exit" for closing the application.

<P>
Image data may be read in raw data format (name.<strong>r</strong>)
that is accompanied by an ASCII header file (name.<strong>h)</strong>
or in HDF5 data format (name.<strong>gpi</strong>). Images of general
formats (gif, bmp, etc) may be translated with gpiv_img2gpiv from the
Gpivtools software package. In case of cross-correlation, it is expected
that the second frame is sticked to the first image frame. This may be
performed manually with: <br> "img2gpiv -c ncols -r nrows imgA" <br>
"img2gpiv -c ncols -r nrows imgB" && "cat imgB.r >> imgA.r"

<P>
The maximum image dimensions that may be used are defined in
gpiv_gtk.h by IMAGE_WIDTH_MAX and IMAGE_HEIGHT_MAX or by the options
--enable-img-width and --enable-img-hight of the ./configure script.
The maximum image dimensions can not be changed during execution of
Gpiv. In case the image dimensions are larger, ./configure will have
to be executed (or gpiv_gtk modified) and Gpiv will have to be
recompiled. In case IMAGE_WIDTH_MAX and IMAGE_HEIGHT_MAX will have to
be redefined, it is recommended to set them at the minimum needed
values in order to minimize memory usage. When a camera is connected
to the computer, the image dimensions of the camera are used
automatically. If no camera is connected, image dimensions will be
used from the setting of Gpiv. These may be changed by the
settings->preferences menu or by the command line keys
--columns=NCOLUMNS and--rows=NROWS.
<br>
After loading, the file basename is displayed in the buffer list and
the complete image name is displayed in the "Image Info" tabulator of
the console.  A display window (or viewer) is launched that shows the
image together with the interrogation area's and its name is displayed
in the application bar of the viewer as well (<a
href="#fig2.2">Figure 2.2</a>.
 
<P>
<IMG SRC = "figures/gpiv-fig_display.png"><br>
<A NAME="fig2.2" id="fig2.2">Figure 2.2 Buffer display 
containing image, Interrogation Area contours and data</A>
<P>
<P>

<P>
Saving the image and data is done in raw binary data or HDF5 format,
depending on the program settings or start-up keys (--hdf and
--hdf_img). Image data may also be loaded with "drag and drop" of a
single filename or a selection of filenames from the Gnome
file-manager NAUTILUS into the buffer list.

<P>
The settings menu contains the menus "gpiv buttons" and "tabulator" to
(un)display these parts of the console and "preferences" for defining
all Gpiv settings. Closing the "preferences" menu with "OK" stores the
settings for future sessions. "Apply" only affects the current
session. "Cancel" closes the preferences window without action. Some
parameter settings (image width and image height) need to restart
Gpiv. You will be acknowledged in that case.
<P>
The "help" menu contains "show tooltips" for obtaining additional
help. Tooltips are small windows that pop up when an item is
highlighted and contain more extended information about the item than
can be displayed in the short line of the application bar. The "manual"
menu shows this document. "About" gives short info concerning this
application.

<P>
The toolbar is a quick way for opening/saving/closing images and data,
executing/stopping processes that are enabled by the process toggle
buttons below of the toolbar, for closing buffers and for exiting the
program. Though a printer button and print dialog have already been
implemented, printing is not yet possible with Gpiv.



<A NAME="sect2.3"><H2>2.3 Process toggle-buttons</H2></A>

The process toggle-buttons may be switched on in order to define a
chain of processes (pipeline). These processes include recording,
interrogation of images, validation and post-processes of the PIV
estimators. The parameter settings of the processes are defined in the
tabulators of the Gpiv console. The pipeline process is invoked by the
"Execute" button on the toolbar and, eventually, interrupted by the
"Stop" button.


<A NAME="sect2.4"><H2>2.4 Buffer list and display window</H2></A>

The buffer list displays a number and the file basename (i.e. the
filename without directory name and extension) of the loaded
images. Images may be loaded directly into the buffer list by means of
"drag and drop" from the Gnome file-manager NAUTILUS. A single buffer
may be selected by pointing to it and left mouse clicking. Several
buffers may be selected by clicking the first and last buffer while
holding the "Shift" key. The execution of processes will than
be performed on every selected buffer. The selected buffers will be
closed following the Window manager protocol (mostly by pressing
Ctrl-W).

<P>
For each buffer, a display window is launched that contains the image,
squared frames that represent the contours of interrogation areas
during the initial and the final step of an iterative interrogation
process, a vector field representing the PIV estimators and solid,
coloured, squares expressing the magnitudes of derived scalars
obtained from the PIV estimators by post processing. The interrogation
areas are highlighted when the pointer moves over them. At the bottom
of the display window an application bar shows information concerning
the data. If displaying of interrogation area frames is disabled,
image intensities are shown. Else, the centre point of the highlighted
interrogation area and, eventually, values of the PIV estimators and
its derived quantities are shown. If the settings of Interrogation
Areas are changed or, for some other reason not in accordance with the
settings the PIV data have been generated, the PIV values will not be
displayed. The same information is displayed in the application bar of
the Gpiv console as well. When clicking the right mouse button when
pointing within the display, a menu pops up for magnifying (zooming)
the window, (un)displaying data and selecting vector length and color
coding.



<A NAME="sect2.5"><H2>2.5 Tabulator</H2></A>

The tabulator contains pages with parameter settings and
buttons to invoke the processes for image recording, information and
interrogation, PIV-data validation and post-processing.

<A NAME="sect2.5.1"><H3>2.5.1 Record</H3></A> 

The most left tabulator 'Record' (<a href="#fig2.1">Figure 2.1</A>)
contains all settings for the triggering of camera and lasers and for
the camera. Triggering is performed by a Linux kernel module from the
Gpivtrig software package which sends its trigger pulses over the
parallel port. It uses the RealTimeLinux Application Interface 
(<a href="http://www.rtai.org">RTAI</a>), which
is a real time micro kernel to perform processes at accurate timings,
independently of the computing load of the system. 
<br> 

The base-name of the images to be recorded are defined in the
entry. The last 5 names that have been used during the actual or
previous Gpiv sessions are stored. The name may be extended with the
current date and time.
<br>

Different timing schedules may be used. For PIV, "Indefinite", "Duration"
and "Double exposure" are most relevant. "Indefinite" will continue until
"stop timings" button (or "Stop" button from the main tool bar of the
application) is pressed. The images are displayed and updated in frame
buffer #0. This setting is convenient for pointing, adjusting and
focussing the camera. For the other timing settings, images are stored
in subsequent buffers, starting at #0. A maximum of GPIV_NIMG_MAX
(defined in gpiv.h of Libgpiv and currently set to fourty) buffers
may be retrieved. Duration will only send a limited amount of trigger
pulses as defined in "frames (N)".
<br>

TODO "Interrupt" ... 
<br>

"Increment dt" will increase the timing of pulses to the lasers as
defined in "inc. dt (ms).,
<br>

TODO "double exposure" ...
<br>

"Dt" represents the time beween two laser pulses of an image-pair.
<br><br>

The camera uses the IEEE1394 (Firewire), IIDC-compliant protocol. The
"Node.." menu selects the camera if different cameras are connected to
the computer. All other menu-options and settings that belong to the
selected camera are updated and enabled/disabled
automatically. "Format .., selects the image format, "... fps" the
frame rate, TRIGGER MODE ...", "Exp", "Iris", "Shut", "Gain", "Temp",
"Zoom" "Pan" and "Tilt" are obvious.

Enabling "RTAI trigerring" will use the application's trigger
system. If "record" and "stop record" are pressed, the recording of
images and the triggering is started and stopped.



<A NAME="sect2.5.2"><H3>2.5.2 Image</H3></A>

The 'Image' (<a href="#fig2.3">Figure 2.3</A>) tab displays information
of the image. Some settings, like image file name, correlation type,
image dimensions and image colour depth are only displayed for
informative purposes and can not be changed. The image filename is
determined during recording or loading the image. The image
dimensions, correlatation type and colour depth may be modified from
the Gpiv settings or from the command line keys. During loading of an
image it is checked whether the image header info is in agreement with
these settings.
<P>
<IMG SRC = "figures/gpiv-fig_console_image.png"><br> <A NAME="fig2.3"
id="fig2.3"></A>Figure 2.3 GPIV console with image information
tabulator</A>
<P>
<P>

<br> 
Time scaling, spatial scaling, the positions of row #0 and column #0
(related to a typical location in the experiment) are identic as in
the Post processing tabulator. These parameters are used for scaling
and positioning the PIV data. 

<br> 

Spatial scaling may be determined interactively by pointing a ruler in
a image. The number of pixels that are spanned by the imaged ruler may
be obtained in arbitrary, horizontal or vertical direction by
activating the subsequent radio buttons. Entering the viewer, then,
will change the pointer image to cross-hair. Pressing and holding the
left pointer button within the image starts drawing a straight line
and shows the pointer position in the application bar. By releasing
the pointer button, the straight line disappears, the span length is
written to the "span" entry and the "spatial scale" entry is updated
for the new value. When pointing in arbitrary direction, Pythagoras'
rule is applied for calculating the correct spanned length by the
ruler image. The length of the ruler that has been spanned, expressed
in mm, will have to be specified manually. Changing this
value will automatically update the "spatial scale" value, as well. If
"span" or "length" are not changed, the spatial scale setting, like
all other image header information and process settings, is read from
the system wide gpiv.conf or from ~/.gpivrc during launching Gpiv.

<br>
The items Creation Date, Author, Usertext, Copyright, Software,
Source, Warning, Disclaimer and "Comment" Comment are typical header
comments, often required, for example, in PNG formatted images.



<A NAME="sect2.5.3"><H3>2.5.3 Interrogation</H3></A>

The 'Interrogation' tab (<a href="#fig2.4a">Figure 2.4a, b</A>)show all the
settings for interrogation an image (pair). 
<P> 
<P>
<IMG SRC = "figures/gpiv-fig_console_interrogat_upper.png"><br>
<A NAME="fig2.4a" id="fig2.4a">
Figure 2.3a Gpiv console with Interrogation tabulator, upper part</A>
<P>
<IMG SRC = "figures/gpiv-fig_console_interrogat_lower.png"><br>
<A NAME="fig2.4b" id="fig2.4b">
Figure 2.3b Gpiv console with Interrogation tabulator, lower part</A>
<P>
<P>

- The upper-left corner of the image represents pixel # (0,0). The
starting point (first col/row) and the end-point (last col/row) of the
image to be interrogated may be defined in the entry-fields as well as
a global pre-shift in horizontal (pre-shift col) and vertical
(pre-shift row). The first column and row, as defined in the entry's will
always be included in the interrogations. The last column/row of the image
to be analyzed depends on Interrogation Area sizes and shifts, but
will never exceed the last column/row as defined in the
entry-fields. 
<P>

- The size of the interrogation area's (I.A.) and adjacent shift,
expressed in image pixels, may be defined by entry's (for arbitrary
dimensions) or by radio-buttons (which is convenient for power of 2
dimensions) in 'Int. Size 1', 'Int. Size 2' and 'Shift'. The size of
the second I.A. has to be equal or larger than the first one in order
to perform adaptive dimensions during an iterative interrogation
process. Some of the settings in the entries and of the radio buttons,
then, may be disabled for manipulation or its value to be entered may
be limited. In case adaptive dimensions of the I.A.'s is applied, zero
offsetting is enabled and the grid of the nodes at which estimators
are calculated, is adapted during each iteration. This will often
increase computation speed and the stability of the
calculation. Starting by a course grid with I.A. dimensions of
'Int. Size 2' and 50% overlap. During each iteration, the sizes of the
I.A.'s and adjacent shifts are halved until 'Int. Size 1' and adjacent
shifts as defined in 'Shift' have been reached. The new estimators at
the finer grid, used as local pre-shift values for zero offsetting,
are obtained from the previous interrogation at a courser grid by
linear or, if possible (i.e. an internal node) bi-linear
interpolation. Finally, an additional interrogation, then, should
guarantee an optimum estimator.
<P>
If the settings of I.A.'s are changed after aninterrogation, the PIV
values will not be displayed when moving the pointer over the data.
<P>

<H4>Mouse select</H4>
<ul>
<li>"None": disables mouse activity within the viewer window.

<li>"Area": entering a viewer window, holding the left mouse
button and moving the mouse creates a rectangular frame that defines the area
to be interrogated. This is an alternative for using the entries "first/last
col/row". The entry values will be updated automatically.

<li>"Single int.": entering a viewer window and clicking the left
mouse button invokes a new interrogation at the highlighted
interrogation area. The actual interrogation takes place after
releasing of the mouse button. The pointer has to be at the identic
interrogation area during pressing and during releasing of the
button. When the pointer has been moved out of the interrogation area
during releasing, nothing will happen and a new interrogation may be
invoked immediately. In case a successfull interrogation has taken
place, the mouse selection will be set to "None" in order to prevent
accidential interrogations. For multiple interrogations, hold down the
shift key during releasing of the mouse button. Other, already
existing estimators will be conserved.

<li>"Single point": entering a viewer window and clicking the left
mouse button invokes a new interrogation at an arbitrary point.  The
mouse selection will be set to "None" in order to prevent accidential
interrogations. For multiple interrogations, hold down the shift key
during releasing of the mouse button. Already existing estimators will
be thrown away!

<li>"Drag int.": entering a viewer window causes to displace (drag)
the highlighted interrogation area. An adjacent interrogation area is
highlighted and dragged in case the pointer is closer to its centre
point. Clicking the right mouse button invokes an interrogation at the
centre point of the (displaced) interrogation area. The actual
interrogation takes place after releasing of the mouse button. The
pointer has to be at the identic interrogation area during pressing
and during releasing of the button. When the pointer has been moved
out of the interrogation area during releasing, nothing will happen
and a new interrogation may be invoked immediately. In case a
successfull interrogation has taken place, the mouse selection will be
set to "None" in order to prevent accidential interrogations. For
multiple interrogations, hold down the shift key during releasing of
the mouse button. Other, already existing estimators will be
conserved.

<li>"Vert. line": a vertical line in the image may be defined at which
a single column of interrogation areas are to be drawn. Interrogation
of the line has to be performed by clicking the "piv" button at the
bottom of the "Evaluation" tabulator or by enabling the "piv" process
button and pressing the "Execute" button on the toolbar.

<li>"Hor. line": a horizontal line in the image may be defined at which a 
single row of interrogation areas are to be drawn.Interrogation
of the line has to be performed by clicking the "piv" button at the
bottom of the "Evaluation" tabulator or by enabling the "piv" process
button and pressing the "Execute" button on the toolbar.
</ul>



<H4>Sub-pixel Interpolation</H4>

Selects an interpolation scheme for estimating the correlation peak at
sub-pixel level.



<H4>Peak #</H4>

Normally the highest correlation peak is used (or the second highest
in case of auto-correlation, which is done automatically if
auto-correlation has been enabled). An erroneous velocity vector,
though, might be caused by a high noise peak in the correlation
function that overwhelms the 'true' particle displacement
peak. Searching the second or third highest peak may result in a
correct estimation.



<H4>Interrogation scheme</H4>

Image deformation uses all estimators of the entire displacement field
to deform the image towards the moment in-between the two images have
been recorded. The deformed and shifted Interrogation Areas are
obtained by interpolation of the image data with a fith order B-spline
interpolation routine  <a href="#ref1">[1]</a>.
<p>
In case zero offset (at an integer number of pixels) is enabled,
i.e. a second interrogation is performed with a pre-shift of the local
estimator, the new correlation peak is found between -1 and +1
pixels. The 'classic' forward
interrogation scheme or a central differential scheme may be
used. Interrogation following the central differential scheme is done
by displacing the interrogation area of the first image with half the
magnitude of the pre-shift value in negative direction and displacing
the interrogation area of the second image in positive direction (of
identic, integer magnitude).
<p>
A linear weight kernel in order to correct for biasing effects that is
generated by the estimation of the correlation function.
<p>
"Image deformation", "Central differential" and "Zero offset" are
iterative processes that continue until the convergence criterium has
been reached.  The total amount of differences in the estimators
between two succesive iteration steps, related to the number of
gridpoints, is used as criterium for convergence and amounts to 0.25
pixels (defined by GPIV_EPSI_MIN).

The estimators are validated on outliers after each iteration step of the
interrogation procedure. Erroneous vectors are subsequently
substitued (and re-validated) by the second or third highest
correlation peak or by the quantity as specified in "Outliers" in the
Validation tabulator.

<H4>Correlation</H4> 

In case subsequent recordings have been performed on separate image
frames ("Cross") or on one single frame ("Auto"). This option is
informative and can not be changed here. The setting may be defined
with the optional key -x or --cross during starting-up of the
application or may changed in Settings->Preferences of the console
menu. During loading of an image it is checked whether this this
parameter in the image header info is identic.

<H4>Interrogation areas and correlation</H4>

The "Monitor" button allows to monitor the interrogation process by
visualizing the interrogation areas, the correlation function and the
estimated displacement vector. Coloured areas, that are 128x128 pixels
in size, are displayed as indication of the dimensions. The
interrogation areas and correlation function may be magnified by the
"Zoom" entry. The vector length may be adjusted by "Vector scale". By
zooming and scaling, the dimensions of the images and the vector may
exceed the coloured area's. For that case, only a part of the images
and vector is displayed. Monitoring the interrogation process will
slightly slow down the calculation speed.

<br>
Tip: by enabling "Single Int" of the mouse selection, each
interrogation area may be monitored individually, which might often be
more convenient than monitoring the interrogation of an entire image.
<P>



<H4>piv</H4>

At the bottom of the "Evaluation" tabulator the "piv" button may be
invoked to interrogate the image, which is identic as enabling the
'piv' check-button in the process toolbar of the console and pressing
the 'Execute' button. The function of this button is similar to that
of the command line program <b>rr</b> of the Gpivtools package.


<A NAME="sect2.5.4"><H3>2.5.4 Validation </H3></A>

<P>
<IMG SRC = "figures/gpiv-fig_console_valid.png"><br>
<A NAME="fig2.5" id="fig2.5">Figure 2.5 Gpiv console with Validation 
tabulator</A>



<H4>Disable data</H4> 

Put PIV data into  (in)active state for further processing.
At inactive state the vector color will be displayed red. 
<ul>
<li>"None": disables mouse activity within the viewer window.

<li>"Enable": puts data in active state by pointing and clicking a
single PIV estimator.

<li>"Disable point": puts data in inactive state by pointing and
clicking a single PIV estimator.

<li>"Enable area": puts a rectangular area containing PIV data in
active state. The starting corner of the area (upper-left) is defined
by pressing the right mouse button. The opposite corner is defined by
moving the mouse with holding the button pressed and releasing it at the
location of the opposite corner. A rectangular frame is drawn during
the operation.

<li>"Disable area": puts a rectangular area containing PIV data in
inactive state. The starting corner of the area (upper-left) is defined
by pressing the right mouse button. The opposite corner is defined by
moving the mouse with holding the button pressed and releasing it at the
location of the opposite corner. A rectangular frame is drawn during
the operation.
</ul>



<H4>Histograms</H4> 

<ul>
<li>"residu" displays the (log) inverse histogram of median
residus. The critical residu value for accepting/rejecting outliers is
determined by the slope of the straight line plotted through the
histogram data. The critical value is calculated and displayed in the
"Threshold" entry. The function of this process is similar to that of
the command line program <b>errvec</b> of the Gpivtools package.</li>

<li>"sub-pixel" displays a histogram of sub-pixel estimators of the
PIV dataset. The function of this process is similar to that of the
command line program <b>peaklck</b> of the Gpivtools package.</li>

<li>The "U-comp" and "V-comp" buttons display the histograms of
horizontal and vertical particle displacement estimators. These data
may be stored by "Save" in filename.pdf.</li>


</ul>


<H4>Validate on velocity gradient</H4>

Calculates velocity gradient over an interrogation area and displays
vectors in red color if they exceed the critical value. The critical
value is defined in libgpiv/include/gpiv/valid.h: GRADIENT_THRESHOLD
and is set to 2 pixels, i.e. identic to the optimum particle image
diameter. This quantity is chosen in order to prevent a too wide, or
even a splitting up, of the highest correlation peak.


<H4>Outliers</H4>

To set the parameters for testing and substituting on erroneous
vectors. The number of the surrounding displacement data of a point
under investigation may be defined by "Neighbors". The number
represents the two-dimensional array, which is typically 3x3 and may
have a maximum of 9x9. The "Data yield" is needed to calculate the
threshold value from the residu statistics. This value has to be
filled in manually and should be obtained from the mean number of
particles within an interrogation area. One way to obtain the particle
density, is by enabling the "Monitor" button and "Single int" of the
mouse selection in the "Interrogation" tabulator and analyzing some points
in the image. 
<p>

The critical threshold may be filled in manually or may
be obtained by invoking "residu" button.
<p>

The type of residus may be chosen between "Normalized median",
"Median" or "Snr". The normalized median option uses the ratio between
the residu (obtained from the actual didplacement and the median
displacement from the neighboring data) and between the median residu
(resulting from the neighbors). The threshold, then, may be kept at 2
pixels for obtaining a data yield of 90% <a href="#ref2">[2]</a>. This
setting should be advantageous if turbulence is heterogeneous within
the area of observation. The median option uses the residu between
actual data point and the median displacement from its surroundings.
<p>

Outliers may be substituted by the local mean value of the surrounding
vectors, by the median value of the surrounding vectors or by the
displacement from the next highest correlation peak. Unless "Nothing"
has been choosen, the data will first be substituted subsequently by a
PIV estimator from the next highest correlation peak, the median
displacement value, and local mean. If the residu still exceeds the
threshold after trying these substitutions, the PIV estimator will be
substituted by the preferred option as enabled here.
<p>

Finally, the validation on outliers is performed by pressing the
"validate on outliers" button or by enabling "validate" in the process
toolbar of the Gpiv console and pressing "Execute". Validation is also
performed after each step of the interrogation procedure if the
Interrogation scheme is set to "Image deformation", "Central
differential" or "Zero offset". The function of testing on outliers
and substituting is similar to that of the command line program
<b>errvec</b> of the Gpivtools package.

<A NAME="sect2.5.5"><H3>2.5.5 Post processing </H3></A>

The "Post processing" tab (<a href="#fig2.6">Figure 2.6</A>) contains
tools to apply modifications on PIV estimators and to calculate
derived quantities from the PIV estimators.
<P>

<H4>Scaling</H4> 

<ul>
<li>"Spatial scale" is calculated by measuring the number of pixels per
mm. The values will have to be set manually or may be obtained interactively 
from the <a href="#5.1">Image info</A> tabulator.

<li>"time scale" represents the time between
two successive image recordings (mostly the separation time between
two laser flashes). 

<li>"pos. of col #0": The horizontal location of the image within an
experiment is defined by the position of column #0, related to
a marker point in the experiment.

<li>"pos. of row #0": The vertical location of the image within an
experiment is defined by the position of column #0, related to
a marker point in the experiment.

The function of this
process is similar to the command line program <b>scale </b> of the 
Gpivtools package.
</ul>
<P>

Vorticity, shear and normal strain may be derived from the PIV
estimators with different numerical schemes; Central differential
scheme, Least squares, Richardson and the Circulation method (only for
the calculation of vorticity). The function of this process is similar
to the command line program <b> vorstra </b> of
the Gpivtools package.

<P>
<IMG SRC = "figures/gpiv-fig_console_post.png"><br>
<A NAME="fig2.6" id="fig2.6">Figure 2.6 Gpiv console with Post processing
tabulator</A>
<P>
<P>
<P>
<H4>References</H4>

<a id="ref1"> [1] P. Thvenaz, T. Blu, M. Unser, "Interpolation
Revisited," IEEE Transactions on Medical Imaging, vol. 19, no. 7,
pp. 739-758, July 2000</a>
<P>
<a id="ref2"> [2] J. Westerweel, F. Scarano, "Universal outlier
detection for PIV data", Exp. in Fluids (2005) 39:1096-1100</a>

<P>
<P>
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