SUBS
An example of subscanning, which is partitioning an image and scanning it for local variation in the fractal dimension and lacunarity. The image, a simulated branching cell, was scanned as grayscale using a regular array subscan and automatically colour-coded to show the fractal dimension at each location.
Sub Sampling Images for Local Fractal Dimensions
Overview of Sub Scans
Introduction to Sub Sampling
Use subscans to automatically detect and scan
multiple particles in single images, and to
sample images as regular arrays
or using random samples.
Use them with
colour-coding
and other
graphics
to show how locally calculated
fractal dimensions are distributed
in an image or array and how they depend on
sample size.
If the options for subscanning are disabled or not visible
on the SUB SCAN panel,
they are not available for the currently selected
scan type. To use subscanning,
select Sub Scan or
Multifractal Scan from the
FracLac panel.
Visualizing Sub Scan Results
The images below illustrate the basic outputs of the two major types of subscan - particle analyzer and rectangular. The pictures were generated by selecting the colour code option for a subscan.
The binary contours above were automatically partitioned within the image by running a FracLac scan that invokes the ImageJ particle analyzer.
The grayscale texture above was systematically scanned in blocks. As seen in the image, the scan automatically detected two areas of difference in the texture, which are artifacts created using blurring and sharpening in ImageJ on ROIs on the original image. The artifacts are circled on the lower image. The results of the scan, the colour coded blocks, show the corresponding general areas where the differences were found as a difference in the local DB Gray.
Local Variation in the Fractal Dimension Attributable to Digitization.
The simple binary circle was scanned with a rectangular scan, to illustrate local variation attributable to digitization.
Sub Scans and the ROI Manager
Sub-sampling can be done using the ROI Manager or not. To subscan regions previously stored in ImageJ's ROI Manager, set up a subscan then run the scan using the ROIs button on FracLac. This will treat each ROI in the manager as a separate image, and that ROI will then be sub-scanned.
Sub-sampling scans are limited in some ways. One important way is that they are limited to using 1 grid position. Thus, FracLac cannot do filtered or averaged scans when using a subscan method. If you wish to take full advantage of grid positions and can store the ROIs you wish to scan, use the ROI Manager in a standard box count to scan multiple areas on an image.
Results Files
In addition to graphics files, a subscan generates results files. The main results file of a sub area scan is the same file as from a regular scan, except that it contains several rows for each image, corresponding to several samples taken during the sub area scan. To interpret the results file from a subscan, see the main Results file page.
Sub Scan Options
Use the SUB SCAN panel to sample images for regular box counting and multifractal analysis. The options are disabled or do not appear on the panel for all other scan types. To activate subscanning, close this dialog and select one of those scan types from the FracLac panel.
To set up a subscan after setting up the image type and grid:
- Select a sampling method from the subscan method drop-down menu.
- Set other options if they appear below the drop-down.
Choose a Method for Partitioning Images for Sub Sampling
method - Dropdown for sampling methods
Use the dropdown on the SUB SCAN panel to select a method for breaking an image or ROI into subareas. The image below highlights graphically some of the subscan methods. Scroll down to read about them or if subscans are currently activated on the panel, click on the drop down to jump to the relevant section.
Different Methods of Sub Sampling a Binary Image
This figure is a compilation of 5 scans of the image shown on the bottom right (i.e., an image of biological cells processed to binary). Each of the panels shows a Sub Scan method. The colour-coded results were enabled by selecting the colour-code option.
Particle Analyzer Sub Sampling Option
ANALYZER - use ImageJ's Particle Analyzer on binary images
Select this option from the drop-down menu on the SUB SCAN panel to use ImageJ's built-in Particle Analyzer. This setting automatically detects particles in a binary image and analyzes them individually. (See illustration.)
The Analyzer option is available for
binary image types only,
doing
sub scans with regular box counting.
It is disabled for all other scan types and does not appear on the
dropdown unless the appropriate scan and image type are selected. To
show the option in the
drop-down menu
when it is not showing,
select a binary option for the sub scan
image type, or, if
the current scan is not a sub scan,
close this dialog and select one from the
FracLac panel.
This scan type ignores
the settings for
sample size and
number of samples,
so these are unavailable if a Particle Analyzer scan is selected.
Instead, after this
type of scan has been selected on the panel, the panel has been
OK'd, and a scan has been started by clicking on a
SCAN button
on the FracLac panel, a dialog pops up displaying the
background colour that will be used and asking to set
parameters for the particles to assess.
| Particle Analyzer Scan | |
|---|---|
|
Binary image partitioned automatically using the Particle Analyzer, then each particle automatically scanned and colour coded to show its fractal dimension. |
Regular Array Sampling
RECTANGLES - rectangular ROIs in non-overlapping array
OVALS - oval ROIs in non-overlapping array
Select one of these options from the
drop-down menu on the
SUB SCAN panel
to partition an image as a
non-overlapping rectangular
array, then take a sample within each partition
using the specified shape, oval
or rectangle.
These options are available for
sub scans with regular box counting
only, and within that category are
not available for Particle Analyzer scans.
To make an option available, close the dialog and select an
appropriate scan type.
The method used with both of these options
divides an image into a regularly
spaced non-overlapping array using the
sample size
selected on the panel.
The actual shape of the sample taken from this regular array
depends on which option was selected.
The figure below shows the same image scanned using a rectangular
sample (top) and on oval sample (bottom). Each rectangle or
oval was analyzed as a separate image, and its fractal dimension
represented by a colour (see
colour coding).
Oval vs Rectangular Sampling Shapes
There are two notions of shape to consider in FracLac: the shape discussed here refers to the element used to get subscan samples, which is independent of the shape of the element used to gather box counting data within each sample. See RANDOM SAMPLING for an illustration.
Random Sampling
RANDOM RECTANGLES - randomly placed rectangular ROIs
RANDOM OVALS - randomly placed oval ROIs
Select one of these choices from the
drop-down menu
on the
SUB SCAN
panel to have the program randomly sample
an image and do a full scan of each sample independent of
the rest of the image.
Select
RANDOM RECTANGLES to
take square samples, or
RANDOM OVALS
to take oval samples.
Both of these options are available for
Sub Scans. Rectangular
samples but not oval are available for
random multifractal scans. These options are disabled
for all other scans. To enable them, close this dialog
and select one of the scans listed above.
Use the sliders
or their associated number boxes to set the
number of samples and the
size of each sample.
As was
illustrated at the top of this page,
random samples may overlap whereas those
taken using
regular arrays cannot.
Oval Samples with Oval and Rectangular Scanning Elements
The shape of the element used to get subscan samples is independent of the shape of the element used to gather box counting data. The image shows 2 oval random samples taken from an image then scanned using a rectangular (top) and oval (bottom) box counting element.
Sample Pixel By Pixel
LOCAL NOT CONNECTED - sample by pixel
Select this option from the drop-down menu on the SUB SCAN panel to scan an image pixel by pixel, determining an area centered on each pixel and finding its local dimension.
This can be very slow. This method determines the mass dimension around every nth pixel horizontally and vertically using the value in slide x, so is very sensitive to that setting. (NB: this is different from Local Connected Fractal Dimension scans.)
No Sub Sampling Selected or Sub Sampling is Not Available
NO SUB SAMPLING - Not selected or else unavailable
This option is displayed on the drop-down menu on the SUB SCAN panel in two cases:
- A Multifractal Scan has been selected but random sampling has not been selected. To enable sub scanning in this case, click on the drop-down menu and choose one of the options.
- If not the above, then a scan type other than Sub Scan was selected on the FracLac panel, so the option is not available.
To enable subscanning, close this dialog then from the FracLac panel select a Sub Scan or a Multifractal Scan.
Set the Size of Each Sub Area
sample size - Sub sample size in pixels or %
This option is enabled for
Subscans
and Multifractal scans
only. To enable it, close the dialog
and select one of those type from the FracLac panel.
Type or set the slider for this setting on the
SUB SCAN panel to a number for the
size of the side of the basic square for partitioning
images during subscanning for random
and array subscanning.
(See also Number of Subsamples.)
For
particle analyzer scans,
particle size is set through the Analyzer
so this option is not available if that type of
subscan is selected; see Particle
Analyzer Scans for details.
Set the sample size as either a
number of pixels
or a % of image size, depending
on the text displayed on the label. To toggle
between these options, select or deselect the
button beside the slider.
The % value is read
with respect to the size of the ROI currently
selected or the entire image if there is no ROI
currently selected.
If the option displayed on the label beside the slider
on the
SUB SCAN panel
is sample size (%),
type the number you wish to use, without a % sign.
For example, to use a sample size of
50% of the current ROI or image, type 50.
If the option is sample size (pix),
type the number of pixels you wish to use.
For example, to sample an image in blocks or ovals that are
100 pixels wide and 100 pixels high, type 100.
Use sample size (%),
when you do not know the image size ahead of time.
Use sample size (pix) when you know the
image size and want to use the same value for all images.
FracLac samples images in rectangles or ovals (see shape ) that are made as wide and as tall as the size selected. For regular subscans, each sample is treated as a separate image, similar to a batch job, for random and regular array subscans. For multifractal scans, which are subscanned using the random sampling option, random samples are tallied together and one dataset is created. Note that doing subscans takes considerably more time for 1) larger images and 2) smaller sample sizes.
Sub sample size is not the same as box size.
Toggle Sub Sample Size in Pixels vs % of Image or Roi
% vs pixels - toggle the button to change how sample size is determined
Select or unselect this button on the SUB SCAN panel to switch between methods for defining sample size.
This option is available only when the sample size components are visible (e.g., it is not available for Particle Analyzer scans).
Set the Number of Random Samples
number of samples - Enabled for random sampling methods only (see Random Samping)
Type or set the slider for this setting on the SUB SCAN panel to choose the number of random samples to take. Note that random samples are independent of each other and can overlap.
Random Blocks Can Overlap
The image above shows random
rectangular samples
overlapping. The samples were colour
coded according to the fractal dimension of each sample
by selecting the
colour code
option.
This option is for random sampling with subscans and multifractal scans. It is not available if the option for a random sample is not selected. To enable it, select a random sample method from the subscanning method drop-down menu.
For subscans, each sample is treated as a separate image, using the settings currently in the grid set. For random multifractal scans, the samples are tallied together as one dataset.
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