NAME¶
RegBounds - Region Boundaries
SYNOPSIS¶
Describes how spatial region boundaries are handled.
DESCRIPTION¶
The golden rule for spatial region filtering was first enunciated by Leon
VanSpeybroeck in 1986:
Each photon will be counted once, and no photon will be counted more than once.
This means that we must be careful about boundary conditions. For example, if a
circle is contained in an annulus such that the inner radius of the annulus is
the same as the radius of the circle, then photons on that boundary must
always be assigned to one or the other region. That is, the number of photons
in both regions must equal the sum of the number of photons in each region
taken separately.
With this in mind, the rules for determining whether a boundary image pixel or
table row are assigned to a region are defined below.
Image boundaries - radially-symmetric shapes (circle, annuli, ellipse)
For image filtering, pixels whose center is inside the boundary are included.
This also applies non-radially-symmetric shapes. When a pixel center is
exactly on the boundary, the pixel assignment rule is:
- •
- the outer boundary of a symmetric shape does not include such pixels
- •
- the inner boundary of a symmetric shape (annulus) includes such
pixels
In this way, an annulus with radius from 0 to 1, centered exactly on a pixel,
includes the pixel on which it is centered, but none of its neighbors.
These rules ensure that when defining concentric shapes, no pixels are omitted
between concentric regions and no pixels are claimed by two regions. When
applied to small symmetric shapes, the shape is less likely to be skewed, as
would happen with non-radially-symmetric rules. These rules differ from the
rules for box-like shapes, which are more likely to be positioned adjacent to
one another.
Image Boundaries - non-radially symmetric shapes (polygons, boxes)
For image filtering, pixels whose center is inside the boundary are included.
This also applies radially-symmetric shapes. When a pixel center is exactly on
the boundary of a non-radially symmetric region, the pixel is included in the
right or upper region, but not the left or lower region. This ensures that
geometrically adjoining regions touch but don't overlap.
Row Boundaries are Analytic
When filtering table rows, the boundary rules are the same as for images, except
that the calculation is not done on the center of a pixel, (since table rows,
especially X\-ray events rows, often have discrete, floating point positions)
but are calculated exactly. That is, an row is inside the boundary without
regard to its integerized pixel value. For rows that are exactly on a region
boundary, the above rules are applied to ensure that all rows are counted once
and no row is counted more than once.
Because row boundaries are calculated differently from image boundaries, certain
programs will give different results when filtering the same region file. In
particular, fundisp/funtable (which utilize analytic row filtering) perform
differently from funcnts (which performs image filtering, even on tables).
Image Boundaries vs. Row Boundaries - Practical Considerations
You will sometimes notice a discrepancy between running funcnts on an binary
table file and running fundisp on the same file with the same filter. For
example, consider the following:
fundisp test1.fits"[box(4219,3887,6,6,0)]" ⎪ wc
8893 320148 3752846
Since fundisp has a 2\-line header, there are actually 8891 photons that pass
the filter. But then run funtable and select only the rows that pass this
filter, placing them in a new file:
./funtable test1.fits"[box(4219,3887,6,6,0)]" test2.fits
Now run funcnts using the original filter on the derived file:
./funcnts test2.fits "physical; box(4219,3887,6,6,0)"
[... lot of processed output ...]
# the following source and background components were used:
source region(s)
----------------
physical; box(4219,3887,6,6,0)
reg counts pixels
---- ------------ ---------
1 7847.000 36
There are 1044 rows (events) that pass the row filter in fundisp (or funtable)
but fail to make it through funcnts. Why?
The reason can be traced to how analytic row filtering (fundisp, funtable)
differs from integerized pixel filtering(funcnts, funimage). Consider the
region:
box(4219,3887,6,6,0)
Analytically (i.e., using row filtering), positions will pass this filter
successfully if:
4216 <= x <= 4222
3884 <= y <= 3890
For example, photons with position values of x=4216.4 or y=3884.08 will pass.
Integerized image filtering is different in that the pixels that will pass this
filter have centers at:
x = 4217, 4218, 4219, 4220, 4221, 4222
y = 3885, 3886, 3887, 3888, 3889, 3890
Note that there are 6 pixels in each direction, as specified by the region. That
means that positions will pass the filter successfully if:
4217 <= (int)x <= 4222
3885 <= (int)y <= 3890
Photons with position values of x=4216.4 or y=3884.08 will NOT pass.
Note that the position values are integerized, in effect, binned into image
values. This means that x=4222.4 will pass this filter, but not the analytic
filter above. We do this to maintain the design goal that either all counts in
a pixel are included in an integerized filter, or else none are included.
[It could be argued that the correct photon limits for floating point row data
really should be:
4216.5 <= x <= 4222.5
3884.5 <= y <= 3890.5
since each pixel extends for .5 on either side of the center. We chose to the
maintain integerized algorithm for all image-style filtering so that funcnts
would give the exact same results regardless of whether a table or a derived
non-blocked binned image is used.]
SEE ALSO¶
See
funtools(7) for a list of Funtools help pages