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-.\" ========================================================================
-.\"
-.IX Title "regbounds 7"
-.TH regbounds 7 "April 14, 2011" "version 1.4.5" "SAORD Documentation"
-.SH "NAME"
-RegBounds \- Region Boundaries
-.SH "SYNOPSIS"
-.IX Header "SYNOPSIS"
-Describes how spatial region boundaries are handled.
-.SH "DESCRIPTION"
-.IX Header "DESCRIPTION"
-The golden rule for spatial region filtering was first enunciated by
-Leon VanSpeybroeck in 1986:
-.PP
-Each photon will be counted once, and no photon will be counted
-more than once.
-.PP
-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.
-.PP
-With this in mind, the rules for determining whether a boundary image
-pixel or table row are assigned to a region are defined below.
-.PP
-\&\fBImage boundaries - radially-symmetric shapes (circle, annuli, ellipse)\fR
-.PP
-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:
-.IP "\(bu" 4
-the outer boundary of a symmetric shape does not include such pixels
-.IP "\(bu" 4
-the inner boundary of a symmetric shape (annulus) includes such pixels
-.PP
-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.
-.PP
-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.
-.PP
-\&\fBImage Boundaries: non-radially symmetric shapes (polygons, boxes)\fR
-.PP
-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.
-.PP
-\&\fBRow Boundaries are Analytic\fR
-.PP
-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.
-.PP
-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).
-.PP
-\&\fBImage Boundaries vs. Row Boundaries: Practical Considerations\fR
-.PP
-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:
-.PP
-.Vb 2
-\& fundisp test1.fits"[box(4219,3887,6,6,0)]" | wc
-\& 8893 320148 3752846
-.Ve
-.PP
-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:
-.PP
-.Vb 1
-\& ./funtable test1.fits"[box(4219,3887,6,6,0)]" test2.fits
-.Ve
-.PP
-Now run funcnts using the original filter on the derived file:
-.PP
-.Vb 1
-\& ./funcnts test2.fits "physical; box(4219,3887,6,6,0)"
-.Ve
-.PP
-.Vb 1
-\& [... lot of processed output ...]
-.Ve
-.PP
-.Vb 4
-\& # the following source and background components were used:
-\& source region(s)
-\& ----------------
-\& physical; box(4219,3887,6,6,0)
-.Ve
-.PP
-.Vb 3
-\& reg counts pixels
-\& ---- ------------ ---------
-\& 1 7847.000 36
-.Ve
-.PP
-There are 1044 rows (events) that pass the row filter in fundisp (or
-funtable) but fail to make it through funcnts. Why?
-.PP
-The reason can be traced to how analytic row filtering (fundisp, funtable)
-differs from integerized pixel filtering(funcnts, funimage). Consider the
-region:
-.PP
-.Vb 1
-\& box(4219,3887,6,6,0)
-.Ve
-.PP
-Analytically (i.e., using row filtering), positions will pass this
-filter successfully if:
-.PP
-.Vb 2
-\& 4216 <= x <= 4222
-\& 3884 <= y <= 3890
-.Ve
-.PP
-For example, photons with position values of x=4216.4 or y=3884.08 will pass.
-.PP
-Integerized image filtering is different in that the pixels that will
-pass this filter have centers at:
-.PP
-.Vb 2
-\& x = 4217, 4218, 4219, 4220, 4221, 4222
-\& y = 3885, 3886, 3887, 3888, 3889, 3890
-.Ve
-.PP
-Note that there are 6 pixels in each direction, as specified by the region.
-That means that positions will pass the filter successfully if:
-.PP
-.Vb 2
-\& 4217 <= (int)x <= 4222
-\& 3885 <= (int)y <= 3890
-.Ve
-.PP
-Photons with position values of x=4216.4 or y=3884.08 will \s-1NOT\s0 pass.
-.PP
-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.
-.PP
-[It could be argued that the correct photon limits for floating point
-row data really should be:
-.PP
-.Vb 2
-\& 4216.5 <= x <= 4222.5
-\& 3884.5 <= y <= 3890.5
-.Ve
-.PP
-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.]
-.SH "SEE ALSO"
-.IX Header "SEE ALSO"
-See funtools(7) for a list of Funtools help pages