## Regions: Spatial Region Filtering

## Summary

This document contains a summary of the user interface for spatial region filtering images and tables.

## Description

Spatial region filtering allows a program to select regions of an image or rows of a table (e.g., X-ray events) to process using simple geometric shapes and boolean combinations of shapes. When an image is filtered, only pixels found within these shapes are processed. When a table is filtered, only rows found within these shapes are processed.

Spatial region filtering for images and tables is accomplished by means of region specifications. A region specification consists of one or more region expressions, which are geometric shapes,combined according to the rules of boolean algebra. Region specifications also can contain comments and local/global processing directives.

Typically, region specifications are specified using bracket notation appended to the filename of the data being processed:

      foo.fits[circle(512,512,100)]

It is also possible to put region specification inside a file and then pass the filename in bracket notation:

      foo.fits[@my.reg]

When region filters are passed in bracket notation in this manner, the filtering is set up automatically when the file is opened and all processing occurs through the filter. Programs also can use the filter library API to open filters explicitly.

## Region Expressions

More specifically, region specifications consist of one or more lines containing:

      # comment until end of line
      global   keyword=value keyword=value  ... # set global value(s)
      # include the following file in the region descriptor
      @file
      # use the FITS image as a mask (cannot be used with other regions)
      @fitsimage
      # each region expression contains shapes separated by operators
      [region_expression1], [region_expression2], ...
      [region_expression], [region_expression], ...

A single region expression consists of:

      # parens and commas are optional, as is the + sign
      [+-]shape(num , num , ...) OP1 shape num num num OP2 shape ...

    e.g.:

      ([+-]shape(num , num , ...) && shape num  num || shape(num, num)
      # a comment can come after a region -- reserved for local properties
      [+-]shape(num , num , ...)  # local properties go here, e.g. color=red

Thus, a region descriptor consists of one or more region expressions or regions, separated by comas, new-lines, or semi-colons. Each region consists of one or more geometric shapes combined using standard boolean operation. Several types of shapes are supported, including:

      shape:        arguments:
      -----         ----------------------------------------
      ANNULUS       xcenter ycenter inner_radius outer_radius
      BOX           xcenter ycenter xwidth yheight (angle)
      CIRCLE        xcenter ycenter radius
      ELLIPSE       xcenter ycenter xwidth yheight (angle)
      FIELD         none
      LINE          x1 y1 x2 y2
      PIE           xcenter ycenter angle1 angle2
      POINT         x1 y1
      POLYGON       x1 y1 x2 y2 ... xn yn

In addition, the following regions accept accelerator syntax:

      shape      arguments
      -----      ------------------------------------------
      ANNULUS    xcenter ycenter radius1 radius2 ... radiusn
      ANNULUS    xcenter ycenter inner_radius outer_radius n=[number]
      BOX        xcenter ycenter xw1 yh1 xw2 yh2 ... xwn yhn (angle)
      BOX        xcenter ycenter xwlo yhlo xwhi yhhi n=[number] (angle)
      CIRCLE     xcenter ycenter r1 r2 ... rn              # same as annulus
      CIRCLE     xcenter ycenter rinner router n=[number]  # same as annulus
      ELLIPSE    xcenter ycenter xw1 yh1 xw2 yh2 ... xwn yhn (angle)
      ELLIPSE    xcenter ycenter xwlo yhlo xwhi yhhi n=[number] (angle)
      PIE        xcenter ycenter angle1 angle2 (angle3) (angle4) (angle5) ...
      PIE        xcenter ycenter angle1 angle2 (n=[number])
      POINT      x1 y1 x2 y2 ... xn yn

Note that the circle accelerators are simply aliases for the annulus accelerators. See region geometry for more information about accelerators.

Finally, the following are combinations of pie with different shapes (called "panda" for "Pie AND Annulus") allow for easy specification of radial sections:

      shape:  arguments:
      -----   ---------
      PANDA   xcen ycen ang1 ang2 nang irad orad nrad   # circular
      CPANDA  xcen ycen ang1 ang2 nang irad orad nrad   # circular
      BPANDA  xcen ycen ang1 ang2 nang xwlo yhlo xwhi yhhi nrad (ang) # box
      EPANDA  xcen ycen ang1 ang2 nang xwlo yhlo xwhi yhhi nrad (ang) # ellipse

The panda and cpanda specify combinations of annulus and circle with pie, respectively and give identical results. The bpanda combines box and pie, while epanda combines ellipse and pie. See region geometry for more information about pandas.

The following "shapes" are ignored by funtools (generated by ds9):

      shape:        arguments:
      -----         ---------
      PROJECTION    x1 y1 x2 y2 width    # NB: ignored by funtools
      RULER         x1 y1 x2 y2          # NB: ignored by funtools
      TEXT          x y                  # NB: ignored by funtools
      GRID                               # NB: ignored by funtools
      TILE                               # NB: ignored by funtools
      COMPASS                            # NB: ignored by funtools

All arguments to regions are real values; integer values are automatically converted to real where necessary. All angles are in degrees and run from the positive image x-axis to the positive image y-axis. If a rotation angle is part of the associated WCS header, that angle is added implicitly as well.

Note that 3-letter abbreviations are supported for all shapes, so that you can specify "circle" or "cir".

## Columns Used in Region Filtering

By default, the x,y values in a region expression refer to the two "image binning" columns, i.e. the columns that would be used to bin the data into an image. For images, these are just the 2 dimensions of the image. For tables, these usually default to x and y but can be changed as required. For example, in Funtools, new binning columns are specified using a bincols=(col1,col2) statement within the bracket string on the command line.

Alternate columns for region filtering can be specified by the syntax:

      (col1,col2)=region(...)

e.g.:

      (X,Y)=annulus(x,y,ri,ro)
      (PHA,PI)=circle(x,y,r)
      (DX,DY)=ellipse(x,y,a,b[,angle])

## Region Algebra

(See also Region Algebra for more complete information.)

Region shapes can be combined together using Boolean operators:

      Symbol        Operation       Use
      --------      ---------       -----------------------------------
      !             not             Exclude this shape from this region
      & or &&       and             Include only the overlap of these shapes
      | or ||       inclusive or    Include all of both shapes
      ^             exclusive or    Include both shapes except their overlap

Note that the !region syntax must be combined with another region in order that we be able to assign a region id properly. That is,

      !circle(512,512,10)

is not a legal region because there is no valid region id to work with. To get the full field without a circle, combine the above with field(), as in:

      field() && !circle(512,512,10)

## Region Separators Also Are Operators

As mentioned previously, multiple region expressions can be specified in a region descriptor, separated by commas, new-lines, or semi-colons. When such a separator is used, the boolean OR operator is automatically generated in its place but, unlike explicit use of the OR operator, the region ID is incremented (starting from 1).

For example, the two shapes specified in this example are given the same region value:

      foo.fits[circle(512,512,10)||circle(400,400,20)]

On the other hand, the two shapes defined in the following example are given different region values:

      foo.fits[circle(512,512,10),circle(400,400,20)]

Of course these two examples will both mask the same table rows or pixels. However, in programs that distinguish region id's (such as funcnts ), they will act differently. The explicit OR operator will result in one region expression consisting of two shapes having the same region id and funcnts will report a single region. The comma operator will cause funcnts to report two region expressions, each with one shape, in its output.

In general, commas are used to separate region expressions entered in bracket notation on the command line:

      # regions are added to the filename in bracket notation
      foo.fits[circle(512,512,100),circle(400,400,20)]

New-lines are used to separate region expressions in a file:

      # regions usually are separated by new-lines in a file
      # use @filename to include this file on the command line
      circle(512,512,100)
      circle(400,400,20)

Semi-colons are provided for backward compatibility with the original IRAF/PROS implementation and can be used in either case.

If a pixel is covered by two different regions expressions, it is given the mask value of the first region that contains that pixel. That is, successive regions do not overwrite previous regions in the mask, as was the case with the original PROS regions. In this way, an individual pixel is covered by one and only one region. This means that one must sometimes be careful about the order in which regions are defined. If region N is fully contained within region M, then N should be defined before M, or else it will be "covered up" by the latter.

## Region Exclusion

Shapes also can be globally excluded from all the region specifiers in a region descriptor by using a minus sign before a region:

      operator      arguments:
      --------      -----------
      -             Globally exclude the region expression following '-' sign
                    from ALL regions specified in this file

The global exclude region can be used by itself; in such a case, field() is implied.

A global exclude differs from the local exclude (i.e. a shape prefixed by the logical not "!" symbol) in that global excludes are logically performed last, so that no region will contain pixels from a globally excluded shape. A local exclude is used in a boolean expression with an include shape, and only excludes pixels from that include shape. Global excludes cannot be used in boolean expressions.

## Include Files

The @filename directive specifies an include file containing region expressions. This file is processed as part of the overall region descriptor:

      foo.fits[circle(512,512,10),@foo]

A filter include file simply includes text without changing the state of the filter. It therefore can be used in expression. That is, if the file foo1 contains "pi==1" and foo2 contains "pha==2" then the following expressions are equivalent:

      "[@foo1&&@foo2]"   is equivalent to   "[pi==1&&pha==2]"
      "[pha==1||@foo2]"  is equivalent to   "[pi==1||pha==2]"
      "[@foo1,@foo2]"    is equivalent to   "[pi==1,pha==2]"

Be careful that you specify evaluation order properly using parenthesis, especially if the include file contains multiple filter statements. For example, consider a file containing two regions such as:

      circle 512 512 10
      circle 520 520 10

If you want to include only events (or pixels) that are in these regions and have a pi value of 4, then the correct syntax is:

        pi==4&&(@foo)

since this is equivalent to:

        pi==4 && (circle 512 512 10 || circle 520 520 10)

If you leave out the parenthesis, you are filtering this statement:

        pi==4 && circle 512 512 10 || circle 520 520 10)

which is equivalent to:

        (pi==4 && circle 512 512 10) || circle 520 520 10)

The latter syntax only applies the pi test to the first region.

For image-style filtering, the @filename can specify an 8-bit or 16-bit FITS image. In this case, the pixel values in the mask image are used as the region mask. The valid pixels in the mask must have positive values. Zero values are excluded from the mask and negative values are not allowed. Moreover, the region id value is taken as the image pixel value and the total number of regions is taken to be the highest pixel value. The dimensions of the image mask must be less than or equal to the image dimensions of the data. The mask will be replicated as needed to match the size of the image. (Thus, best results are obtained when the data dimensions are an even multiple of the mask dimensions.)

An image mask can be used in any image filtering operation, regardless of whether the data is of type image or table. For example, the funcnts ) program performs image filtering on images or tables, and so FITS image masks are valid input for either type of data in this program.. An image mask cannot be used in a program such as fundisp ) when the input data is a table, because fundisp displays rows of a table and processes these rows using event-style filtering.

## Global and Local Properties of Regions

The ds9 image display program describes a host of properties such as color, font, fix/free state, etc. Such properties can be specified globally (for all regions) or locally (for an individual region). The global keyword specifies properties and qualifiers for all regions, while local properties are specified in comments on the same line as the region:

      global color=red
      circle(10,10,2)
      circle(20,20,3) # color=blue
      circle(30,30,4)

The first and third circles will be red, which the second circle will be blue. Note that funtools currently ignores region properties, as they are used in display only.

## Coordinate Systems

For each region, it is important to specify the coordinate system used to interpret the region, i.e., to set the context in which position and size values are interpreted. For this purpose, the following keywords are recognized:

      name                  description
      ----                  ------------------------------------------
      PHYSICAL              pixel coords of original file using LTM/LTV
      IMAGE                 pixel coords of current file
      FK4, B1950            sky coordinate systems
      FK5, J2000            sky coordinate systems
      GALACTIC              sky coordinate systems
      ECLIPTIC              sky coordinate systems
      ICRS                  currently same as J2000
      LINEAR                linear wcs as defined in file
      AMPLIFIER             mosaic coords of original file using ATM/ATV
      DETECTOR              mosaic coords of original file using DTM/DTV

## Specifying Positions, Sizes, and Angles

The arguments to region shapes can be floats or integers describing positions and sizes. They can be specified as pure numbers or using explicit formatting directives:

      position arguments    description
      ------------------    ------------------------------
      [num]                 context-dependent (see below)
      [num]d                degrees
      [num]r                radians
      [num]p                physical pixels
      [num]i                image pixels
      [num]:[num]:[num]     hms for 'odd' position arguments
      [num]:[num]:[num]     dms for 'even' position arguments
      [num]h[num]m[num]s    explicit hms
      [num]d[num]m[num]s    explicit dms

      size arguments        description
      --------------        -----------
      [num]                 context-dependent (see below)
      [num]"                arc seconds
      [num]'                arc minutes
      [num]d                degrees
      [num]r                radians
      [num]p                physical pixels
      [num]i                image pixels

When a "pure number" (i.e. one without a format directive such as 'd' for 'degrees') is specified, its interpretation depends on the context defined by the 'coordsys' keyword. In general, the rule is:

All pure numbers have implied units corresponding to the current coordinate system.

If no such system is explicitly specified, the default system is implicitly assumed to be PHYSICAL.

In practice this means that for IMAGE and PHYSICAL systems, pure numbers are pixels. Otherwise, for all systems other than linear, pure numbers are degrees. For LINEAR systems, pure numbers are in the units of the linear system. This rule covers both positions and sizes.

The input values to each shape can be specified in several coordinate systems including:

      name                  description
      ----                  ----------------------------
      IMAGE                 pixel coords of current file
      LINEAR                linear wcs as defined in file
      FK4, B1950            various sky coordinate systems
      FK5, J2000
      GALACTIC
      ECLIPTIC
      ICRS
      PHYSICAL              pixel coords of original file using LTM/LTV
      AMPLIFIER             mosaic coords of original file using ATM/ATV
      DETECTOR              mosaic coords of original file using DTM/DTV

If no coordinate system is specified, PHYSICAL is assumed. PHYSICAL or a World Coordinate System such as J2000 is preferred and most general. The coordinate system specifier should appear at the beginning of the region description, on a separate line (in a file), or followed by a new-line or semicolon; e.g.,

      global coordsys physical
      circle 6500 9320 200

The use of celestial input units automatically implies WORLD coordinates of the reference image. Thus, if the world coordinate system of the reference image is J2000, then

      circle 10:10:0 20:22:0 3'

is equivalent to:

      circle 10:10:0 20:22:0 3' # j2000

Note that by using units as described above, you may mix coordinate systems within a region specifier; e.g.,

      circle 6500 9320 3' # physical

Note that, for regions which accept a rotation angle:

    ellipse (x, y, r1, r2, angle)
    box(x, y, w, h, angle)

the angle is relative to the specified coordinate system. In particular, if the region is specified in WCS coordinates, the angle is related to the WCS system, not x/y image coordinate axis. For WCS systems with no rotation, this obviously is not an issue. However, some images do define an implicit rotation (e.g., by using a non-zero CROTA value in the WCS parameters) and for these images, the angle will be relative to the WCS axes. In such case, a region specification such as:

    fk4;ellipse(22:59:43.985, +58:45:26.92,320", 160", 30)

will not, in general, be the same region specified as:

    physical;ellipse(465, 578, 40, 20, 30)

even when positions and sizes match. The angle is relative to WCS axes in the first case, and relative to physical x,y axes in the second.

More detailed descriptions are available for: Region Geometry, Region Algebra, Region Coordinates, and Region Boundaries.

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##### Last updated: November 17, 2005