Note, if you will be rebining a sequence of input arrays and then co-adding them into a single array, the alternative AST_REBINSEQX routines will in general be more efficient.
You should use a rebinning function which matches the numerical type of the data you are processing by replacing
in the generic function name AST_REBINX
by an appropriate 1- or 2-character type code. For example, if you are rebinning data with type REAL,
you should use the function AST_REBINR (see the
" Data Type Codes
" section below for the codes
appropriate to other numerical types).
Rebinning of the grid of input data is performed by transforming the coordinates of the centre of each input grid element (or pixel) into the coordinate system of the output grid. The input pixel value is then divided up and assigned to the output pixels in the neighbourhood of the central output coordinates. A choice of schemes are provided for determining how each input pixel value is divided up between the output pixels. In general, each output pixel may be assigned values from more than one input pixel. All contributions to a given output pixel are summed to produce the final output pixel value. Output pixels can be set to the supplied bad value if they receive contributions from an insufficient number of input pixels. This is controlled by the WLIM argument.
Input pixel coordinates are transformed into the coordinate system of the output grid using the
forward transformation of the Mapping which is supplied. This means that geometrical features in the
input data are subjected to the Mapping
’ s forward transformation as they are transferred from the
input to the output grid.
In practice, transforming the coordinates of every pixel of a large data grid can be time-consuming, especially if the Mapping involves complicated functions, such as sky projections. To improve performance, it is therefore possible to approximate non-linear Mappings by a set of linear transformations which are applied piece-wise to separate sub-regions of the data. This approximation process is applied automatically by an adaptive algorithm, under control of an accuracy criterion which expresses the maximum tolerable geometrical distortion which may be introduced, as a fraction of a pixel.
This algorithm first attempts to approximate the Mapping with a linear transformation applied over the whole region of the input grid which is being used. If this proves to be insufficiently accurate, the input region is sub-divided into two along its largest dimension and the process is repeated within each of the resulting sub-regions. This process of sub-division continues until a sufficiently good linear approximation is found, or the region to which it is being applied becomes too small (in which case the original Mapping is used directly).
The number of input coordinates used by this Mapping (as given by its Nin attribute) should match the number of input grid dimensions given by the value of NDIM_IN below. Similarly, the number of output coordinates (Nout attribute) should match the number of output grid dimensions given by NDIM_OUT.
Note that LBND_IN and UBND_IN together define the shape and size
of the input grid, its extent along a particular (J
’ th) dimension being
They also define the input grid
’ s coordinate system, each pixel having unit
extent along each dimension with integral coordinate values at its centre.
The storage order of data within this array should be such that the index of the first grid dimension varies most rapidly and that of the final dimension least rapidly (i.e. normal Fortran array storage order).
If the AST__USEVAR flag is not set, no input variance estimates are required and this array will not be used. A dummy (e.g. one-element) array may then be supplied.
"Pixel Spreading Schemes
"section below. If a value of zero is supplied, then the default linear spreading scheme is used (equivalent to supplying the value AST__LINEAR).
"Pixel Spreading Schemes
If no additional parameters are required, this array is not used. A dummy (e.g. one-element) array may then be supplied.
"section below for a description of the options available. If no flag values are to be set, a value of zero should be given.
’s coordinate system.
If piece-wise linear approximation is not required, a value of zero may be given. This will ensure that the Mapping is used without any approximation, but may increase execution time.
If the value is too high, discontinuities between the linear approximations used in adjacent panel will be higher, and may cause the edges of the panel to be visible when viewing the output image at high contrast. If this is a problem, reduce the tolerance value used.
If a smaller value is used, the input region will first be divided into sub-regions whose size does not exceed MAXPIX pixels in any dimension. Only at this point will attempts at approximation commence.
This value may occasionally be useful in preventing false convergence of the adaptive algorithm in cases where the Mapping appears approximately linear on large scales, but has irregularities (e.g. holes) on smaller scales. A value of, say, 50 to 100 pixels can also be employed as a safeguard in general-purpose software, since the effect on performance is minimal.
If too small a value is given, it will have the effect of inhibiting linear approximation altogether (equivalent to setting TOL to zero). Although this may degrade performance, accurate results will still be obtained.
If the AST__USEBAD flag is set via the FLAGS argument, then this value is used to test for bad pixels in the IN (and IN_VAR) array(s).
In all cases, this value is also used to flag any output elements in the OUT (and OUT_VAR) array(s) for
which rebined values could not be obtained (see the
" Propagation of Missing Data
" section below for
details of the circumstances under which this may occur).
Note that LBND_OUT and UBND_OUT together define the shape, size and coordinate system of the output grid in the same way as LBND_IN and UBND_IN define the shape, size and coordinate system of the input grid.
Note that LBND and UBND together define the shape and position of a (hyper-)rectangular region of the input grid which is to be included in the rebined output array. This region should lie wholly within the extent of the input grid (as defined by the LBND_IN and UBND_IN arrays). Regions of the input grid lying outside this region will not be used.
The output variance values will be calculated on the assumption that errors on the input data values are statistically independent and that their variance estimates may simply be summed (with appropriate weighting factors) when several input pixels contribute to an output data value. If this assumption is not valid, then the output error estimates may be biased. In addition, note that the statistical errors on neighbouring output data values (as well as the estimates of those errors) may often be correlated, even if the above assumption about the input data is correct, because of the pixel spreading schemes employed.
If the AST__USEVAR flag is not set, no output variance estimates will be calculated and this array will not be used. A dummy (e.g. one-element) array may then be supplied.
D: DOUBLE PRECISION
B: BYTE (treated as signed)
UB: BYTE (treated as unsigned)
For example, AST_REBIND would be used to process DOUBLE PRECISION data, while AST_REBINI would be used to process integer data (stored in an INTEGER array), etc.
Note that, unlike AST_RESAMPLEX, the AST_REBINX set of functions does not yet support unsigned integer data types or integers of different sizes.
The binning algorithm used has the ability to introduce artifacts not seen when using a resampling algorithm. Particularly, when viewing the output image at high contrast, systems of curves lines covering the entire image may be visible. These are caused by a beating effect between the input pixel positions and the output pixels position, and their nature and strength depend critically upon the nature of the Mapping and the spreading function being used. In general, the nearest neighbour spreading function demonstrates this effect more clearly than the other functions, and for this reason should be used with caution.
The following values (defined in the AST_PAR include file) may be assigned to the SPREAD parameter. See the AST_RESAMPLEX documentation for details of these schemes including the use of the FSPREAD and PARAMS arguments:
In addition, the following schemes can be used with AST_REBINX but not with AST_RESAMPLEX:
AST__GAUSS: This scheme uses a kernel of the form exp(-kxx), with k a positive constant determined by the full-width at half-maximum (FWHM). The FWHM should be supplied in units of output pixels by means of the PARAMS(2) value and should be at least 0.1. The PARAMS(1) value should be used to specify at what point the Gaussian is truncated to zero. This should be given as a number of output pixels on either side of the central output point in each dimension (the nearest integer value is used).
AST__USEBAD: Indicates that there may be bad pixels in the input array(s) which must be recognised by comparing with the value given for BADVAL and propagated to the output array(s). If this flag is not set, all input values are treated literally and the BADVAL value is only used for flagging output array values.
AST__USEVAR: Indicates that variance information should be processed in order to provide estimates of the statistical error associated with the rebined values. If this flag is not set, no variance processing will occur and the IN_VAR and OUT_VAR arrays will not be used. (Note that this flag is only available in the Fortran interface to AST.)
An input pixel is considered bad (and is consequently ignored) if its data value is equal to BADVAL and the AST__USEBAD flag is set via the FLAGS argument.
In addition, associated output variance estimates (if calculated) may be declared bad and flagged with the BADVAL value in the OUT_VAR array for similar reasons.
"interface for this function should be used. This alternative interface uses 8 byte integer arguments (instead of 4-byte) to hold pixel indices and pixel counts. Specifically, the arguments LBND_IN, UBND_IN, LBND_OUT, UBND_OUT, LBND, UBND are changed from type INTEGER to type INTEGER8. The function return type is similarly changed to type INTEGER8. The function name is changed by inserting the digit
"before the trailing data type code. Thus, AST_REBINX becomes AST_REBIN8X.