7.6 Image analysis

Image analysis is a very broad subject covering essentially all that  does or would like to do plus specialized programs designed to analyze a user’s particular image in the light of his favorite astrophysical theories.  provides some general programs to perform geometric conversions, image filtering or enhancement, and model fitting and subtraction. These are the subjects of the following sections. Specialized programs for spectral-line, VLBI, and single-dish data reduction are described in Chapter 8, Chapter 9, and Chapter 10, respectively. Chapter 11 of Synthesis Imaging in Radio Astronomy⁶ covers the topic of image analysis in more detail.

7.6.1 Geometric conversions

The units of the geometry of an image are described in its header by the coordinate reference values, reference pixels, axis increments, axis dimensions, and axis types. The types of coordinates (celestial, galactic, etc.) and the type of tangent-plane projection (SIN from the VLA, TAN from optical telescopes, ARC from Schmidt telescopes, NCP from the WSRT) are specified in the  headers by character strings. See §6.1.2 and  Memo No. 27 for details of these projections. A “geometric conversion” is an alteration of one or more of these geometry parameters while maintaining the correctness of both the header and the image data. The  tasks which do this interpolate the data from the pixel positions in the input image to the desired pixel positions in the output image.

The simplest geometric conversion is a re-gridding of the data with new axis increments and dimensions with no change in the type of projection or coordinates. The task LGEOM performs this basic function and also allows rotation of the image. One use of this task is to obtain smoother displays by re-gridding a sub-image onto a finer grid. To rotate and blow up the inner portion of a 512² image, enter:

LGEOM allows shifts of the image center, an additional scaling of the y axis relative to the x axis, and polynomial interpolations of up to 7^th order. OGEOM is similar to LGEOM, but handles blanked pixels in a manner that does not increase the blanked area.

A much more general geometric transformation is performed by OHGEO and HGEOM, which convert one image into the geometry of a second image. The type of projection, the axis increments, the rotation, and the coordinate reference values and locations of one image are converted to those of a second image. One of these tasks should be used before comparing images (with COMB, KNTR, PCNTR, BLANK, TVBLINK, etc.) made with different geometries, i.e., radio and optical images in different types of projection or VLA images taken with different phase reference positions. Use EXPLAIN OHGEO  C R to obtain the details and useful advice. SKYVE re-grids images from the Digital Sky Survey (optical DSS) into coordinates recognized by .

A potentially very powerful transformation is performed by PGEOM. In its basic mode, it converts between rectangular and polar coordinates. An example of this operation is illustrated in Figure 7.1. However, PGEOM can also “de-project” elliptical objects to correct for their inclination and “unwrap” spiral objects. Type EXPLAIN PGEOM  C R for information.

7.6.2 Mathematical operations on a single image

The task MATHS allows the user to do a mathematical operation on a single image on a pixel by pixel basis. Currently supported mathematical operators are: SIN, COS, TAN, ASIN, ACOS, ATAN, LOG, LOGN, ALOG, EXP, POLY, POWR, and MOD. An example of MATHS follows, in which the output image (OUT) is computed in terms of the natural logarithm of the input image (IN) as follows: OUT = 4 + 2 × (log(3 × IN) - 1)

Undefined output pixels (in the current example, all pixels in the input image ≤ 0) are either blanked (CPARM(6) ≤ 0) or put to zero (CPARM(6) > 0). Type EXPLAIN MATHS  C R for further information on the available operators and the meaning of CPARM for any particular operator.

7.6.3 Primary beam correction

PBCOR allows correction for the attenuation due to the shape of the primary beam. Its use is straightforward:

The default behavior requested above uses the position in the header as the pointing position and uses the empirically determined shape of the EVLA, VLA, MeerKAT, GMRT, or ATCA primary beam; PBCOR will scale the primary beam shape according to the frequency provided in the image header and use the parameters associated with the particular antenna feed. These defaults can be overridden by specifying particular values of COORDIN and PBPARM. They beam parameters are frequency dependent within each band, so PBCOR determines the beam value at the two tabulated frequencies nearest to the image frequency and then interpolates. In 31DEC21, Gaussian and polynomial beam patterns have been added as options specified with OPCODE and APARM. Beam parameters for MeerKAT and GMRT were added to 31DEC22 and 31DEC23, respectively, and are known to all tasks which correct for the primary beam.

The task SPCOR may be used to apply corrections both for primary beam and for spectral index. The latter are based on images of spectral index and spectral index curvature such as those used in IMAGR (§5.3.4.4). Such corrections may be significant in Faraday-rotation synthesis (§7.2, §7.5.5).

An image of the primary beam may be generated with the task PATGN using OPCODE ’BEAM’  C R with other adverbs to give the antenna type, frequency, cell size, image size, and, optionally, the parameters of the beam shape.

7.6.4 Changing the resolution of an image

CCRES allows you to change the resolution of a Cleaned image by removing any Clean components in the image and then restoring Clean components with your choice of resolution. The task may also be used to remove Clean components to create a residual image or to restore Clean components to an existing residual image. CCRES allows you to smooth or hyper-resolve your image. Unlike RSTOR, CCRES re-scales the residual image to put it into units of Jy/beam for the new beam. This may be a superior way to image with a beam that does not replicate the central portion of the dirty beam. IMAGR leaves the residual image in units of Jy per dirty beam while restoring the Clean components in units of Jy per the Clean beam given in the header.

Note that CCRES only changes the Clean components, not the residual image resolution. Furthermore, CCRES does not take into account the varying resolutions of the many planes in an image cube. CONVL on the other hand, with OPCODE ’GAUS’, will convolve both the Clean components and the residual to the requested resolution, taking into account the change in input resolution as a function of frequency.

7.6.5 Filtering

For our purposes here, we can define “filtering” as applying an operator to an image in order to enhance some aspects of the image. The operators can be linear or nonlinear and do, in general, destroy some of the information content of the output image. As a result, users should be cautious about summing fluxes or fitting models in filtered images. (Technically, these remarks can also be made about Clean and self-calibration.) However, filtered images may bring out important aspects of the data and often make excellent, if unfamiliar-looking, displays of particular aspects.

NINER produces an image by applying an operator to each cell of an image and its 8 nearest cells. The task offers three nonlinear operators which enhance edges (regions of high gradient in any direction). It also offers linear convolutions with a 3 × 3 kernel which can be provided by the user or chosen from a variety of built-in kernels. Among the latter are kernels to enhance point sources and kernels to measure gradients in any of 8 directions. The ’SOBL’ edge-enhancement filter can bring out jets, wisps, and points in the data, while the gradient convolutions produce images which resemble a landscape viewed from above with illumination at some glancing angle (as when viewing the Moon). Both are very effective when displayed on the TV or by the KNTR / LWPLA combination (see Figure 7.1). Enter EXPLAIN NINER  C R for additional information.

MWFLT, at present, applies any one of six non-linear, low-pass filters to the input image. Each filter is applied in a user-specified window surrounding each input pixel. One of the operators is a “normalization” filter designed to reduce the dynamic range required for the image while bringing out weaker features. Two of the operators are a “min” and “max” within the window. When applied in succession, they produce a useful low-pass filtered image (Rudnick, L. 2002, PASP, 114, 427). Other operators produce, at each pixel, the weighted sum of the input and the median, the “alpha-trimmed” mean, or the alpha-trimmed mode of the data in the window surrounding the pixel. These filters can be turned into high-pass filters by subtracting the output of MWFLT from the input with COMB. Type EXPLAIN MWFLT  C R for further information.

Histogram equalization provides another form of non-linear filtering. HISEQ converts the intensities of the full input image to make an output image with a nearly flat histogram. This magnifies small differences in the heavily occupied parts of the histogram (usually noise) and diminishes large differences in the less occupied parts (often real signal). TVHLD is an interactive task that loads an image to the TV with histogram equilization and then allows the intensity range and method of computing the histogram to be modified. It can write out at the end an equilized image in arbitrary (non-physical) units. AHIST does an “adaptive” histogram equalization on each pixel using a rectangular window centered on that pixel. This will magnify small differences in a more local sense, bringing out structures in smooth areas of different brightness. SHADW generates a shadowed image as if a landscape having elevation proportional to image value were illuminated by the Sun at a user-controlled angle. Although these tasks magnify noise, they are likely to elucidate real structures in large areas of nearly constant brightness.