### 9 Highlighting faint diffuse objects

Three small applications are included in ESP for the purposes of detecting faint diffuse objects in an image. The algorithms employed are used to generate versions of the source image in which the contrast has been heightened for an object of a given scale length. They are described in the sections that follow. For all the commands given here, if the image IN has a SKY co-ordinate frame in its WCS component, the PSIZE parameter will be calculated automatically and need not be given explicitly.

#### 9.1 Self-correlation

The ESP application SELFC generates an image on which areas displaying a degree of symmetry are more easily identified. The algorithm employed examines the position of all the pixels within a given radius of the pixel currently being considered and from that creates a set of pairs consisting of pixels equidistant from, and on opposite sides of it. A sum is then made which is maximised if the pixels pairs are both above the sky value and also of similar brightness. The sum derived is normalised and inserted into the pixel on the output image corresponding to the current pixel.

The normalisation is not to the 0–1 range but instead supplies a value above or below zero. Any object with a value below zero on the output image must be a statistical fluke or arises from poor flat field, whilst objects with values above zero may be real. Given the simple normalisation employed it is difficult to determine exactly what is real statistically. However, a good guess may be made in the following way. Generate a self-correlated image (IMAGE1) from the source image using SELFC. Then, scramble the source image using the ESP application MIXUP to generate a noise equivalent image (IMAGE2). Apply SELFC to IMAGE2 and then find the modal pixel value (BACK) and its associated standard deviation (SIGMA) using HISTPEAK. The rule is then that any object brighter than BACK$+$3$×$SIGMA in IMAGE1 is probably real. For the highest possible accuracy the values of BACK and SIGMA should be derived from examination of 10 scrambled versions of IMAGE1, but the calculation time involved may be substantial.

The application can be used with the following syntax:

% selfc in=ic3374 out=ic3374s diam=10 psize=0.96 back=727

The above examples perform the self-correlation on image ic3374 using a local modal pixel value for the image of 727 counts. The sampling area used is a circle of 10 arc second width and all correlation values generated will be placed in the output NDF image ic3374s.

The correlation is performed in such a way that objects of bigger or smaller than the size requested are improperly sampled. However, they will still generate a response, as the detection method does not depend critically on the size of the template. Consequently, a compromise is involved in selecting the object size. If a large object size is requested the calculations take longer and the resolution of the output image drops, but if a small object size is requested noise quickly becomes a problem and offsets the increased speed and resolution.

It might be supposed that symmetry would not be a very good basis for correlation, given the wide range of possible galaxy shapes known. Despite this, trials suggest that the method works well with a wide range of galaxy types. The only disadvantage is that two bright objects close together can give rise to spurious objects between them. This effect can be minimised by using TOPPED to remove very bright pixels from the image. Any object containing such bright pixels will already have made its presence very obvious!

#### 9.2 Cross-correlation

The ESP application CORR generates a cross-correlation image by correlating a mask with the input image. As with SELFC, you again input a size but in this case it defines the scale length of the galaxy for which the correlation should be optimised. The radius of the circular exponential mask used (simulating a face on galaxy) with which the image will be correlated is varied accordingly. It should be noted that this optimisation is such that the correlation will still be sensitive to objects of scale lengths in the approximate range 0.25 to 4 times the scale length requested.

The correlation results placed in the output image generated are normalised to the range 0–1. If no arbitrary value of correlation coefficient is being employed to define the reality of a detection, a suitable value may be derived using the method described for SELFC.

The application can be used with the following syntax:

% corr in=hh1826 out=correl scale=8. psize=0.3 back=3265 useall=true

Correlates image hh1826 with a mask-template optimised for galaxies of 8 arc second scale length. The image pixel size is .3 arc seconds per pixel and the background value is 3265. The output cross-correlation image will be called correl.

#### 9.3 Hybrid cross/self-correlation

The SELFCW application performs a calculation that is essentially the same as that of CORR but where the raw pixel values used are replaced by RMS (sign maintained) values derived from a list of diameterically opposed equidistant pixel pairs found within the mask region. It thus represents a mixture of the symmetry based SELFC and the template cross-correlation CORR. This hybrid self/cross-correlation appears to produce fewer spurious objects than the two previous methods and appears to be less sensitive to noise. It is again normalised to the 0–1 range and significance testing may be performed as before.

The application can be used with the following syntax:

% selfcw in=p2 out=scp2 scale=15. psize=1. back=1000. useall=true

Using this example a hybrid correlation image is generated which has been optimised to detect galaxies of 15 arc second scale length on the image p2. No pixels have been excluded from the calculations. Other examples of the syntax required to use this application are given Appendix 0.