The human eye is capable of recognising a source in a fraction of a second. In the blink of an eye we can tell if a dark forest is empty or home to a hungry tiger - if we couldn't do this, our ancestors wouldn't have survived. True, many of them didn't. But enough did. Our visual capabilities are both extremely accurate and extremely fast, even by the standards of modern computers.
Pretty much everyone accepts the need to look at data at some level. It simply isn't possible to objectively quantify every conceivable sort of source geometry; if you want to spot something weird, by far the simplest option is to just look at the damn data. This can influence everything from the structure of individual galaxies to the counter-intuitive structures visible (or not visible) in the noise.
I don't want to give the impression that there's some pervading anti-visual bias in the astronomical community. There isn't, and there are times when the data set is so large that visual techniques just aren't possible. What I do want to stress though is that great care needs to be taken when we have to proceed purely algorithmically, and that there's nothing inherently better or worse than either technique. See the data structures page to understand the basics of the data I describe here.
Despite human visual prowess, merely glancing at the data isn't enough. For AGES our strategy is to inspect the data using a series of different approaches, progressively becoming more and more sensitive :
This isn't always as linear as it sounds. In regions contaminated by interference there are often many structures that look for all the world like galaxies, and even elsewhere it can be damn hard to distinguish between a faint ripple in the noise and a genuine signal. So we often flick back and forth between different viewing techniques, and then we might jointly decide as a team if something is worth keeping or not. We also inspect the spectra as well as using other, independent visualisation techniques.
A related point is that we can also compare the optical images of the regions where we think we've detected something. I emphasise "can" because whether this is a good idea or not depends on what you want to do ! If you're interested in dark galaxies this is often a bad idea, since you risk biasing your sample in favour of detections which have a corresponding galaxy. But if you find a faint signal in a region you can see is badly affected by interference, this can be a valuable way to save yourself a lot of hassle : as a rule, objects without optical counterparts tend to be far more likely to be spurious than real. This extra check needs to be used carefully, and there isn't a foolproof guide as to how to do this. The only real way to learn source extraction is by experience – though it isn't difficult, and can be easily grasped in a few days. In fact I'm pretty sure a monkey could do it, if we had access to a monkey... stupid, narrow-minded funding agencies... grrr !
Likewise, we can also supplement the data with known catalogues. For example if we know a galaxy is present in our survey volume, we can just extract the spectrum at that point and see what's there. Knowing the coordinates and redshift of a galaxy make even a faint signal detected at that location a lot more convincing. Again, this method is perfectly legitimate in the right circumstances, but it needs to be used judiciously.
Finally, the above procedures were developed in conjunction with the dedicated visualisation and cataloguing package FRELLED (page to be written). Prior to that we used kvis, which has no cataloguing features (coordinates need to be recorded by the moral obscenity of manually typing them !) and no 3D display. In those days we used to go through each projection of the cube one by one. Masking sources was possible but incredibly tedious, leaving us with a frankly stupid choice : don't mask and hope we didn't record the same sources twice, or do the masking and risk dying of boredom. And we'd have all of this done by at least two or three different people. Fortunately with FRELLED all that has passed into oblivion. Even so, we normally use an automatic extractor as a fifth step in the process.