Why are Gaussian filters used as low pass filters in image processing?

In 1d signal processing, many types of low pass filters are used. Gaussian filters are almost never used, though.

Why are they so popular in image processing applications? Are these filters a result of optimizing any criterion or are just ad hoc solution since image 'bandwidth' is usually not well defined.

Answer

Image processing applications are different from say audio processing applications, because many of them are tuned for the eye. Gaussian masks nearly perfectly simulate optical blur (see also point spread functions). In any image processing application oriented at artistic production, Gaussian filters are used for blurring by default.

Another important quantitative property of Gaussian filters is that they're everywhere non-negative. This is important because most 1D signals vary about 0 ($x \in \mathbb{R}$) and can have either positive or negative values. Images are different in the sense that all values of an image are non-negative ($x \in \mathbb{R}^+$). Convolution with a Gaussian kernel (filter) guarantees a non-negative result, so such function maps non-negative values to other non-negative values ($f: \mathbb{R}^+ \rightarrow \mathbb{R}^+$). The result is therefore always another valid image.

In general, frequency rejection in Image processing in not as crucial as in 1D signals. For example, in modulation schemes your filters need to be very precise to reject other channels transmitted on different carrier frequencies, and so on. I can't think of anything just as constraining for image processing problems.