What is image and video signal ?
A signal doesn't have to be a single quantity; the variation doesn't have to happen along a single axis, either.

An image is information (e.g. brightness) varying in two dimension (e.g. along a X- and a Y-axis).

Simple as that; counts both for digital and analog images.

That information that changes might be one-dimensional (e.g. only brightness for a black and white / grayscale image), or multidimensional (e.g. red, green, blue for a color picture). 

Video is information varying in three dimensions: two dimensions like an image, and time as third dimension.