How to use Composition when the functions have two parameter

Question

There are some basic instructions about Composition on this site, but I'm still confused on how to use it when the functions I am composing have two parameter, such as:

t := RandomImage[1, {50, 50}, ColorSpace -> "RGB"]
picList = Array[t &, 3];
ImageResize[#, 500] &@*ColorConvert[#, "Grayscale"] & /@ picList

But when the composition functions just have one parameter, the behavior is more predictable:

hh@*ff /@ picList

Can anybody explain this strange behavior?

Answer 1

& has a very low operator precedence, in particular it's lower than @*'s precedence. That means that the right-hand & is actually defining an unnamed function with the body:

ImageResize[#, 500] & @* ColorConvert[#, "Grayscale"]

You can fix this by wrapping the right-hand function in parentheses:

ImageResize[#, 500] & @* (ColorConvert[#, "Grayscale"] &) /@ piclist

Or both of them for consistency:

(ImageResize[#, 500] &) @* (ColorConvert[#, "Grayscale"] &) /@ piclist

Of course, as you mentioned in a comment, that doesn't help much compared with

(ImageResize[#, 500] &) /@ (ColorConvert[#, "Grayscale"] &) /@ piclist

If you want to avoid the parentheses altogether, you could still define a pure function via the Function, but of course, that's even less terse, and technically you've just replaced parentheses with square brackets:

Function[ImageResize[#, 500]] @* Function[ColorConvert[#, "Grayscale"]] /@ piclist

You can also use the full form of @* instead:

Composition[ImageResize[#, 500] &, ColorConvert[#, "Grayscale"] &] /@ piclist

Alternatively, you could apply both transformations in a single function:

ImageResize[ColorConvert[#, "Grayscale"], 500] & /@ piclist

Or use infix notation for a nicer reading order:

# ~ColorConvert~ "Grayscale" ~ImageResize~ 500 & /@ piclist