is `inv` on Colors well defined? about colors.jl

[johnnychen94]

Is there a reason to not want to overload inv?

From ?inv, it is required to satisfy inv(x) * x == x * inv(x) == one(x) so clearly that inv(x::Real) = one(x) - x doesn't satisfy this property. Hence we can't overload Base.inv function. We might introduce a new function, e.g., invert_color.

I was trying to mess around with some of the common filters like inverting the colors, and it seems this would be well defined.

This concept is more like a "mirror" operation and might only be well defined for "linear" color space such as RGB, XYZ. For non-linear color space such as Lab, I don't know, it might be sufficient to only invert the L channel.

[kimikage]

FYI, you can use ColorVectorSpace.complement (formerly Images.complement) for AbstractRGB.
See also the second half of JuliaGraphics/ColorVectorSpace.jl#125 (comment).

[anandijain]

Thanks, yes I was worried about the roundoff error. This is helpful, I know really little about color spaces. Is there a type specifically for the Linear spaces so that invert_color could be extended?

julia> dump(inv(inv(purp)) - purp)
RGB{Float64}
  r: Float64 0.0
  g: Float64 -2.7755575615628914e-17
  b: Float64 0.0

It's not a big deal to not have this, since it is so easy to write. I was mainly just curious

[kimikage]

Anyway, since inv is no longer a topic of this discussion, I think it would be better to change the subject of this issue or open a new issue.

I have no objection to adding the functionality to get the complementary "color" (not "numbers"), but I don't think we should introduce our own definition for it. We should refer to papers or well-known tools on color science or image processing.