Colored image will become black and white
Input validation

If the received image is not RGB, throwing an IllegalArgumentException without a custom message is not very friendly. Users would have to look at the code to understand what went wrong exactly.

The long chain image.getColorModel().getColorSpace().getType() is extracted to an imageType local variable that's only used for validation.
I would be good to move the validation to a dedicated helper method, let's say validateImageType.

Java conventions

Member variables should be declared at the top, followed by constructors, followed by methods. Very roughly speaking. So move the declaration of threshold higher.

Naming

As the interface name already implies the conversion to black and white,
the method name toBlackAndWhite is redundant. I'd rename it to simply convert.

Misc

0x000000FF is the same as 0xFF, so you can shorten it.