Hi, this is an interesting question for a challenging research.
I believe that if there is a method that we can apply in reality (i.e. by human brain without the use of computer) the problem become solvable if the human knowledge experience is captured and presented as an algorithm to apply.
The most important attributes that we need to address the problem stated in your question is the distinguished characteristics, features, and entities that differentiate and recognise different race and ethnicity of individuals based on their photos.