It depends on what exact shading of 'opposite' you are after.

Superimposition is actually better rendered in English by the proper English word 'overlay', and its opposite is 'underlay'

But again, it depends what you mean. Instead of underlay, you may mean withdrawing altogether a layer from the stack of layers that constitute an image, in which case other words, such as 'unlayering', may be called for. If you mean disentangling waves, a number of other words such as disentangle, disassociate, de-splice, etc., may be appropriate.

As Chris Ransford pointed out there is no antonym for the word 'Superimposition' (noun). 

Web defines the meaning for the word 'superimposed' (adjective).

The antonym of this word are congenital, congenital, essential, immanent, inborn, inbred, indispensable, indwelling, infixed, ingrained, inherent, inhering, innate, inseparable, internal, intrinsic, inwrought, native, natural, subjective.

Based on the context, you can make use one among the above.

Actually, to describe the mathematics of partial presence which is in my name, I used the term superimposition of sets. The idea started with the following example: when we overwrite, the overwritten portion looks darker due to superimposition.

I would now like to define the opposite of superimposition. Unfortunately, I could not find a suitable word to define the opposite of superimposition.  

You 'separate out' sets .....

There is no substantive, so build the sentence so as to allow for use of the verb.

Alternatively, you may define your own word, which is always legitimate in English. As in : 'Let's call 'cleavage' the separating out of sets (the reverse of superimposition) ..... 

Best

Chris

You are suggesting the word cleavage to mean splitting. Suppose, I write, cleavage of sets to mean the reverse of superimposition of sets. Will that be okay?

Sure, but make sure you define it as such first.

Include a preliminary written definition of cleavage of sets as the reverse of what you called their superimposition. It is customary to define terms in scientific papers.

Maybe you could simply say that the sets that are superimposed are darker than the sets that are not superimposed...or the sets that do not overlap.

Just as there were operations of union of sets and intersection of sets in mathematics, I defined an operation of superimposition of sets. Now I would like to define the opposite of superimposition. As Ransford has suggested, cleavage of sets may be a good option, yes.

Cleavage is a noun anyway. The point is, had it been a verb, I could have used something like cleavagization possibly! Would that be okay, Professor Marek ?

 "Unstratified"  /or "Subjacent"

In a casual discussion with my son, who is M. A. English with NET qualification and a graduation in Maths, I happened to raise this question. He suggests denudation, or even the common word subtraction with definition of the proper connotation. This connotation is related to 'overwrite'. Scalloping, undermining, erosion and undercutting may be other options. He is sure that one of these will fit.

Dhruba,

Subjacent means lying below the top. This would not be appropriate perhaps. 

Dear Professor Thammayya,

Denudation is a geological term defining the very long process of deformation of the Earth's crust. Would that be appropriate enough?

I couldn't find the word superimposition in the typical reference sources for definitions and synonyms and antonyms.   Unfortunately is is not a word in common use.  I'm not sure what sense of that word you are looking for.  However, superimpose is in the English language sources. 

From superimpose we get uncover as an antonym. 

Uncover = expose, discover, reveal, unearth, bare, find, disclose, find out,

Exposition = elucidation, clarification, exhibition, display, demonstration, showcase

I don't know if any of these words help you with the meaning you are looking for.

Good luck!

Two terms which connote the opposite of superimposed are:

1. Unstratified

2. Subjacent

Till now, the word cleavage suggested by Professor H. Chris Ransford seems most appropriate. I am thinking whether cleavaging of sets or cleavage of sets should be used in my case. 

Please give your comments, Professor Ransford. Should it be cleavage or cleavaging? 

Cleavage as a noun, but 'separating out' as a verb.

By the way, 'to cleave' as a verb is one of a handful of odd English words that can mean both itself and its opposite - to cleave may mean to split (in that case akin to the German verb 'klieben', meaning to split, and to the English word cleft), or 'to stick to' (a separate homonym akin to the separate German 'kleben' meaning to glue, see Klebstoff meaning glue)

So 'to cleave' is best shunned. Cleavage as a verb does not exist and is just plain awful.

Regards

Dear Professor Ransford,

So, I should stick to cleavage. After all, cleaving (in the gerund form) can be of double meaning.

Actually, I am feeling slightly uneasy about the word cleavage, because as you would know, this word is in use to mean something that has hardly anything to do with mathematics!

I doubt whether the "cleavage" means the opposite of "superimposition"; to my understanding it does not, except in any specific situation (Of Mr Barua) which I am not aware of.

PA, there is no such thing as an opposite of superimposition, please do read the thread, it totally hinges on context (e.g., you can't use underlay for de-splicing a superimposition of sets or of wave packets, for instance, and so on.)

'Cleavage' can be used in definite contexts - such as in minerals, geometry, mining, fashion, and so on, but if you're going to shun words based on their possible use in certain contexts you're going to end up very constricted as to the vocabulary you're going to be able to use ... perhaps turn your phrases in such a way that only the verb form is ever needed (separate out) and where you eschew the substantive altogether ?

Well, going to shun is not really the matter! It indeed is an appropriate word. There is no doubt about that.

Two words are possible antonyms: subjacent; unstratified

The word stratified has been in use in mathematics in a particular sense already. Indeed, in contrast to simple random sampling in which the population remains unstratified, there is what is known as stratified random sampling in which the population is stratified into different strata, and thereafter simple random sampling is performed from every stratum. My need to define the opposite of superimposition is not in that sense. Therefore, using the same word in a different sense would not be correct. 

As for the word subjacent, I have already mentioned that it would not actually mean the opposite of superimposition satisfying my definition.

Scarification is another word which may suit.

Scarification would mean peeling off from top downwards. But my requirement is removing not just from the top, from the bottom or from any level as well, if necessary.

It is a good suggestion of course. Thank you, Professor Thammaya. 

no further clue. sorry