Java generic interface calling with abstract parameter

I know there's many similar question but I had no luck finding a nice and clean solution if it's possible at all. I'm implementing a generic interface with subclasses of an abstract type. Problem is that when I'm calling them I either must do type cast in a switch/case or cast type in every method inside interface implementations and I can't figure out a nice and clean approach... I'll better just write down a short example.

// An abstract type with 2 implementations...
public abstract class ObjTypeAbstract {}

public class ObjType extends ObjTypeAbstract {}
public class ScriptType extends ObjTypeAbstract {}

Now the processor for both types with an interface

interface ProcessorInterface<T extends ObjTypeAbstract> {
    public void abcMethod(T obj);
}

public class ObjProcessor implements ProcessorInterface<ObjType> {
    public void abcMethod(ObjType obj) {}
}
public class ScriptProcessor implements ProcessorInterface<ScriptType> {
    public void abcMethod(ScriptType obj) {}
}

What I'm struggling with is a way of calling those processors based on ObjAbstractType. I have a single class that servers as middleware?? or how should I call it.:

Idea was to simple get the right processor via a single switch/case:

public class Processor {
    private ProcessorInterface objProcessor = new ObjProcessor();
    private ProcessorInterface scriptProcessor = new ScriptProcessor();

    public methodAbc(ObjAbstractType obj) {
        getProcessor(obj).abcMethod(obj);
    }

    private ProcessorInterface getProcessor(ObjAbstractType obj) {
        if (obj instanceof ObjType) {
            return objectProcessor;
        } else if (obj instanceof ScriptType) {
            return scriptProcessor;
        }

        return nullProcessor;
    }
}

This is what I'd like to have, it also takes care of type casting of objAbstract to actual type for abcMethod, problem is that it results in RawType warning which won't break the code, but I'd like to get rid of it.

And thats where I'm stuck... because if I cast processors to specific type like this:

private ProcessorInterface<ObjType> objProcessor = new ObjProcessor();
private ProcessorInterface<ScriptType> scriptProcessor = new ScriptProcessor();

I won't be able to return an abstract one from getProcessor method so I would have to implement those interfaces with an ObjAbstractType with all it's method and have type casting in all methods of every processor like:

public class ScriptProcessor implements ProcessorInterface<ObjAbstractType> {
    public void abcMethod(ObjAbstractType obj) {
        ScriptType scr = (ScriptType) obj;
    }
}

The other solution might be having a switch/case inside Processor middleware class and cast ObjAbstractType in it, but I'd have to write that switch inside abcMethod and all others or from getProcessor method returns both the Processor and casted ObjType... so I'd have to return some dto containing both. :/

Do you have any ideas / patterns that might help me to get rid of RawType call warning without extending the code with more switch/case or type casts? Wish you a nice day and I'll be glad for any discussion, David.

You need a way to store the mapping between a ObjTypeAbstract class and a ProcessorInterface instance.
You could use a Map that associates ObjTypeAbstracts (as key) to ProcessorInterfaces (as value).
About the raw type issue, you could use ProcessorInterface<? extends ObjTypeAbstract> for the declared variable but you will still need to perform a unsafe cast to ProcessorInterface<ObjTypeAbstract> to be able to invoke ProcessorInterface.abcMethod() with as parameter a ObjTypeAbstract declared type.
This cast is unavoidable with your actual design.

It could give something like :

public class Processor {

    private Map<Class<? extends ObjTypeAbstract>, ProcessorInterface<? extends ObjTypeAbstract >> map = new HashMap<>();

    public Processor(){
        map.put(ObjType.class, new ObjProcessor());
        map.put(ScriptType.class, new ScriptProcessor());   
    }
    public void methodAbc(ObjTypeAbstract obj) {
        @SuppressWarnings("unchecked")
        ProcessorInterface<ObjTypeAbstract> processorInterface = (ProcessorInterface<ObjTypeAbstract>) map.get(obj.getClass());
        processorInterface.abcMethod(obj);
    }

}