Ancient Messages

Since it says that there are no guarantees about scale or anything, it means that the images have to be topologically equivalent, which for 2D, means they have the same number of "holes" in them. Looking at the pictures, it's clear that this is the case as they all have different numbers of holes

once you've "unpacked" the picture

1. find the background by iterating around the entire edge of the picture and flood filling
2. iterate through the entire picture. when you find a hole, fill it and increment the count
3. lookup which symbol matches the count

import java.util.*;
public class c {

	Scanner in=new Scanner(System.in);
	public static void main(String[] args) {
		new c().go();
	}
	private void go() {
		int cnum=0;
		while(true){
			cnum++;
			int r=in.nextInt();
			int c=in.nextInt();
			if(r==0&&c==0)return;
			in.nextLine();
			int[][] a=new int[r][c*4];
			int[] count=new int[6];
			for(int i=0;i<r;i++){
				String line=in.nextLine();
				for(int j=0;j<a[0].length;j++){
					a[i][j]=(Integer.parseInt(line.substring(j/4,j/4+1),16)>>(3-j%4))&1;
				}
			}
			for(int i=0;i<a[0].length;i++){
				if(a[0][i]==0)flood(a,0,i,-1);
				if(a[a.length-1][i]==0)flood(a,a.length-1,i,-1);
			}
			for(int i=0;i<a.length;i++){
				if(a[i][0]==0)flood(a,i,0,-1);
				if(a[i][a[0].length-1]==0)flood(a,i,a[0].length-1,-1);
			}
			for(int i=0;i<a.length;i++){
				for(int j=0;j<a[0].length;j++){
					if(a[i][j]==1)count[shapeFlood(a,i,j)]++;
				}
			}
			System.out.printf("Case %d: ", cnum);
			for(int i=0;i<count[1];i++)System.out.print("A");
			for(int i=0;i<count[5];i++)System.out.print("D");
			for(int i=0;i<count[3];i++)System.out.print("J");
			for(int i=0;i<count[2];i++)System.out.print("K");
			for(int i=0;i<count[4];i++)System.out.print("S");
			for(int i=0;i<count[0];i++)System.out.print("W");
			System.out.println();
		}

	}
	private int shapeFlood(int[][] a, int i, int j) {
		Queue<Integer> q=new LinkedList<Integer>();
		q.offer(i);
		q.offer(j);
		int holes=0;
		while(!q.isEmpty()){
			i=q.poll();
			j=q.poll();
			if(i<0||j<0||i>=a.length||j>=a[0].length)continue;
			if(a[i][j]==2)continue;
			if(a[i][j]==-1)continue;
			if(a[i][j]==0){
				holes++;
				flood(a,i,j,2);
			}
			a[i][j]=2;
			q.offer(i);
			q.offer(j+1);
			q.offer(i);
			q.offer(j-1);
			q.offer(i+1);
			q.offer(j);
			q.offer(i-1);
			q.offer(j);
		}
		return holes;
	}

	private void flood(int[][] a, int i, int j, int k) {
		Queue<Integer> q=new LinkedList<Integer>();
		q.offer(i);
		q.offer(j);
		while(!q.isEmpty()){
			i=q.poll();
			j=q.poll();
			if(i<0||j<0||i>=a.length||j>=a[0].length)continue;
			if(a[i][j]!=0)continue;
			a[i][j]=k;
			q.offer(i);
			q.offer(j+1);
			q.offer(i);
			q.offer(j-1);
			q.offer(i+1);
			q.offer(j);
			q.offer(i-1);
			q.offer(j);
		}
	}
}
//Ancient Messages
//ascii
//topology
//flood fill