Data Structures, Algorithms, & Applications in Java
Chapter 10, Exercise 27

Nothing fancy is needed here. We need merely change all uses of a queue to uses of a stack. There is no particular advantage to using a stack over a queue and vice versa. Stack operations are slightly faster than queue operations, so we may prefer a stack for this reason.

The modified code is given below. Changes from the queue version are shown in red. 
public class ImageComponentsUsingAStack
{
   // top-level nested class
   private static class Position
   {
      // data members
      private int row;   // row number of the position
      private int col;   // column number of the position

      // constructor
      private Position(int theRow, int theCol)
      {
         row = theRow;
         col = theCol;
      }

      // convert to string suitable for output
      public String toString()
      {
         return new String(row + " " + col);
      }
   }
   
   // data members
   private static int [][] pixel;
   private static int size;      // number of rows and columns in the image
   
   // methods
   /* not yet implemented */
   private static void welcome() {};
   
   /** input the image */
   private static void inputImage()
   {
      // define the input stream to be the standard input stream
      MyInputStream keyboard = new MyInputStream();

      System.out.println("Enter image size");
      size = keyboard.readInteger();

      // create and input the pixel array
      pixel = new int [size + 2][size + 2];
      System.out.println("Enter the pixel array in row-major order");
      for (int i = 1; i <= size; i++)
         for (int j = 1; j <= size; j++)
             pixel[i][j] = keyboard.readInteger();
   }
   
   /** label the components */
   private static void labelComponents()
   {
      // initialize offsets
      Position [] offset = new Position [4];
      offset[0] = new Position(0, 1);   // right
      offset[1] = new Position(1, 0);   // down
      offset[2] = new Position(0, -1);  // left
      offset[3] = new Position(-1, 0);  // up
      
      // initialize wall of 0 pixels
      for (int i = 0; i <= size + 1; i++)
      {
         pixel[0][i] = pixel[size + 1][i] = 0; // bottom and top
         pixel[i][0] = pixel[i][size + 1] = 0; // left and right
      }
   
      int numOfNbrs = 4; // neighbors of a pixel position
      ArrayStack s = new ArrayStack();
      Position nbr = new Position(0, 0);
      int id = 1;  // component id
   
      // scan all pixels labeling components
      for (int r = 1; r <= size; r++)      // row r of image
         for (int c = 1; c <= size; c++)   // column c of image
           if (pixel[r][c] == 1)
           {// new component
              pixel[r][c] = ++id; // get next id
              Position here = new Position(r, c);
   
              while (true)
              {// find rest of component
                 for (int i = 0; i < numOfNbrs; i++)
                 {// check all neighbors of here
                    nbr.row = here.row + offset[i].row;
                    nbr.col = here.col + offset[i].col;
                    if (pixel[nbr.row][nbr.col] == 1)
                    {// pixel is part of current component
                       pixel[nbr.row][nbr.col] = id;
                       s.push(new Position(nbr.row, nbr.col));
                    }
                 }
   
                 // any unexplored pixels in component?
                 if (s.empty())
                    // no unexplored positions
                    break;
                 here = (Position) s.pop(); // a component pixel
              }
   
           } // end of if, for c, and for r
   }
   
   /** output labeled image */
   private static void outputImage()
   {
      System.out.println("The labeled image is");
      for (int i = 1; i <= size; i++)
      {
         for (int j = 1; j <= size; j++)
            System.out.print(pixel[i][j] + "  ");
         System.out.println();
      }
   }
   
   /** entry point for component labeling program */
   public static void main(String [] args)
   {
      welcome();
      inputImage();
      labelComponents();
      outputImage();
   }
}