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10.15.2. Free Response - Gray Image B

The following is part b of a free response question from 2012. It was question 4 on the exam. You can see all the free response questions from past exams at https://apstudent.collegeboard.org/apcourse/ap-computer-science-a/exam-practice.

Question 4. A grayscale image is represented by a 2-dimensional rectangular array of pixels (picture elements). A pixel is an integer value that represents a shade of gray. In this question, pixel values can be in the range from 0 through 255, inclusive. A black pixel is represented by 0, and a white pixel is represented by 255. The declaration of the GrayImage class is shown below.

public class GrayImage
{
   public static final int BLACK = 0;
   public static final int WHITE = 255;

   /** The 2-dimensional representation of this image.
    *  Guaranteed not to be null.
    *  All values in the array are within the range
    *  [BLACK, WHITE], inclusive.
    */
   private int[][] pixelValues;

   /** Processes this image in row-major order and
    *  decreases the value of each pixel at position (row, col)
    *  by the value of the pixel at position (row + 2, col + 2)
    *  if it exists.
    * Resulting values that would be less than BLACK are replaced
    *   by BLACK.
    * Pixels for which there is no pixel at
    *   position (row + 2, col + 2) are unchanged.
    */
   public void processImage()
   { /* to be implemented in part (b) */ }
}

Part b. Write the method processImage that modifies the image by changing the values in the instance variable pixelValues according to the following description. The pixels in the image are processed one at a time in row-major order. Row-major order processes the first row in the array from left to right and then processes the second row from left to right, continuing until all rows are processed from left to right. The first index of pixelValues represents the row number, and the second index represents the column number.

The pixel value at position (row, col) is decreased by the value at position (row + 2, col + 2) if such a position exists. If the result of the subtraction is less than the value BLACK, the pixel is assigned the value of BLACK. The values of the pixels for which there is no pixel at position (row + 2, col + 2) remain unchanged. You may assume that all the original values in the array are within the range [BLACK, WHITE], inclusive.

The following diagram shows the contents of the instance variable pixelValues before and after a call to processImage. The values shown in boldface represent the pixels that could be modified in a grayscale image with 4 rows and 5 columns.

Figure 1: Example before and after a call to processImage

public class GrayImage
{
   public static final int BLACK = 0;
   public static final int WHITE = 255;

   /** The 2-dimensional representation of this image.
    *  Guaranteed not to be null.
    *  All values in the array are within the range
    *  [BLACK, WHITE], inclusive.
    */
   private int[][] pixelValues;

   /** Processes this image in row-major order and
    *  decreases the value of each pixel at position (row, col)
    *  by the value of the pixel at position (row + 2, col + 2)
    *  if it exists.
    * Resulting values that would be less than BLACK are replaced
    *   by BLACK.
    * Pixels for which there is no pixel at
    *   position (row + 2, col + 2) are unchanged.
    */
   public void processImage()
   { /* to be implemented in part (b) */ }
}

10.15.2.1. How to solve this problem

Once again, this problem starts with looping through the array of pixels, using a nested for loop for the 2D array. As we loop we will need to subtract pixel values from one another.

9-10-2-1: Which is the simplest way to subtract one integer value from another integer value?

• result = int1 - int2;
• While the syntax here is correct, there's an even simpler way to execute subtraction that doesn't create a new variable.
• int1 -= int2;
• The "-=" syntax correct subtracts int2 from int1, without creating an additional variable, which is ideal in our solution for this problem.
• int1.subtract(int2);
• Because the pixels are of primitive type "int," there is not subtract() method which can be executed in this case.

When comparing our pixel values to values deeper in the array, we need to be careful to correctly set the terminating conditions on the for loops. The code below has a mistake in it, can you spot what the problem is and fix it?

public class Test { public static void main(String[] args) { int[][] values = { {9, 8, 7, 6, 5}, {7, 6, 5, 4, 3}, {4, 3, 2, 1, 0}, {4, 3, 2, 1, 0} }; for (int i = 0; i < values.length; i++) { for (int j = i; j < values[i].length; j++) { System.out.print(values[i][j] - values[i+2][j+2]); } System.out.println(); } } }

You can step through the code above using the Java Visualizer by clicking on the following link <http://cscircles.cemc.uwaterloo.ca/java_visualize/#code=public+class+Test%0A%7B%0A+++public+static+void+main(String%5B%5D+args)%0A+++%7B%0A+++++int%5B%5D%5B%5D+values+%3D+%7B%7B9,+8,+7,+6,+5%7D,%0A+++++++++++++++++++++++%7B7,+6,+5,+4,+3%7D,%0A+++++++++++++++++++++++%7B4,+3,+2,+1,+0%7D,%0A+++++++++++++++++++++++%7B4,+3,+2,+1,+0%7D%7D%3B%0A+++++for+(int+i+%3D+0%3B+i+%3C+values.length%3B+i%2B%2B)%0A+++++%7B%0A+++++++for+(int+j+%3D+0%3B+j+%3C+values%5Bi%5D.length%3B+j%2B%2B)%0A+++++++%7B%0A+++++++++System.out.print(values%5Bi%5D%5Bj%5D+-+values%5Bi%2B2%5D%5Bj%2B2%5D)%3B%0A+++++++%7D%0A+++++++System.out.println()%3B%0A+++++%7D%0A+++%7D%0A%7D&mode=display&curInstr=6>_.

Try to write the code for the method processImage. When you are ready click “Run” to test your solution.

public class GrayImage { public static final int BLACK = 0; public static final int WHITE = 255; /** The 2-dimensional representation of this image. * Guaranteed not to be null. * All values in the array are within the range * [BLACK, WHITE], inclusive. */ private int[][] pixelValues; /** constructor that takes a 2D array */ public GrayImage(int[][] theArray) { pixelValues = theArray; } /** Processes this image in row-major order and * decreases the value of each pixel at position (row, col) * by the value of the pixel at position (row + 2, col + 2) * if it exists. * Resulting values that would be less than BLACK are replaced * by BLACK. * Pixels for which there is no pixel at * position (row + 2, col + 2) are unchanged. */ public void processImage() { } public void printValues() { for (int r = 0; r < pixelValues.length; r++) { for (int c = 0; c < pixelValues[0].length; c++) { System.out.print(pixelValues[r][c] + ", "); } System.out.println(); } } /** main for testing */ public static void main (String[] args) { int[][] values = { {221, 184, 178, 84, 135}, {84, 255, 255, 130, 84}, {78, 255, 0, 0, 78}, {84, 130, 255, 130, 84} }; GrayImage image = new GrayImage(values); image.printValues(); image.processImage(); System.out.println("after process image"); image.printValues(); } }

10.15.2.2. Video - One way to code the solution

The following video is also on YouTube at https://youtu.be/8j34xQkjsJI. It walks through coding a solution.

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