Huff(man)ing and Puffing - Huffman Images

Morgan McGuire and Thomas P. Murtagh
Williams College

Summary Huff(man)ing and Puffing -- A project composed of three laboratory assignments that explores aspects of image processing that culminates in an experimental evaluation of several Huffman-code based image compression schemes.
All three laboratory assignments are primarily focused on developing skills in array processing. In addition, the second assignment explores inheritance, and the final assignment involves a recursive algorithm.
Appropriate for the end of CS 1 or beginning of CS 2.
The assignments for the three weeks of this project are respectively introductory, intermediate, and advanced.
The strength of this project is that it simultaneously teaches programming, algorithm design, and scientific methodology. Students build an experimental tool using a broad spectrum of array techniques. It combines image processing (which students love) with an scientific/experimental twist (which instructors love).
  1. The complete project would occupy several weeks of course laboratory time.
  2. The project depends on SImage, a non-standard class for representing images. (It also depends on a second non-standard class for GUI event handling, but this dependence could easily be eliminated as discussed below.)
All of the weekly assignments require knowledge of basic control structures, class and method definitions, and the construction of simple Swing GUI interfaces. The last two assignments assume that the students have familiarity with arrays. The last assignment assumes knowledge of recursive methods and requires that some class time be devoted to the explanation of Huffman codes.
We use these three assignments in conjunction with lecture presentations that overlap with the project as part of an integrated introduction to array processing. With some care, one could replace one or both of the first two steps of the project with other labs that develop array processing skills and then use the last week of our series of labs as an independent exercise.

A Multi-week Image Processing Project

For years, each of the exercises in our CS1 course were completed in a single week independent of all of the other exercises. The assignment described here, on the other hand, is one of a series of multi-week projects we have designed as part of a revision of our CS1.

There are clear advantages to assigning projects that are longer than one week. With the extra time, it is possible for students to tackle problems that are more interesting and to produce final products that better satisfy their creative impulses. These larger projects also make it easier to expose students to design issues during the first course. Finally, it gives students more time to develop fundamental skills by amortizing over multiple weeks the overhead required to learn the context for the problem.

There are, however, several obstacles to using multi-week assignments in CS1. Given the pace at which new programming techniques are typically introduced in CS1, any single handout that described a two or three week project would probably describe aspects of the project requiring programming skills the students would not acquire until some time in the midst of working on the project. There is also the issue of compounding failure. If a student gets stuck on one of the early steps of the project, they could easily fall critically behind as the deadline for the complete project approaches.

With these issues in mind, we have designed our multi-week projects, including the one described here, as a series of tightly integrated, single-week assignments. The students receive a new lab handout each week. The handout describes a program the students should complete as an independently useful application whose construction only requires skills they have already learned. From the instructor's perspective, however, the modules of the programs completed in the early weeks of a project are designed to build upon one another, eventually serving as components of the larger program produced in the last week of the project.

The project described here leads the students to construct an image processing program that is eventually used to experiment with the effectiveness of a number of image compression techniques. The assignment begins with simple manipulations, such as those available in the popular Photoshop image editing software. These are applied to specially prepared images to yield fun surprises when the students have a correct implementation. The tail of the assignment uses the same building blocks as today's real compression algorithms. However, as can be seen in the lab handouts linked below, the word "compression" does not even appear in any of the lab materials until the last week. As a result, while we view the three assignments described below as part of a single project, others could choose to adopt just one or two of the labs as assignments.

Step 1: Pixel Brightness Value Manipulation

For the first week of this project, the students produce a program that allows them to load image files and then alter the images by either scaling the brightness values of all of the pixels in the image, or by reducing the number of distinct values used to represent brightnesses, effectively reducing the number of colors used to present the image.

A snapshot of the program's main window is shown on the right. The interface provides three buttons. Pressing the "Load Image" button displays a dialog box that can be used to select the image displayed in the window. Pressing either of the other two buttons creates a new window in which one of the two forms of adjustment described above can be performed.

For example, pressing the "Requantize" button would make the window shown on the left appear. In this window, the slider at the bottom is set to the value 2 (which is displayed to the right of the image), indicating that only two distinct brightness values should be used to display the image.

You can experiment with this program or either of the programs we ask students to construct in the following two weeks of this project by downloading our archive of sample image processing lab solutions. When unpacked, this archive should produce a folder containing four .jar files and a sub-folder of sample images.

The .jar files named Step1Solution.jar, Step2Solution.jar, and Step3Solution.jar are executable and correspond to the programs the students are asked to produce during the three weeks of the project. For example, to run the lab from the first week, you would double-click on Step1Solution.jar. Once the program window appears, click on the "Load Image" button and navigate into the AllImages folder in the same folder to select an image to manipulate.

The squintV2.8.jar file contains the small library of classes this project depends upon. The library is called Squint. This project only depends on the GUIManager and SImage classes from the library. Click here for complete documentation of the Squint library.

The dependency of these exercises on the Squint library can be easily reduced to the use of the single SImage class. Students will need to be familiar with some mechanism to create a GUI interface in order to complete these labs. In our course, students learn how to do this using Squint. Others might teach their students how to create GUIs using only standard Swing classes or using the classes in the ACM Java Task Force libraries. These lab could easily be adapted to replace the use of the Squint GUIManager class with either of these other libraries.

The lab handout for the first week of the project reflects another unusual aspect of many of our labs. While in the past we made sure to discuss each programming technique in class before we would expect students to use it in lab, we now often give students a first exposure to a new technique in lab. Then, we take advantage of the practical experience students have gained in lab to provide a more effective general introduction to the new topic in class. The topics introduced in this lab are arrays and array indexing. Our students have no previous introduction to arrays before completing the lab. As a result, the handout is written more as a tutorial than our typical lab handouts.

From our point of view as instructors, it is the tutorial nature of this lab that makes it nifty. Who would ever guess that students could learn arrays on their own? In particular, who would guess that they could learn arrays on their own by learning "more complex" 2D arrays before 1D arrays? Luckily, the connection between what they already know about cartesian coordinates and the way subscripts are used to select pixels is strong enough that students handle this without great difficulty and come to class well prepared to learn more general ways to use arrays.

From the point of view of our students, this lab is nifty because it is their first change to manipulate images. The visual feedback is surprisingly satisfying to them.

Step 2: Pixel Brightness Value Manipulation

Both of the imaging operations that students implement in the first week involve only simple array operations. They write two sets of nested loops that apply a given formula independently to all of the pixel brightness values in a 2D array. In the second week, we seek to expand the set of techniques used to include 1D arrays, loops to find minimum and maximum values, and operations that combine values from several positions in an array or from different arrays.

The interface for the program the students are asked to complete in the second week of the project is shown below.

The interface allows a user to manipulate two images at the same time, one on the left side of the program window and the other on the right. Independent controls are provided for each image. Some of these controls repeat the functionality from the first lab and are implemented using the same code (e.g., the "Brightness levels" slider performs the "Requantize" function).

There are several new controls present on both the left and right panels. The user can save a modified image. By adjusting the "Block Size" slider the user can change the spatial resolution of the image displayed. In the snapshot above, the setting of the right "Block size" slider results in an image in which each pixel has been replaced by the average brightness of a 6x6 block of pixels. The "Show Histogram" button causes the program to display a histogram of the brightness values in a separate window as shown on the right. The "Expand Range" button causes the program to scale the brightness values so that they extend through the full range from 0 to 255. This requires first finding the minimum and maximum brightness values in the original image.

In addition, there are several controls at the bottom of the window that provide for interactions between the two images displayed. "Move Left-> Right" simply replaces the image on the right with the image on the left while "Insert Left-> Right" pastes a copy of the left image over the right image. The "Show difference" button displays an image whose brightness values are determined by computing the differences between corresponding pixels in the images on the left and right. A snapshot of such an image is shown on the left. The details of all of these operations are described in the lab handout for week 2 of the project.

Completing this assignment clearly provides the students with ample opportunity to exercise their knowledge of arrays. The block averaging and image differencing operations require them to combine information from different entries of arrays in interesting ways. Building the array of histogram values and finding the minimum and maximum values gives practice with 1D arrays.

For students, the "nifty" in this assignment comes from some of the surprising results of applying the operations they implement. Basically, the sample images we provide are rigged to make these transformations interesting. For example, if one loads the image file "grifSecret.gif", a picture of Griffin Hall, the stately campus building shown in the snapshot of the program's interface above, copies it to the right, changes the copy to be displayed using only 16 brightness levels and then presses "Show Difference", an image like the one on the right appears. Not very interesing!

If, however, you then press "Expand Range", the image changes dramatically to appear like the image shown below displaying an aerial view of the pentagon (perhaps encouraging the Homeland Security Department to visit your lab!). The original image is an example of steganography. The brightness values for the image of the Pentagon are hidden in the low-order bits of the brightness values of the image of Griffin Hall.

There are several other such surprises in the collection of image file provided with our lab materials. All of the images in the "ExpandRange" folder reveal interesting images when the "Expand Range" operation is applied. "There be dragons" (well, at least one) in the 10x10.png image found in the "Average" folder if you change its block size to 10. Computing the difference of the two nearly identical images in the "Difference" folder yields a Halloween treat. (Guess when we first assigned this lab!)

Starter code

Above, we mentioned that one risk of having a multi-week project in a CS1 course is that students who fall behind early might never catch up. The obvious way to deal with this is to provide students with a solution for week N's work as they begin week N+1. We take a slight variation on this approach. We provide all of the students with starter code in week N+1 that is similar enough to what they completed in week N to make it easy for them to understand but different enough that all students are expected to use the starter code rather than what they produced the preceding week. This way, at the end of the project, everyone who does well throughout the project feels like they wrote "the whole thing" because they realize they could have easily adapted their code instead of using the starter code. On the other hand, students who have a bad week don't fall behind.

Step 3: Evaluating Image Compression Techniques

During the final week of this project, students write a program that allows them to measure the effect of applying several compressing techniques to images. Then, we ask them to write a lab report describing the results they obtain.

We do two things in lecture to prepare for this exercise. First, we explain the basics of Huffman codes. This is a topic we include fairly early in the course to show students an example of an interesting algorithm and to get them thinking about issues of data representation. When we present Huffman codes, they know very little about Java programming. They don't implement any part of the algorithm early in the course. They just solve homework problems drawing Huffman trees on paper to compress short text messages.

In lecture, after the students complete step 2 of the project, we point out how many bits it takes to encode even a relatively small image and ask if they can see any way to reduce the number of bits required. With a bit of luck, some of them remember Huffman codes and suggest applying them to images. Unfortunately, the naive scheme does not work very well. The distribution of brightness values in most images is too uniform for Huffman codes to be efficient. Using the program they completed for week 2, however, we can demonstrate an effective alternative. If you examine the histogram of an image produced by computing the difference between an image and a "block averaged" version of the same image, the distribution is far from uniform. Huffman coding this difference image can be quite effective. Thus, we propose the following scheme for compressing images. Compute a 4x4 block average of the original. This image should take about 1/16th as many bits as the original. Compute the difference between the original and the block average. Huffman coding the difference image often gives 50% compression. Together, the differences and the block averages encode all of the original information at a fraction of the original size.

For the lab, we then give them a handout describing several other such schemes and ask them to measure the effectiveness of these schemes on a collection of sample images. Some of the schemes are lossy, so this involves both measuring compression ratios and subjectively evaluating image quality.

A snapshot of the interface for the program they write is shown below.

The image loaded on the left side of the main window is the image to be compressed. The menu in the lower right corner of the window is used to select the scheme to be applied, "Waterfall" in this case. All of the schemes are described in the lab handout for the third week of this project.

When the user presses the "-->> Compress -->> Uncompress" button, the scheme selected is applied to the image, a new window like that shown on the left below the main window is displayed showing the revised representation of the image, and the result of undoing the transformation is displayed on the right side of the main window. If one then presses the "Show Histogram" button in the window displaying the revised representation, the program displays histograms of the red, green and blue brightness components along with a figure for the number of bits per pixel required to store this representation using a Huffman code.

Implementing this program requires implementing interesting algorithms involving both single and two dimensional arrays. This includes implementing part of Huffman's algorithm. Surprisingly, the part of Huffman's algorithm that the students implement does not involve any tree data structures. Instead, it has a great deal in common with selection sort. In the standard description of Huffman coding, one builds larger and larger trees by repeatedly combining the two trees corresponding to the smallest occurrence counts or occurrence frequencies. If all one wants to do is determine how many bits are required to encode a message rather than actually determining the exact form of the encode message, keeping track of the trees becomes unnecessary. As a result, the algorithm the students implement (following the description in the handout) involve repeatedly replacing the two smallest numbers in a list with their sum.


By the end of the three weeks of this project, students have covered quite a bit of territory. In terms of programming skills, they have learned techniques for constructing and processing 1 and 2 dimensional arrays ranging from using simple nested loops to process individual elements, to the application of the wavelet decomposition that requires them to recursively subdivide and them combine the contents of an array. In between, they encounter basic techniques including accumulating the sum of a set of array elements, finding minima and maxima, and rotating the elements of a 2D array. They also encounter a number of interesting algorithms and data representation schemes including Huffman encoding, steganography, histograms, and the use of wavelets in image processing. Perhaps most importantly, the experimental component of the lab exposes them to the issue of evaluating the effectiveness of algorithms and data structures used to solve a particular problem.

Additional Resources