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You use bitmap image data as a displacement map, whereas other lters you ve seen in this book use a matrix. This is simply a matter of managing data. In previous lters, you ve used relatively small matrices. To determine the offset of a pixel, you need to store two values for its offset in x and y. And you need an offset value for every pixel in the source image, so two matrices of size W H are required, where the input image is W by H pixels. Dealing with, and generating or loading, these potentially huge matrices would be unwieldy. Instead, a bitmap image is used to store the data. Each pixel s color is a combination of red, green, blue, and alpha channels, and you exploit this to store multiple channels of data (the x and y offsets) in one image. You can store four 8-bit (1-byte) values in every position of a bitmap image in Flash Player if you consider each color channel independently. In a displacement map, only two are used. Each channel can store values in the range [0, 255], which are normalized (scaled and shifted) to the range [ 0.5, 0.5]. This has one important implication: a black (0x00000000) pixel in the distortion map actually encodes the maximum negative displacement in both directions, not a zero-distance displacement. A 50 percent gray (0x80808080) pixel encodes this instead. Say you have an input image input, and a displacement map image map, and you ve decided to encode the x offsets in map s red channel and the y offsets in its green channel. In pseudocode,

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offset(x, y) = (normalize(map(x, y).red) * scaleX, normalize(map(x, y).green) * scaleY) output(x, y) = input((x, y) + offset(x, y))

After careful study of this chapter, you should be able to do the following: 1. Understand the role of statistical tools in quality improvement 2. Understand the different types of variability, rational subgroups, and how a control chart is used to detect assignable causes 3. Understand the general form of a Shewhart control chart and how to apply zone rules (such as the Western Electric rules) and pattern analysis to detect assignable causes 4. Construct and interpret control charts for variables such as X , R, S, and individuals charts 5. Construct and interpret control charts for attributes such as P and U charts 6. Calculate and interpret process capability ratios

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You can use an algorithm to generate a displacement map programmatically, using the bitmap drawing methods described in 36, Programming Bitmap Graphics, or using vector drawing tools and

7. Calculate the ARL performance for a Shewhart control chart 8. Construct and interpret a cumulative sum control chart 9. Use other statistical process control problem-solving tools Answers for most odd numbered exercises are at the end of the book. Answers to exercises whose numbers are surrounded by a box can be accessed in the e-text by clicking on the box. Complete worked solutions to certain exercises are also available in the e-text. These are indicated in the Answers to Selected Exercises section by a box around the exercise number. Exercises are also available for some of the text sections that appear on CD only. These exercises may be found within the e-Text immediately following the section they accompany.

capturing the drawing in a BitmapData object with the draw() method. For projections de ned by optics or geometry, it makes sense to generate these maps in code. You can also simply load an image as a Bitmap and use its bitmapData. No matter how the displacement map is created, you pass it to the DisplacementMapFilter as BitmapData. Following are the lter s properties:

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The quality of products and services has become a major decision factor in most businesses today Regardless of whether the consumer is an individual, a corporation, a military defense program, or a retail store, when the consumer is making purchase decisions, he or she is likely to consider quality of equal importance to cost and schedule Consequently, quality improvement has become a major concern to many US corporations This chapter is about statistical quality control, a collection of tools that are essential in quality-improvement activities Quality means tness for use.

mapBitmap The displacement map. mapPoint When the displacement map and input image are not aligned, a Point that

For example, you or I may purchase automobiles that we expect to be free of manufacturing defects and that should provide reliable and economical transportation, a retailer buys nished goods with the expectation that they are properly packaged and arranged for easy storage and display, or a manufacturer buys raw material and expects to process it with no rework or scrap In other words, all consumers expect that the products and services they buy will meet their requirements Those requirements de ne tness for use Quality or tness for use is determined through the interaction of quality of design and quality of conformance By quality of design we mean the different grades or levels of performance, reliability, serviceability, and function that are the result of deliberate engineering and management decisions.

componentX Which color channel from the map bitmap encodes the horizontal displacement. One of BitmapDataChannel.RED, BitmapDataChannel.GREEN, BitmapDataChannel.BLUE, or BitmapDataChannel.ALPHA. componentY Which color channel from the map bitmap encodes the vertical displacement. See componentX for possible values. scaleX The maximum absolute horizontal displacement. scaleY The maximum absolute vertical displacement. mode How to displace pixels along the edges. This lter suffers from a similar

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