Digitization

Image capture devices create images by first superimposing an invisible grid over (usually) continuously varying real-world scenes. This segments scenes into small rectangles that are represented by a single image pixel. Next the devices compute an average value (color intensity) that best represents the contents within each grid rectangle. The devices then quantize the values to give a final representation pixel value.

When quantizing a continuous tone image into a digital image, each pixel sample is assigned an integer value which denotes the pixel’s intensity value. Within an image, each pixel value ranges from zero to a maximum value which usually has a value of 2ⁿ–1 such as 1 (2¹–1), 3 (2²–1), 7 (2³–1), 15 (2⁴–1), 31 (2⁵–1), 64 (2⁶–1), 127 (2⁷–1), 255 (2⁸–1),..., 4095 (2¹²–1), etc. This allows a uniform number of bits, sometimes called the bit depth, to represent all assigned pixel values within an image (1, 2, 3, 4, 5, 6, 7, 8, and 12, respectively).

As with quantization, digitization can introduce artifacts. When we compute the average value within a sample rectangle, details will disappear (average out). For example, in the previous map example, a house might contribute to the average altitude of a topographic map, but we are not sampling at a fine enough grid to know there is a house there.

Another digitization artifact occurs when you don’t sample fast enough—the sampling rectangles are not closely spaced and do not average (blur) the image enough. For example, taking every other rectangle in a map may introduce sudden altitude changes that are not real. In the image domain, sampling so infrequently can introduce sudden changes in intensity that appear as edges that are not real or beating patterns (regular lines) in the image. These artifacts are due to aliasing—a phenomenon that also gives straight lines the “jaggies.”

Another aspect of forming a digital image is digitizing in time, often called “framing.” A digital image is a “snapshot” in time, and any movement during the creation of the image will cause blurring and other artifacts. Movies flicker still images together to give the perception of movement (as mentioned in the human vision chapters). As with digitization, sampling too slowly introduces artifacts (temporal aliasing), such as wheels appearing to spin backwards.

Probability

Suppose you analyze a digital image’s intensities by determining their various values and counting how often each occurs. This allows you to graph the various pixel values versus how often they occur. The chart is called a histogram and allows users to predict how macro image adjustments affect the resulting image. However, histograms have limited utility since they do not indicate intensity positions, only their relative numbers. So, a checkerboard has the same histogram as any pattern that leaves half an area white and half black. The VIDEO.C program produces histograms for the original and all derived images.

Wave Frequency

Figure 11-2  Wave pattern

Bruce Brown’s famous movie Endless Summer affectionately refers to one of Southern California’s most notorious and dangerous body surfing beaches as “the dirty old Wedge.” Located at the southern end of Newport Beach’s Balboa Peninsula, the Wedge faces due south and catches summer storm swells that travel unimpeded from Antarctica. On a good Wedge day, arriving swells careen off of the Newport Harbor jetty and join with the following wave, forming ominous wedge-shaped liquid pockets that advance straight to shore. The huge lumbering aquatic slabs plummet into shallow water, causing explosive ground convulsions spectators revel. Combined with the violent backwash, it’s not unheard of for body surfers to drop 40 feet onto slightly wet sand. As is true in digital imaging, big waves transmit tremendous energy.

Digital imaging refers to wave energy as well. Figure 11-2 illustrates a single wave pattern which is actually a combination of two wave patterns: a relatively large lumbering wave pattern and a smaller choppy wave pattern that rides on top of the larger wave. As at the Wedge, the huge wave pattern has a low spatial frequency and transmits most of the image’s energy (information). Conversely, the nuisance choppy wave has a high spatial frequency and provides detail which image processing may remove. In some instances, such as natural scenes, there is no significant visual impairment by removing detail. Such information is referred to as irrelevant information, and procedures that remove it are referred to as visually lossless. However, removing high spatial frequency from scanned text document images usually causes havoc and should be avoided.