Chapter 5 Cigansky Book

Monica Stoica

This chapter describes the world of images. From it you will learn:

• the various ways in which an image represents the real world, and the ways in which it is never a perfect representation;

• how images are formed, optically, photographically, and electronically and how the quality of images is measured and expressed;

• how images that were never visible in the real world (such as radar, medical ultrasonics imaging, and so forth) may be created by computer;

• how images are represented in computers by binary numbers and how color information is expressed and stored;

• how the human eye works, including its color discrimination and stereo vision capability; and how it is possible to represent continuous motion with still images.

Images• The old adage that maintains that ``a picture is

worth ten thousand words'' recognizes that a visual image conveys a lot of information at once.

• Definition: An image is a representation (usually two-dimensional) of objects in the real world.

• the film-based camera is over 150 years old. Recent advances have provided a variety of alternatives to the use of conventional film, but the basic image formation process has not changed. This process may be familiar to you from experience with basic optics, and is illustrated in the next figure

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Pictures• The essential components of this system are: the object or

scene to be imaged, the lens, and the image recording medium (retina of the eye, film, or other device).

• The image recording medium is usually located in a plane parallel to the lens, known as the image plane. Note that the image that is formed is  inverted; this is usually of no consequence because the display device may easily correct this condition.

• The resulting image represents a projection from the three-dimensional object world to the two-dimensional image world.

The focal length• The focal length    specifies the distance from the lens to

the image plane. More useful to us, it also indicates the degree of magnification of the lens.

• From 35 mm photography, we know that a lens of 50 mm focal length is considered ``normal'' (in the sense that the resulting photo will contain the same expanse of image that a human would see from the same point as the camera);

• one of 28 mm focal length is ``wide angle,'' and one of 135 mm focal length is ``telephoto.'' For a different film (image) size,those focal lengths would change, but the principle remains the same.

So for example• if we have an aerial photograph of farmland and we know

the altitude of the camera, we can calculate the area of each field or other object in the image.

• Similarly, if we have X-ray images of the heart as it pumps, we can determine the cross-sectional areas of the ventricles, and hence their pumping efficiencies.

• In robotics, a video camera may be used to determine precisely the location of a robot arm with respect to the work, and hence provide motion guidance.

• This process of reducing the dimensionality of the information (from three dimensions to two in photography) is referred to as projection and is fundamentally a mathematical concept.

Human eye• When dealing with printers we often quote the resolution in

terms of dots per inch, or pixels per inch. • 550 dots per inch would be sufficient to fool any eye into

thinking a picture was rendered without pixelization if the paper were held at distances of a foot or greater. This explains the long-term popularity of 600 dots per inch (dpi) laser and ink jet printers.

• Of course,by holding the paper closer, we can get greater perception of resolution;this explains the utility of printers with even higher resolutions than 600 dpi. How close we will hold a picture for viewing is, of course, a consideration in judgments about sufficient resolution.

Printed images and the human eye• We call the shortest distance at which a person can focus on

an object that person's accommodation distance. • This distance typically varies with age from about 7 cm

(2.75 inches) at age 10 to about 200 cm (78 inches) at age 65.At age 47, the accommodation is approximately the 12 inches used in the above example, and anything better than about 600 dpi resolution is wasted on the unaided eye.

• The student at 17 years of age with an accommodation of 9 cm (3.5 inches), on the other hand, feels cheated with anything less than a printer capable of 1200 dpi, motivating the use of 1200 dpi and greater printing resolutions in the magazine industry.

Non standard types of images• Lens-based cameras are not the only means by which

images may be formed from the real world. Several other examples of image formation systems include radar, sonar, X-rays, and tomography (``CAT scans''). These systems differ from traditional cameras in two ways:

• (1) the type of energy used to form the image (instead of visible light, radio,sound waves, X-rays, or radio emissions of nuclei under the influence of a magnetic field are used);

• (2) the geometry of the system that relates the locations of the objects in the real world (three-dimensional) to the image world (two-dimensional). A type of image that we are all at least somewhat familiar with (from TV weather forecasts) is the radar image. ``Radar'' stands for``Radio Detection and Ranging,'' and is an excellent example of an imaging system that is fundamentally different in several ways from normal photography.

These differences include:

• The type of energy used to form the image (radio waves vs. light waves);

• The fact that the illumination must be supplied by the imaging system, rather than the surrounding ambient conditions. That is, cameras and human eyes operate with visible light; radar, however, must supply its own ``illumination'' using radio waves;

• The geometry of the image (based on polar coordinates rather than rectangular coordinates). The image is formed by rays emanating from the center of the image, corresponding to the radar location;

Differences continued• The fact that the radar site (camera) is

located in the image plane rather than perpendicular to the image plane and some distance away. This is convenient because it means, for example, that to get a radar image of several hundred square miles of the earth's surface, we don't have to take a camera an equivalent distance above the earth; we just position the radar on the surface at the center of the area.

Another unusual type of image• One more unusual type of imaging system is holography• This system is fundamentally unique in that it captures

three-dimensional information from the original scene. • It requires illumination from a special (laser) source, and

a rather complex optical setup. • The viewing requirements for a single holographic

image are modest; recently advances in viewing technologies allow video holograms, color holograms, and presentation of holograms to groups of people. 

Converting images to digital form• continuous information is a quantity that can take on the

infinite number of possible values that belong to a continuum.

• Discrete information, on the other hand, implies that the quantity can assume only a finite number of values (at finite instances in time or finite locations in space).

• Much of what we measure in the world is continuous, whether or not our measurements are capable of representing continuous information. By definition, binary digits are discrete, because they can take on only two values. Furthermore, only discrete information can be perfectly represented using binary digits.

Converting - continued• This means that whenever we use bits to

represent some continuous quantity, we are making an approximation and introducing some error by ``throwing away'' information.

• We must convert information from continuous form to discrete form as the first step in digitizing the information. Such a conversion, also known as an analog to digital conversion, necessarily requires some loss of information and precision.

Converting an image to digital• we must perform two processes, each of which

provides an approximation to transform a continuous quantity into a discrete quantity.

• First, we must reduce the spatial resolution of the image from a continuous area representation into a finite number of small picture elements, or pixels, each  representing small areas rather than infinitesimal points within a spatial continuum.

• Then,we must convert the brightness level corresponding to each pixel into code representing the approximate gray level.

Pixelization• Each pixel in an image corresponds to a small

area (usually, but not always, square) of that image. Each pixel represents a single intensity (brightness) level.

• Ideally, we would choose this pixel area to be small enough so that when these pixels are put next to each other on a display, they present a pleasing representation of the original analog image to the viewer.

• This process of breaking continuous image into a grid of pixels is sometimes called pixelization, sampling, scanning, or spatial quantization.

• .

How many pixels?

• Given an image of fixed size, the spatial resolution of the image-which affects our perception of the quality or fidelity of the image-is dependent on  the number of pixels in the image. If we use too few pixels, then the image appears ``coarse'' or ``blocky'', and the effects of pixelization are apparent.

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Brightness• Each pixel must be converted into binary data. To do this,

we determine the number of brightness levels that we wish to represent.

• For example, if we wish to use 8 bits to represent the brightness at each pixel, we would have 256 brightness levels a binary number with 8 bit positions may take on 256 different values, or equivalently that 2 raised to the power 8 equals 256 which we generally evenly distribute between pure black and brightest white.

• Then, each pixel would be associated with an 8-bit number corresponding to whichever of the 256 brightness levels is closest to the actual analog image brightness at that location in the image. This process is known as quantization

Brightness• the same photo is shown at the same spatial

resolution, but with 6 bits (for 64 gray levels), 3 bits (8 gray levels), and 1 bit (2 gray levels) used to represent and store each pixel.

• You can see the effect of differing gray-scale resolutions on image quality is clearly discernible, but is of a different nature than the effect of differing spatial resolutions.

Different gray levels of the same picture

•.

The smallest level of brightness.

How much memory

• if we choose to represent the photo by an array of 64 x 64pixels, and decide that 32 gray levels (5 bits) is enough,then our image can be stored using 64 x 64 x 5 bits, or 2560 bytes, or 2.5 kB.

Colored Images• we can represent a color with three numbers

indicating the amounts of red, green, and blue light that combine to produce that color. This system for specifying colors is known as the RGB system.

• For example, 10 units of red, green, and blue will form white of a certain intensity. If we increase this to 20 units of red, green, and blue, we will still have a white light, but it will be more intense.  

• Why does the eye perceive combinations of red, green, and blue as a full spectrum of colors?

The human eye

• The impaired human (that is, someone who possesses ``trichromatic vision'' and does not suffer from a variety of color blindness ailments such as monochromatism ordichromatism) has three kinds of cells in the eye that are sensitive to different ranges of wavelengths of light and are used to distinguish color.

• The three values for red, green, and blue content in an RGB can produce a response by the eye like that of any other color because our eyes can only interpret a color from the three responses or the respective cells.

TV image

• Standard color televisions use tight clusters of red,green, and blue color sources to create the illusion of other colors.

• Because these sources are small and closely spaced, the human eye cannot discern the individual components, and we just see the color combination as a single shade.

• However, standard color television systems do not use a completely digitized version of the image; each row of the display, or raster, is transmitted as continuous information for each of the color components.

Human eye• The average person can discern about 100 saturated (that is,

pure) colors from each other. When both luminance and hue are varied, one can discern about 6,000 variations of color intensity.

• Finally, about another 60 levels of saturation are discernible, for a grand total of approximately 360,000 recognizable colors.

• With appropriate encoding,we would expect to need 19 bits per pixel for full color representation, with the same caveats as before of the effects of examining cut outs of such an image in isolation. In practice, though,8 bits per color or 24 bits per pixel are general used for full color representation, for the sake of convenience.