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that these mappings are contractions means that the point sets resulting from the application of these mappings to a portion of an image are diminished in size relative to that original portion of the image.

Once a set of ALC mappings has been determined such that its repeated application produces an acceptable approximation to the target image, the target image is said to have been "compressed." The target image is then compressed because, rather than having to store the entire data of the target images, one needs only to store the values of the parameters that define the ALC mappings. Usually the amount of data required to characterize the ALC mappings is significantly less than that required to store the target image point set. The process of iterative application of the ALC mappings described earlier produces the "decompressed" approximation of the target image.

An essential feature of the decompression process is that it leads to a unique "limit image," so that a given collection of ALC mappings will always yield a sequence of images that converge to the same limiting image [6]. This limit image is a point set that is approached by the sequence of images as the number of applications of the ALC mappings increases without limit. Hence, in practical applications, one must select an image that results from a finite number of applications of the ALC mappings as the approximation to the target image. Another important feature ofthe decompression process is that the limit image produced is independent of the initial image with which the process begins, although the rate at which the sequence of target image approximations approaches the limit image is influenced by the choice of initial image.

A fractal is a geometric structure obtained as the limit image (or attractor) of a specific set of ALC mappings applied to point sets in Euclidean space [7]. That is why compression based on the ALC iterations is called fractal compression. Consequently, target images that are fractals can always be compressed with a set of ALC mappings and can be decompressed with arbitrary accuracy by simply increasing the number of applications of the ALC mappings. A characteristic feature of fractals is "self-similarity," which means that certain subsets of a fractal are compressed versions of the entire fractal; in other words, certain subsets are versions of the entire fractal image under some ALC mapping [7]. Self-similarity of fractals follows as a direct consequence of the repeated application of ALC mappings that generates the fractals. It is important to note that when decompressing an arbitrary image one does not produce the fractal (limit image), but only an intermediate approximation to the fractal, and self-similarity at all scales is not manifested in fractal compressed images. Once the mappings are specified, it is relatively easy to determine the number of iterations necessary to produce an approximate target image that is within a specified distance of the limit image, according to an appropriately defined metric.

The process of decompression of a fractal compressed image is well defined and easily implemented on a computer; one simply implements the iterated application of the ALC mappings. However, the most significant problem one faces when attempting to apply fractal image compression to target images of practical interest is the target image compression process. Even though many naturally occurring physical objects and their photographic images exhibit a certain degree of self-similarity (over several scales), no real-world objects are fractals [8]. Thus, the process of specifying the set of ALC mappings capable of reproducing an arbitrary target image with acceptable fidelity is a difficult one and constitutes the subject of many research activities at this time. Existing methods are not fully automated, requiring involvement of a human operator using a computer-based decision aid [9]. Hence, the time required to compress an arbitrary target image is a matter of concern. Most methods start by partitioning the target image into subsets and search for ALC mappings that can modify one subset to look like the modified version of another subset. Successful application of this procedure requires the target image to exhibit at least "local" self-similarity so that reasonable fidelity can be achieved when decompressing the image. An arbitrary target image may or may not possess such local self-similarity, although experience has shown that many ordinary images do exhibit enough to allow effective fractal compression.

Because a fractal compressed image is decompressed through the repeated application of the ALC mappings and magnification of that image is easily achieved by increasing the value of multiplicative constants in the ALC mappings, fractal compressed images will display detailed structure at all levels of magnification, unlike standard images in which details are obscured with increased magnification as individual pixels become visible. Since the unlimited detail produced by the fractal image decompression process will eventually have no relation to the target image, care must be exercised when interpreting highly magnified, fractal compressed images.

3 Telecommunications

Telecommunications involve the use of wire, radio, optical, or other electromagnetic channels to transmit or receive signals for voice, data, and video communications. This section briefly describes features of technologies, standards, and procedures or protocols that contribute to the speed and reliability of modern telecommunications systems. The seven-part (a.k.a. level or layer) classification scheme for computer communications known as the Open Systems Interconnection (OSI) model of the International Standards Organization (ISO) provides a useful foundation for the discussion that follows. The model can be applied to the scenario illustrated in Fig. 1 where two users of telemedicine systems are connected via communications services. The seven levels and their objectives are as follows [10]:

(1) Physical. Specifies the physical, electrical, and procedural standards for a network, including voltage levels and circuit impedances. The EIA RS-232 serial interface standard is an example of a Level 1 area of responsibility.

(2) Data Link. Describes means to activate, maintain, and close the telecommunications link.

(3) Network. Specifies standards for dial-up, leased, or packet networks. It also provides rules for building data packets and routing through a network.

(4) Transport. Describes rules for message routing, segmenting, and error recovery.

(5) Session. Starts and stops (i.e., log-on and log-off) network sessions. It determines the type of dialogue that will be used (i.e., simplex, half-duplex, or full-duplex).

(6) Presentation. Converts data to the appropriate syntax for the display devices (character sets and graphics); compresses and decompresses and encrypts and decrypts data.

(7) Application. Provides a log-in procedure, checks passwords, allows file upload or download, and tabulates system resources usage.

The transport layer is the highest level concerned with technological aspects of the telecommunications network. It acts as the interface between the telecommunications network and the telemedicine application. The upper three layers manage the content of the telemedicine application. Furthermore, various equipment, software, communications services, and data acquisition and display components of a telemedicine system can be updated and maintained by replacing or modifying hardware or software at each level instead of replacing the whole system.

3.1 Signal Hierarchy and Transfer Rates

To achieve reliable and effective communications, signals must be accurately generated and propagated. Signals associated with telecommunications systems are usually stated in rather self-descriptive terms, for example, digital signal (DS), optical carrier (OC), or synchronous transport signal (STS). Signals, which contain information, are typically described as frequencies. The bandwidth needed to convey the information is the difference between the highest and lowest frequencies of the signals containing the information. The bandwidth of a communications channel is the difference between the highest and lowest frequencies that the channel can accommodate. The bandwidth of the communications channel must be equal to or greater than the bandwidth of the information-carrying signals. Thus, a communications channel that carries the range of voice frequencies (300 to 3000 Hz) must have a bandwidth of at least 3000 Hz. In contrast, approximately 200 KHz of bandwidth is required for FM transmission of high-fidelity music, and 6 MHz for full-motion, full-color television signals.

A digital communications system uses digital pulses rather than analog signals to encode information. The North American high-speed digital telephone service is referred to as the T carrier system. The T carrier system uses pulse code modulation (PCM) techniques to sample and encode information contained in voice-grade channels, and then time division multiplexing (TDM) techniques to form a DS from a group of 24 voice-grade channels. The information carrying signal of each channel is sampled 8000 times per second. The sample is represented or encoded using 8 bits, thus forming frames of information at a rate of 64 bps. Details about the T carrier system are summarized in Table 4. Metrics are bit transfer rates, the number of voice frequency analog signals that are multiplexed to form a DS, and the number of 6 MHz TV channels that can be transmitted via a T carrier.

A single DS-1 signal is usually transmitted over one pair of twisted wires of either a 19-gauge or 22-gauge, known as a T1 line span. Two lines, one for transmit and one for receive, are used in a line span. Repeaters are required about every mile to compensate for power loss. The assemblage of equipment and circuits is known as the T1 carrier system. The lengths of T1 carrier systems range from about 5 miles to 50 miles. The T2 carrier system uses a single 6.312 Mbps DS for transmission up to 500 miles over a low capacitance cable. A T3 carrier moves 672 PCM encoded voice channels over a single metallic cable.

With the development of fiber optic telecommunications systems, signaling standards that were adequate for wire pairs and coaxial cable warranted revision. Fiber-based telecommunications systems are virtually error-free and are capable of reliably moving signals more rapidly than wire systems. The American National Standards Institute (ANSI) published a new standard called Synchronous Optical Network (SONET) in 1988 [10]. It was known as ANSI T1.105 and evolved into an international standard that was adopted by CCITT in 1989. The OC-1 signal is an optical signal that is turned on and off (modulated) by an electrical binary signal that has a signaling rate of 51.84 Mbits/sec, the fundamental line rate from which all other SONET rates are derived. The electrical signal is known as the STS-1 signal (Synchronous Transport Signal — level 1). OC-N signals have data rates of exactly N times the OC-1 rate. Table 5 lists standard transmission bit rates used with SONET and their equivalent STSs.

TABLE 4 T-carrier baseband system [10]

T carrier

Data rate

Digital

Voice grade

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