CAMERA-PEN-TIP MAPPING AND CALIBRATION TECHNICAL FIELD Embodiments of the invention relate to interaction between a positionally encoded medium and a digital pen. More particularly, embodiments of the invention relate to calibrating a digital pen and mapping locations decoded from camera-captured images to corresponding locations of the tip of the pen. BACKGROUND OF THE INVENTION Computer users are accustomed to using a mouse and keyboard as a way of interacting with a personal computer. While personal computers provide a number of advantages over written documents, most users continue to perform certain functions using printed paper. Some of these functions include reading and annotating written documents. In the case of annotations, the printed document assumes a greater significance because of the annotations placed on it by the user. One of the difficulties, however, with having a printed document with annotations is the later need to have the annotations entered back into the electronic form of the document. This requires the original user or another user to wade through the annotations and enter them into a personal computer. In some cases, a user will scan in the annotations and the original text, thereby creating a new document. These multiple steps make the interaction between the printed document and the electronic version of the document difficult to handle on a repeated basis. Further, scanned-in images are frequently non-modifiable. There may be no way to separate the annotations from the original text. This makes using the annotations difficult. Accordingly, an improved way of handling annotations is needed. One technique of capturing handwritten information is by using a pen whose location may be determined during writing. One pen that provides this capability is the Anoto pen by Anoto Inc. This pen functions by using a camera to capture an image of paper encoded with a predefined pattern. An example of the image pattern is shown in Figure 15. This pattern is used by the Anoto pen (by Anoto Inc.) to determine a location of a pen on a piece of paper. However, it is unclear how efficient the determination of the location is with the system used by the Anoto pen. To provide efficient determination of the location of the captured image, a system is needed that provides efficient decoding of the captured image. [04] When annotating a document, a user may mark the document by moving a pen tip with respect to the document. The path of the pen tip may comprise a plurality of strokes, where each stroke corresponds to a series of captured images. Hence, efficiently identifying the path of the pen in order to process the annotation on a document would be desirable. [OS] Further, The x-y coordinates calculated from the center of the captured images may not represent the actual location of the tip of the pen. To map the center of the captured image to the pen tip, techniques for calibrating the relationship between the pen tip and the center of images captured by the camera would be desirable. Conventional calibration techniques, however, typically require complicated equipment and/or involved calibration procedures. [06] Each time a user changes a pen's ink cartridge, which may happen relatively frequently, calibration may be performed. Therefore, techniques for performing calibration should be simple, relatively quick, and accurate. And such techniques should not require complicated equipment of the type typically used in connection with conventional calibration techniques. SUMMARY OF THE INVENTION [07] X-y positions of the pen tip may be determined by using a calibration parameter to map the x-y positions of the respective centers of images captured by the pen's camera to the x-y positions of the tip of the pen. The calibration parameter may be generated by iteratively calculating estimates of the calibration parameter. [08] A calibration module receives calibration input data, which may be produced by a user placing the pen tip at a fixed location on a surface, which may be a positionally encoded medium, such as paper, and then rotating the pen and/or moving the opposite end of the pen in various directions to capture multiple images for use in generating the calibration parameter. A user may perform such a calibration procedure without the need for complicated calibration equipment typically used in connection with conventional calibration techniques. [09] A mapping module may use the calibration parameter and recovered camera-captured-location information to generate recovered pen-tip-location information. [10] A virtual pen tip is used for mapping a recovered image-center location to a recovered pen-tip location. The location of the virtual pen-tip depends on a predetermined relationship between the actual pen-tip and the camera based on the configuration of the pen. The virtual pen-tip is the projected point of the pen-tip on an image sensor plane of the digital pen's camera. [11] Additional features and advantages of the invention will be apparent upon reviewing the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS [12] The foregoing summary of the invention, as well as the following detailed description of preferred embodiments, is better understood when read in conjunction with the accompanying drawings, which are included by way of example, and not by way of limitation with regard to the claimed invention. [13] Figure 1 shows a general description of a computer that may be used in conjunction with embodiments of the present invention. [14] Figures 2A and 2B show an image capture system and corresponding captured image in accordance with embodiments of the present invention. [IS] Figures 3A through 3F show various sequences and folding techniques in accordance with embodiments of the present invention. [16] Figures 4A through 4E show various encoding systems in accordance with embodiments of the present invention. [17] Figures 5A through 5D show four possible resultant comers associated with the encoding system according to Figures 4A and 4B. [18] Figure 6 shows rotation of a captured image portion in accordance with embodiments of the present invention. [19] Figure 7 shows various angles of rotation used in conjunction with the coding system of Figures 4A through 4E. [20] Figure 8 shows a process for determining the location of a captured array in accordance with embodiments of the present invention. [21] Figure 9 shows a method for determining the location of a captured image in accordance with embodiments of the present invention. [22] Figure 10 shows another method for determining the location of captured image in accordance with embodiments of the present invention. 23] Figure 11 depicts a calibration module and a mapping module in accordance with various embodiments of the invention. 24] Figure 12 shows a recovered camera-captured stroke (i.e. recovered from the respective centers of captured images) and a corresponding mapped pen-tip stroke in accordance with an embodiment of the invention. 25] Figure 13 shows an actual pen-tip stroke that is associated with the recovered strokes shown in Figure 12. [26] Figure 14 shows a path recovered based on the respective centers of camera-captured images and a point to which points along the path are mapped via a calibration parameter in accordance with various embodiments of the invention. [27] Figure 15 shows a representation of encoding space in a document according to prior art. DETAILED DESCRIPTION OF THE INVENTION [28] Aspects of the present invention relate to determining the location of a captured image in relation to a larger image. The location determination method and system described herein may be used in combination with a multi-function pen. [29] The following is separated by subheadings for the benefit of the reader. The subheadings include: terms, general-purpose computer, image capturing pen, encoding of array, decoding, error correction, and location determination. Ir Terms [30] Pen - any writing implement that may or may not include the ability to store ink. In some examples, a stylus with no ink capability may be used as a pen in accordance with embodiments of the present invention. [31] Camera - an image capture system that may capture an image from paper or any other medium. II. General Purpose Computer [32] Figure 1 is a functional block diagram of an example of a conventional general-purpose digital computing environment that can be used to implement various aspects of the present invention. In Figure 1, a computer 100 includes a processing unit 110, a system memory 120, and a system bus 130 that couples various system components including the system memory to the processing unit 110. The system bus 130 may be any of several types of bus structures including a memory bus or memory controller, a peripheral bus, and a local bus using any of a variety of bus architectures. The system memory 120 includes read only memory (ROM) 140 and random access memory (RAM) 150. A basic input/output system 160 (BIOS), containing the basic routines that help to transfer information between elements within the computer 100, such as during startup, is stored in the ROM 140. The computer 100 also includes a hard disk drive 170 for reading from and writing to a hard disk (not shown), a magnetic disk drive 180 for reading from or writing to a removable magnetic disk 190, and an optical disk drive 191 for reading from or writing to a removable optical disk 192 such as a CD ROM or other optical media. The hard disk drive 170, magnetic disk drive 180, and optical disk drive 191 are connected to the system bus 130 by a hard disk drive interface 192, a magnetic disk drive interface 193, and an optical disk drive interface 194, respectively. The drives and their associated computer-readable media provide nonvolatile storage of computer readable instructions, data structures, program modules and other data for the personal computer 100. It will be appreciated by those skilled in the art that other types of computer readable media that can store data that is accessible by a computer, such as magnetic cassettes, flash memory cards, digital video disks, Bernoulli cartridges, random access memories (RAMs), read only memories (ROMs), and the like, may also be used in me example operating environment. A number of program modules can be stored on the hard disk drive 170, magnetic disk 190, optical disk 192, ROM 140 or RAM 150, including an operating system 195, one or more application programs 196, other program modules 197, and program data 198. A user can enter commands and information into the computer 100 through input devices such as a keyboard 101 and pointing device 102. Other input devices (not shown) may include a microphone, joystick, game pad, satellite dish, scanner or the like. These and other input devices are often connected to the processing unit 110 through a serial port interface 106 that is coupled to the system bus, but may be connected by other interfaces, such as a parallel port, game port or a universal serial bus (USB). Further still, these devices may be coupled directly to the system bus 130 via an appropriate interface (not shown). A monitor 107 or other type of display device is also connected to the system bus 130 via an interface, such as a video adapter 108. In addition to the monitor, personal computers typically include other peripheral output devices (not shown), such as speakers and printers. In a preferred embodiment, a pen digitizer 165 and accompanying pen or stylus 166 are provided in order to digitally capture freehand input. Although a direct connection between the pen digitizer 165 and the serial port is shown, in practice, the pen digitizer 165 may be coupled to the processing unit 110 directly, via a parallel port or other interface and the system bus 130 as known in the art. Furthermore, although the digitizer 165 is shown apart from the monitor 107, it is preferred that the usable input area of the digitizer 165 be co-extensive with the display area of the monitor 107. Further still, the digitizer 165 may be integrated in the monitor 107, or may exist as a separate device overlaying or otherwise appended to the monitor 107. The computer 100 can operate in a networked environment using logical connections to one or more remote computers, such as a remote computer 109. The remote computer 109 can be a server, a router, a network PC, a peer device or other common network node, and typically includes many or all of the elements described above relative to the computer 100, although only a memory storage device 111 has been illustrated in Figure 1. The logical connections depicted in Figure 1 include a local area network (LAN) 112 and a wide area network (WAN) 113. Such networking environments are commonplace in offices, enterprise-wide computer networks, intranets and the Internet. When used in a LAN networking environment, the computer 100 is connected to the local network 112 through a network interface or adapter 114. When used in a WAN networking environment, the personal computer 100 typically includes a modem 115 or other means for establishing a communications over the wide area network 113, such as the Internet. The modem 115, which may be internal or external, is connected to the system bus 130 via the serial port interface 106. In a networked environment, program modules depicted relative to the personal computer 100, or portions thereof, may be stored in the remote memory storage device. It will be appreciated that the network connections shown are illustrative and other techniques for establishing a communications link between the computers can be used. The existence of any of various well-known protocols such as TCP/IP, Ethernet, FTP, HTTP, Bluetooth, IEEE 802.1 lx and the like is presumed, and the system can be operated in a client-server configuration to permit a user to retrieve web pages from a web-based server. Any of various conventional web browsers can be used to display and manipulate data on web pages. III. Image Capturing Pen Aspects of the present invention include placing an encoded data stream in a displayed form that represents the encoded data stream. (For example, as will be discussed with Figure 4B, the encoded data stream is used to create a graphical pattern.) The displayed form may be printed paper (or other physical medium) or may be a display projecting the encoded data stream in conjunction with another image or set of images. For example, the encoded data stream may be represented as a physical graphical image on the paper or a graphical image overlying the displayed image (e.g., representing the text of a document) or may be a physical (non-modifiable) graphical image on a display screen (so any image portion captured by a pen is locatable on the display screen). This determination of the location of a captured image may be used to determine the location of a user's interaction with the paper, medium, or display screen. In some aspects of the present invention, the pen may be an ink pen writing on paper. In other aspects, the pen may be a stylus with the user writing on the surface of a computer display. Any interaction may be provided back to the system with knowledge of the encoded image on the document or supporting the document displayed on the computer screen. By repeatedly capturing images with a camera in the pen or stylus as the pen or stylus traverses a document, the system can track movement of the stylus being controlled by the user. The displayed or printed image may be a watermark associated with the blank or content-rich paper or may be a watermark associated with a displayed image or a fixed coding overlying a screen or built into a screen. [40] Figures 2A and 2B show an illustrative example of pen 201 with a camera 203. Pen 201 includes a tip 202 that may or may not include an ink reservoir. Camera 203 captures an image 204 from surface 207. Pen 201 may further include additional sensors and/or processors as represented in broken box 206. These sensors and/or processors 206 may also include the ability to transmit information to another pen 201 and/or a personal computer (for example, via Bluetooth or outer wireless protocols). [41] Figure 2B represents an image as viewed by camera 203. In one illustrative example, the field of view of camera 203 (i.e., the resolution of the image sensor of the camera) is 32x32 pixels (where JV=32). In the embodiment, a captured image (32 pixels by 32 pixels) corresponds to an area of approximately 5 mm by 5 mm of the surface plane captured by camera 203. Accordingly, Figure 2B shows a field of view of 32 pixels long by 32 pixels wide. The size of N is adjustable, such that a larger N corresponds to a higher image resolution. Also, while the field of view of the camera 203 is shown as a square for illustrative purposes here, the field of view may include other shapes as is known in the art [42] The images captured by camera 203 may be defined as a sequence of image frames {Ii}, where I is captured by the pen 201 at sampling time tj. The sampling rate may be large or small, depending on system configuration and performance requirement. The size of the captured image frame may be large or small, depending on system configuration and performance requirement. [43] The image captured by camera 203 may be used directly by the processing system or may undergo pre-filtering. This pre-filtering may occur in pen 201 or may occur outside of pen 201 (for example, in a personal computer). [44] The image size of Figure 2B is 32x32 pixels. If each encoding unit size is 3x3 pixels, then the number of captured encoded units would be approximately 100 units. If the encoding unit size is 5x5 pixels, then the number of captured encoded units is approximately 36. [45] Figure 2A also shows the image plane 209 on which an image 210 of the pattern from location 204 is formed. Light received from the pattern on the object plane 207 is focused by lens 208. Lens 208 may be a single lens or a multi-part lens system, but is represented here as a single lens for simplicity. Image capturing sensor 211 captures the image 210. [46] The image sensor 211 may be large enough to capture the image 210. Alternatively, the image sensor 211 may be large enough to capture an image of the pen tip 202 at location 212. For reference, the image at location 212 is referred to as the virtual pen tip. It is noted that the virtual pen tip location with respect to image sensor 211 is fixed because of the constant relationship between the pen tip, the lens 208, and the image sensor 211. [47] The following transformation Fs_p transforms position coordinates in the image captured by camera to position coordinates in the real image on the paper: [48] During writing, the pen tip and the paper are on the same plane. Accordingly, the transformation from the virtual pen tip to the real pen tip is: [49] The transformation Fs→p may be estimated as an affine transform. This simplifies as: (Sequence Removed) as the estimation of Fs_>p, in which 0X, 0y, sx, and sy are the rotation and scale of two orientations of the pattern captured at location 204. Further, one can refine Fs→p by matching the captured image with the corresponding real image on paper. "Refine" means to get a more precise estimation of the transformation Fs→p by a type of optimization algoridim referred to as a recursive method. The recursive mediod treats the matrix Fs→p as the initial value. The refined estimation describes the transformation between S and P more precisely. [50] Next, one can determine the location of virtual pen tip by calibration. [51] One places the pen tip 202 on a fixed location Lpentip on paper. Next, one tilts the pen, allowing the camera 203 to capture a series of images with different pen poses. For each image captured, one may obtain the transformation Fs→p . From this transformation, one can obtain the location of the virtual pen where Lpentip is initialized as (0,0) and [52] By averaging the LlHmul_paillp obtained from each image, a location of the virtual pen tip may be determined. With L^.^, one can get a more accurate estimation of Lpentlp. After several times of iteration, an accurate location of virtual pen tip Lvirtml_penlip may be determined. [53] The location of the virtual pen tip Lvirtual-pentip is now known. One can also obtain the transformation FS_P from the images captured. Finally, one can use this information to determine the location of the real pen tip Lpentip: [54] Mapping the center of camera-captured image to a corresponding pen-tip location in paper coordinates and calibration parameters that may be used in mapping of this type in accordance with various embodiments of the invention are discussed below in sections VIII and IX. IV. Encoding of Array [55] A two-dimensional array may be constructed by folding a one-dimensional sequence. Any portion of the two-dimensional array containing a large enough number of bits may be used to determine its location in the complete two-dimensional array. However, it may be necessary to determine the location from a captured image or a few captured images. So as to minimize the possibility of a captured image portion being associated with two or more locations in the two-dimensional array, a nonrepeating sequence may be used to create the array. One property of a created sequence is that the sequence does not repeat over a length (or window) n. The following describes the creation of the one-dimensional sequence then the folding of the sequence into an array. IV.A. Sequence Construction [56] A sequence of numbers may be used as the starting point of the encoding system. For example, a sequence (also referred to as an m-sequence) may be represented as a q-element set in field Fq. Here, q-pn where n > 1 and p is a prime number. The sequence or m-sequence may be generated by a variety of different techniques including, but not limited to, polynomial division. Using polynomial division, the sequence may be defined as follows: [57] where Pn(x) is a primitive polynomial of degree n in field Fq[x] (having q" elements). Ri(x) is a nonzero polynomial of degree / (where lP ' ^virtual-pemtp > l ~ *iA"'»■'» » i = l,2,—,# where AT is a number of captured images used for generating the calibration parameter and AL, is an offset between an actual pen tip location in an ith frame and Lpentip. 20. The system of claim 19, wherein the calibration module wixMizesL v^ai-ptntip as (0,0), where L virtual-ptn«p is an estimated value oiLviraiali_ptnUp. (Equation Removed) 23. The system of claim 22, wherein, the calibration module repeats the calculations of claims 29 and 30 a plurality of times such that the estimate converges to a substantially more accurate result estimate converges to a substantially more accurate result 24. The system of claim 23, wherein, the calibration module outputs from the calibration module as the calibration parameter for use by the mapping module to map the recovered image-center stroke to the recovered pen-tip stroke. 25. The system of claim 18, wherein the mapping module uses a virtual pen tip to map a recovered camera-captured stroke to a recovered pen-tip stroke, wherein a location of the virtual pen-tip on an image-sensing plane of the digital pen depends on a predetermined relationship between the tip of the pen and the pen's camera, wherein the predetermined relationship is based on the configuration of die pen. 26. A method of calibrating a digital pen substantially as hereinbefore described with reference to the accompanying drawings. 27. A computer-readable medium substantially as hereinbefore described with reference to the accompanying drawings. 28. A system that calibrates a digital pen substantially as hereinbefore described with reference to the accompanying drawings.