Patent Publication Number: US-2004047467-A1

Title: Document encoding by pixel block transformation and document decoding by overlaying

Description:
BACKGROUND  
       [0001] Document generation has become a mainstay use of computers. The term document as used herein is inclusive of any type of data file that can be created using a computer, including text-oriented documents, image- and graphic-oriented documents, as well as other types of documents. Once a document is generated using a computer, it may be delivered electronically, as a data file, or it may be delivered as a hardcopy, printed on a sheet of media such as paper.  
       [0002] Security can become an issue with the delivery of computer-generated documents. Printing a document within an organizational environment may entail outputting the document at a shared printer within a public area. Others may thus review a sensitive document before the individual who generated the document can retrieve it from the printer. Hardcopy documents delivered within inter-office mail, or even by postal mail, are also vulnerable to interception and review by unauthorized personnel.  
       [0003] Electronic documents, as data files, are perhaps no less sensitive to such interception. Unless encrypted email is specifically used, unscrupulous hackers may potentially be able to intercept the email intended for another. While email encryption is available, it is not widely used, and even confidential and sensitive documents are frequently exchanged over unencrypted email.  
       SUMMARY  
       [0004] The invention can be embodied within a method that generates a first plurality of blocks of pixels corresponding to pixels of a document. A second plurality of blocks of pixels is generated by transforming the first plurality of blocks of pixels, based on values of the pixels of the document to which first plurality of blocks of pixels correspond. 
     
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
     [0005] The drawings referenced herein form a part of the specification. Features shown in the drawings are meant as illustrative of only some embodiments of the invention, and not of all embodiments of the invention, unless otherwise explicitly indicated, and implications to the contrary are otherwise not to be made.  
     [0006]FIGS. 1A and 1B are a flowchart of a method and a diagram illustrating an example performance of the method, respectively, according to an embodiment of the invention.  
     [0007]FIGS. 2A and 2B are diagrams of two different types of pixel blocks from which a first section of pixel blocks is randomly assembled as an encoding and decoding section, according to an embodiment of the invention.  
     [0008]FIGS. 3A and 3B are diagrams depicting the decoding process for the pixel blocks of FIGS. 2A and 2B, respectively, where a corresponding, first pixel block and a corresponding second pixel block are instances of the same block, according to an embodiment of the invention.  
     [0009]FIG. 4 is a diagram showing the decoding process for the pixel blocks of FIGS. 2A and 2B, where a corresponding first pixel block and a corresponding pixel block are instances of different blocks, according to an embodiment of the invention.  
     [0010]FIG. 5 is a diagram of a system according to an embodiment of the invention.  
     [0011]FIG. 6 is a diagram illustrating an example decoding process, according to an embodiment of the invention.  
     [0012]FIGS. 7A, 7B,  7 C, and  7 D are diagrams illustrating an actual example of the encoding and decoding process, using the pixel blocks of FIGS. 2A and 2B, and using the decoding process of FIGS. 3A, 3B, and  4 , according to an embodiment of the invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
     [0013] In the following detailed description of exemplary embodiments of the invention, reference is made to the accompanying drawings that form a part hereof, and in which is shown by way of illustration specific exemplary embodiments in which the invention may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention. Other embodiments may be utilized, and logical, mechanical, and other changes may be made without departing from the spirit or scope of the present invention. The following detailed description is, therefore, not to be taken in a limiting sense, and the scope of the present invention is defined only by the appended claims.  
     [0014] Overview  
     [0015]FIG. 1A shows a method  100 , according to an embodiment of the invention, whereas FIG. 1B shows an example illustrative performance  150  of the method  100 , according to an embodiment of the invention. The method  100  can be implemented in one embodiment of the invention as a computer program having instructions to perform the method  100 . The computer program may be stored on a computer-readable medium, such as a removable or fixed storage, a volatile or non-volatile storage, and so on. The program may be executable by a computing device such as a computer, as well as by an image-forming device such as a printer. In the latter instance, the program may be stored as part of the firmware of the image-forming device.  
     [0016] A first section is generated that includes a number of first square blocks of pixels, to yield an encoding and decoding section ( 102 ). The first section may be a data file that can be output onto a media, such as a sheet of paper. The first square blocks of pixels are N×N pixel blocks, where N is greater than one. In FIG. 1B, the performance of  102  of FIG. 1A is depicted as the first section  152 .  
     [0017] A second section is next generated that includes a number of second square blocks, which transform the first square blocks in accordance with a document to encode the document ( 104 ). The second section may be the same or a different data file as the first section, and can be output onto the same or a different piece of media, such as a sheet of paper, as the first section. The document has portions that correspond to the first square blocks of the first section. For example, each pixel of the document may correspond to a first square block of pixels of the first section. Each first block is transformed in accordance with its corresponding portion of the document to generate a second block of pixels. That is, each first block is transformed depending on its corresponding portion of the document to generate the second block. The second section of the second blocks of pixels thus encodes the document, utilizing the first section of the first blocks of pixels as an encoding section.  
     [0018] For instance, where the document is a collection of black and white pixels, each first block may be transformed in one manner if its corresponding document pixel is black, and may be transformed in another manner if its corresponding document pixel is white. For simplicity, the phrase white pixel is used, even where such a pixel may be, in fact, an absence of black. That is, a white pixel may be a pixel that is not a black pixel. Transformation as used herein includes performing no action at all, such that one of the transformations may be to copy the pixels of the first block verbatim to yield the pixels of the corresponding second block. As an example, the first blocks may be transformed in a particular manner where their corresponding document pixels are black, and may be copied to yield the second blocks where their corresponding document pixels are white. It can thus be said that the first section is selectively transformed in accordance with the document to yield the second section.  
     [0019] The second section can be decoded to yield the document only by using the first section that encoded the document, the first section thus also serving as the decoding section. In FIG. 1B, the performance of  104  of FIG. 1A is depicted by transforming the first section  152  relative to a document  154  to yield a section second  156 . Furthermore,  102  and  104  of FIG. 1A may generally be referred to as the encoding process  106 .  
     [0020] The first and second sections are output ( 108 ) so that they can be delivered and thus received ( 110 ). Output may be as the same or separate electronic data files, or as the same or separate pieces of media, such as sheets of paper. To ensure confidentiality and secure transmission and receipt, the sections may be sent separately, by different modes of transport, at different times, and so on. For instance, the first section may be sent by email, whereas the second section may be sent by floppy disk. As another example, the first and the second sections may be printed on separate sheets of paper, and sent in separate envelopes by mail, or at different times by facsimile. As a final example, for secure archival storage, the first and the second sections may be stored at different locations.  108  and  110  of FIG. 1A may generally be referred to as the delivery process  112 , which is depicted in FIG. 1B as the arrow  158 .  
     [0021] The second section is overlaid relative to the first section to decode and display the document ( 114 ). That is, the first and the second sections are overlaid relative to each other so that each second block of pixels is overlaid under or over its corresponding first block of pixels. Because the second section of second pixel blocks was generated by transforming the first section of first pixel blocks in accordance with the document, the document will be made visible, or decoded, by such overlaying. It is noted that the overlaying of the first and the second sections relative to one another is accomplished in an aligned manner. That is, the first pixel blocks of the first section are aligned over or under their corresponding second pixel blocks of the second section to yield the decoded document. If the first pixel blocks are not aligned relative to their corresponding second pixel blocks, the decoded document will not be visible.  
     [0022] In the example previously described where the second pixel blocks are copies of the first pixel blocks where their corresponding document pixels are white, and the second pixel blocks are transformations of the first pixel blocks where their corresponding document pixels are black, the document decoding process is as follows. When the first section of first blocks is overlaid relative to the second section of second blocks, white pixels of the document will be revealed as the corresponding first blocks and the corresponding second blocks being identical to one another, since the second blocks are copies of the first blocks in such instances. Conversely, black pixels of the document will be revealed as the corresponding first blocks and the corresponding second blocks being different from one another, since the second blocks are transformations of the first blocks in such instances.  
     [0023] Thus, the decoded document may be revealed as the document over the background of the first section. In FIG. 1B, the performance of  114  is depicted as the second section  156  and the first section  152  being overlaid relative to one another, to yield the decoded document  154 ′. The decoded document  154 ′ is indicated as different than the document  154  for the embodiment in which the decoded document is revealed as the document over the background of the first section  152 . Finally,  114  of FIG. 1A may generally be referred to as the decoding process  116 . The encoding process  106 , the delivery process  112 , and the decoding process  116  are all described in more detail as specific embodiments of the invention in subsequent sections of the detailed description.  
     [0024] Although the method  100  of the embodiment of FIG. 1A, and the performance  150  of which is exemplary depicted in the embodiment of FIG. 1B, have been substantially described in relation to pixels that are on and off, such as black and white, other types of pixels may also be used. For instance, each pixel may have one of a number of different values, corresponding to different levels of black and white, gray scale, halftone, color, and so on. [Steve—the inventors indicated that the invention is applicable to these various other scenarios, BUT that it would require a significant amount of additional work to “figure out” . . . That&#39;s why there isn&#39;t additional description regarding such alternative embodiments in the application. That said, I&#39;d prefer to leave this sentence in to ensure broadness of claim interpretation.] That is, the method  100  has been described in substantial relation to black-and-white (i.e., two-value) pixels only for explanatory convenience and illustrative clarity, and not to convey a limitation of embodiments of the invention. Similarly, whereas the method  100  has been described in relation to pixel blocks that are square, in alternative embodiments of the invention, they may be more generally rectangular, or any other shape.  
     [0025] Encoding  
     [0026] The encoding process  106  of the method  100  of FIG. 1A can be specifically accomplished in one embodiment of the invention as described in this section of the detailed description. The pixel blocks of the first section are two pixel-by-two pixel blocks, where each pixel is either black or white. More specifically, the pixel blocks of the first section are randomly selected in  102  of FIG. 1A as either the pixel block  300  of FIG. 2A, or the pixel block  350  of FIG. 2B. The pixel blocks  300  and  350  are the inverses of one another. Thus, the pixel block  300  has a black pixel  302 , a white pixel  304 , a white pixel  306 , and a black pixel  308 , corresponding to the pixel block  350 , which has a white pixel  352 , a black pixel  354 , a black pixel  356 , and a white pixel  358 .  
     [0027] To generate the second pixel blocks of the second section in  104  of FIG. 1A, the first pixel blocks of the first section that have been generated are transformed in accordance with a document as follows. For each pixel of the document that is black, the second pixel block is determined as the inverse of the corresponding first pixel block. Thus, where a first pixel block is the block  300 , the corresponding second pixel block is the block  350 , and vice-versa. For each pixel of the document that is white, the second pixel block is determined by copying the corresponding first pixel block. Thus, where a first pixel block is the block  300 , the corresponding second pixel block is also the block  300 . Similarly, where a first pixel block is the block  350 , the corresponding second pixel block is also the block  350 .  
     [0028] The use of the pixel blocks  300  and  350  of FIGS. 2A and 2B, respectively, and the use of an inverse operation to generate the second pixel blocks of the second section only where the corresponding pixels of the document are black, provides for easily visible decoding by essentially performing an exclusive-or operation as is now described. For a white pixel of the document, both the corresponding first pixel block of the first section and the corresponding second pixel block of the second section are either instances of the pixel block  300  or the pixel block  350 . For the former case, as shown in FIG. 3A, overlaying two instances of the pixel block  300  yields the same pixel block  300 . Similarly, for the latter case, as shown in FIG. 3B, overlaying two instances of the pixel block  350  yields the same pixel block  350 . That is, white pixels of the document are displayed in the decoded document as the pixel block  300  or the pixel block  350 .  
     [0029] For a black pixel of the document, one of the corresponding first pixel block of the first section and the corresponding second pixel block of the second section is the pixel block  300 , and the other of the corresponding first and second pixel blocks is the pixel block  350 . As shown in FIG. 4, overlaying an instance of the pixel block  300  and an instance of the pixel block  350  yields a completely solid, or black, pixel block  500 . Thus, black pixels of the document are displayed in the decoded document as the pixel block  500 . This means that the resulting decoded document will be made visible as a number of the pixel blocks  500  against a background of a random assortment of the pixel blocks  300  and  350 .  
     [0030] Delivery  
     [0031] The delivery process  112  of the method  100  of FIG. 1A can be specifically accomplished in one embodiment of the invention as described in this section of the detailed description. FIG. 5 shows a system  600  according to an embodiment of the invention. The system  600  includes a computing device  602 , such as a computer, and one or more of the following optional components: an image-forming device  604 , such as a printer, a network  606 , such as the Internet, a postal mail delivery mechanism  608 , such as a mailbox, a fax machine  610 , and a scanner  618 . A number of these optional components may be combined as a single component. For instance, the image-forming device  604 , the fax machine  610 , and/or the scanner  618  may be combined as a single multi-function device (MFD).  
     [0032] Where the system  600  is for generating and sending first and second sections as have been described, the computer  602  may include a computer-readable medium  612  programmed to cause the computer to generate the first and second sections. The computing device  602  may then send the first and second sections as data files attached to email through the network  606 , or may directly control the fax machine  610 , which may be a faxmodem or other fax device internal to or external from the computing device  602 , to send the first and second sections as facsimiles. The computer  602  may also output the first and second sections onto the same sheet or separate sheets of media, such as paper, transparencies, and so on, using the printer  604 . Such hardcopy may then be sent through the postal mail delivery mechanism  608 , or faxed using the fax machine  610 . Inter-office mail, hand delivery, and so on, may also be used.  
     [0033] In another embodiment of the invention, the printer  604 , which includes a controller  614 , such as firmware, and an image-forming mechanism  616 , may generate and output the first and second sections itself, based on a document received from the computing device  602 . The controller  614  specifically generates the first and second sections, and causes the image-forming mechanism  616  to output the generated sections. The image-forming mechanism  616  may be a laser mechanism, an inkjet mechanism, and so on. The resulting hardcopy can then be sent through the postal mail delivery mechanism  608 , or faxed using the fax machine  610 . Inter-office mail, hand delivery, and so on, may also be used.  
     [0034] Where the system  600  is for receiving the first and second sections and decoding the document therefrom as have been described, the computer-readable medium  612  of the computing device  602  may cause the computing device  602  to decode the document from the first and second sections that have been received. The first and second sections may be received as data files attached to email received through the network  606 , or as data files received through the fax machine  610 , and decoded. The first and second sections may also be received as hardcopy, through the postal mail delivery mechanism  608 , the fax machine  610 , inter-office mail, hand delivery, and so on. The hardcopy may then be scanned in using the scanner  618 , resulting in scanned-in image data files of the first and second sections which are decoded. Alternatively, the user may simply overlay the first section relative to the second section to manually decode the document therefrom.  
     [0035] Decoding  
     [0036] The decoding process  116  of the method  100  of FIG. 1A can be specifically accomplished in one embodiment of the invention as described in this section of the detailed description. FIG. 6 illustrates the performance  700  of the decoding process  116 , according to an embodiment of the invention. The performance  700  is depicted in two different ways in FIG. 6. First, the second section  156  is overlaid relative to the first section  152 , to yield the decoded document  154 ′, which is the document  154  against a background of the first section  152 . Such decoding may be accomplished manually, with the user him or herself aligning the hardcopy of the two sections  152  and  156  over each other, or by a computing device, such as the device  602  of FIG. 5. In the latter instance, the computing device displays the first section  152  over or under the second section  156 .  
     [0037] Second, the performance  700  is depicted in FIG. 6 as the second section  156  being overlaid relative to the first section  152  to yield the original document  154 . That is, the original document  154  is not displayed against a background of the first section  152  as the decoded document  154 ′, as before, but is displayed without such a background. This may be accomplished by a computing device, such as the device  602  of FIG. 5, comparing corresponding first blocks with corresponding second blocks. If a first block corresponds to a second block in the manner by which the first block is transformed when an off, or white, pixel of the document is encountered, then such a white pixel is displayed. Similarly, if a first block corresponds to a second block in the manner by which the first block is transformed when an on, or black, pixel of the document is encountered, then such a black pixel is displayed.  
     [0038] For example, the transformation of a first block of the first section to a second block of the second section may be the copying of the first block when a white pixel of the document is encountered, and the inverse of the pixels of the first block when a black pixel is encountered. Therefore, if a comparison of a first block of the first section to a corresponding second block of the second section indicates that the blocks are identical, then a white pixel is displayed. Conversely, if a comparison of the first block to the corresponding second block indicates that the blocks are inversely related, then a black pixel is displayed. In this way, the original document can be decoded from the first and the second sections. It is noted that decoding and display of the original document in this manner is encompassed under the phrase of displaying the first section over or under the second section to decode the document.  
     EXAMPLE  
     [0039] An actual example of the process by which a document can be encoded, and subsequently decoded, is described with reference to FIGS. 7A, 7B,  7 C, and  7 D. The example depicted in these figures utilizes the pixel blocks of FIGS. 2A and 2B, and the decoding process of FIGS. 3A, 3B, and  4 . As can be appreciated by those of ordinary skill within the art, the example described in this section of the detailed description is for illustrative purposes only, and does not represent a limitation on the invention.  
     [0040]FIG. 7A shows a document  700  that is to be encoded. The document  700  has pixels organized along rows  702 A,  702 B,  702 C,  702 D, and  702 E, and columns  704 A,  704 B,  704 C,  704 D, and  704 E. For sake of description, a pixel of the document  700  is referenced as (x, y), where x is the reference number of the column in which the pixel lies, and y is the reference number of the row in which the pixel lies. Thus, the upper left-hand pixel of the document  700  is referenced as ( 704 A,  702 A), and the lower right-hand pixel of the document  700  is referenced as ( 704 E,  702 E). Black pixels are depicted in FIG. 7A as being shaded, for illustrative clarity. Lines separate adjacent pixels, even where both such pixels are white, also for illustrative clarity. Therefore, all the pixels of the document  700  are white, except for the following, which are black: ( 704 B,  702 B), ( 704 C,  702 B), ( 704 D,  702 B), ( 704 C,  702 C), ( 704 C,  702 D). These black pixels form a capital letter T.  
     [0041]FIG. 7B shows a first section  710  that is made up of a random collection of the pixel blocks  300  and  350  of FIGS. 2A and 2B, respectively. The first section  710  has pixel blocks organized along rows  712 A,  712 B,  712 C,  712 D, and  712 E, and columns  714 A,  714 B,  714 C,  714 D, and  714 E. Each pixel block is two pixels wide by two pixels high, and is either the pixel block  300  of FIG.  2 A, or the pixel block  350  of FIG. 2B. That is, each pixel block (j, k) of the first section  710 , where j is the reference number of the column in which the pixel block lies, and k is the reference number of the row in which the pixel block lies, is randomly selected as either the pixel block  300  of FIG. 2A, or the pixel block  350  of FIG. 2B. For example, the pixel block ( 714 A,  712 A) has been randomly selected as the pixel block  300  of FIG. 2A, whereas the pixel block ( 714 B,  712 A) has been randomly selected as the pixel block  350  of FIG. 2B. In FIG. 7B, pixel blocks are demarcated from one another with solid lines, and pixels within the pixel blocks are demarcated from one another with dotted lines.  
     [0042] Furthermore, the pixel blocks of the first section  710  correspond in number and position to the pixels of the document  700 . There are thus five rows and five columns of pixel blocks in the first section  710 , since there are five rows and five columns of pixels in the document  700 . For example, the pixel block ( 714 A,  712 A) of the first section  710  corresponds to the like-positioned pixel ( 704 A,  702 A) of the document  700 , the pixel block ( 714 B,  712 A) corresponds to the like-positioned pixel ( 704 B,  702 A), and so on.  
     [0043]FIG. 7C shows a second section  720 , which is generated by selectively inversing pixel blocks of the first section  710 , based on whether the corresponding pixel of the document  700  is black or white. More specifically, where a pixel of the document  700  is white, then the corresponding pixel block of the first section  710  is copied verbatim to the second section  720 . Where a pixel of the document  700  is black, then the inverse of the corresponding pixel block of the first section  710  is copied to the second section  720 . Thus, the second section  720  has pixel blocks organized along rows  722 A,  722 B,  722 C,  722 D, and  722 E, and columns  724 A,  724 B,  724 C,  724 D, and  724 E. Each pixel block of the second section  720  can be referenced as (m, n), where m is the reference number of the column in which the pixel block lies, and n is the reference number of the row in which the pixel block lies.  
     [0044] As an example of how some of the pixel blocks of the second section  720  are generated, the pixel block ( 724 A,  722 A) is identical to the corresponding pixel block ( 714 A,  712 A) of the first section  710 . This is because the corresponding pixel ( 704 A,  702 A) of the document  700  is white, so the pixel block ( 714 A,  712 A) of the first section  710  is copied verbatim as the pixel block ( 724 A,  722 A) of the second section  720 . That is, both the pixel block ( 714 A,  712 A) of the first section  710  and the pixel block ( 724 A,  722 A) of the second section  720  are the pixel block  300  of FIG. 2A. The pixel block ( 714 A,  712 A) of the first section  710  was randomly selected as the pixel block  300  of FIG. 2A. Then, because the pixel ( 704 A,  702 A) of the document  700  is white, the pixel block ( 724 A,  722 A) of the second section  720  is generated as a verbatim copy of the pixel block ( 714 A,  712 A) of the first section  710 .  
     [0045] As another example, the pixel block ( 724 C,  722 C) of the second section  720  is the inverse of the corresponding pixel block ( 714 C,  712 C) of the first section  710 . The term inverse in this situation means that the pixels of the pixel block ( 714 C,  712 C) of the first section  710  are switched from black to white or white to black to yield the pixels of the pixel block ( 724 C,  722 C) of the second section  720 . That is, whereas the pixel block ( 714 C,  712 C) of the first section  710  is the pixel block  350  of FIG. 2B, the pixel block ( 724 C,  722 C) of the second section  720  is the pixel block  300  of FIG. 2A. The pixel block ( 724 C,  722 C) of the second section  720  is the inverse of the pixel block ( 714 C,  712 C) of the first section  710  because the corresponding pixel ( 704 C,  702 C) of the document  700  is black.  
     [0046] Thus, the pixel block ( 714 C,  712 C) of the first section  710  was randomly selected as the pixel block  350  of FIG. 2B. Because the pixel ( 704 C,  702 C) of the document  700  is black, the pixel block ( 724 C,  722 C) of the second section  720  is generated as the inverse of the pixel block ( 714 C,  712 C) of the first section  710 . That is, the pixel block ( 724 C,  722 C) of the second section is generated as the pixel block  300  of FIG. 2A, which is the inverse of the pixel block  350  of FIG. 2B.  
     [0047] In FIG. 7D, the decoded document  730  is generated by overlaying the first section  710  over or under the second section  720 . This means that the pixel blocks of the first section  710  are overlaid over or under their corresponding pixel blocks of the second section  720 , and thus that the pixels of each pixel block of the first section  710  are overlaid over or under their corresponding pixels of the corresponding pixel block of the second section  720 . The pixels of the resulting pixel blocks of the decoded document  730  are decoded by such overlaying in the following way. If either or both of a pixel of the first section  710  and its corresponding pixel of the second section  720  is black, then the corresponding pixel of the decoded document  730  is black. Only if both a pixel of the first section  710  and its corresponding pixel of the second section  720  is white, is the corresponding pixel of the decoded document  730  also white.  
     [0048] The decoded document  730  has pixel blocks organized along rows  732 A,  732 B,  732 C,  732 D, and  732 E, and columns  734 A,  734 B,  734 C,  734 D, and  734 E. Each pixel block of the decoded document  730  can be referenced as (p, q), where p is the reference number of the column in which the pixel block lies, and q is the reference number of the row in which the pixel block lies. Each pixel block of the decoded document  730  corresponds to a pixel block of the second section  720 , to a pixel block of the first section  710 , and to a pixel of the document  700 . For example, the pixel block ( 734 A,  732 A) of the decoded document  730  corresponds to the pixel block ( 724 A,  722 A) of the second section  720 , to the pixel block ( 714 A,  712 A) of the first section  710 , and to the pixel ( 704 A,  702 A) of the document  700 .  
     [0049] As an example of how the decoded document  730  is generated, the pixel bock ( 734 A,  732 A) of the decoded document  730  is generated by overlaying the pixel block ( 714 A,  712 A) of the first section  710  over or under the pixel block ( 724 A,  722 A) of the second section  720 . Both the pixel block ( 714 A,  712 A) of the first section  710  and the pixel block ( 724 A,  722 A) of the second section  720  are the pixel block  300  of FIG. 2A. Therefore, the decoding process occurs as depicted in FIG. 3A, and the pixel block ( 734 A,  732 A) of the decoded document  730  is also the pixel block  300  of FIG. 2A. That is, the upper left-hand pixel and the lower right-hand pixel of each of the pixel block ( 714 A,  712 A) of the first section  710  and of the pixel block ( 724 A,  722 A) of the second section  720  are black, resulting in the upper left-hand pixel and the lower right-hand pixel of the pixel block ( 734 A,  732 A) of the decoded document  730  being black. Similarly, the upper right-hand pixel and the lower left-hand pixel of each of the pixel block ( 714 A,  712 A) of the first section  710  and of the pixel block ( 724 A,  722 A) of the second section  720  are white, resulting in the upper right-hand pixel and the lower left-hand pixel of the pixel block ( 734 A,  732 A of the decoded document  730  being white.  
     [0050] As another example, the pixel block ( 734 C,  732 C) of the decoded document  730  is generated by overlaying the pixel block ( 714 C,  712 C) of the first section  710  over or under the pixel block ( 724 C,  722 C) of the second section  720 . The pixel block ( 714 C,  712 C) of the first section  710  is the pixel block  350  of FIG. 2B, whereas the pixel block ( 724 C,  722 C) of the second section  720  is the pixel block  300  of FIG. 2A. Therefore, the decoding process occurs as depicted in FIG. 4, and the pixel block ( 734 C,  732 C) of the decoded document  730  is made up of entirely black pixels. The upper left-hand pixel of one of the pixel block ( 714 C,  712 C) of the first section  710  and of the pixel block ( 724 C,  722 C) of the second section  720  is black, so the resulting upper left-hand pixel of the pixel block ( 734 C,  732 C) of the decoded document  730  is black.  
     [0051] Similarly, the upper right-hand pixel of one of the pixel block ( 714 C,  712 C) of the first section  710  and of the pixel block ( 724 C,  722 C) of the second section  720  is black, so the resulting upper right-hand pixel of the pixel block ( 734 C,  732 C) of the decoded document  730  is black. Because the lower left-hand pixel of one of the pixel block ( 714 C,  712 C) of the first section  710  and of the pixel block ( 724 C,  722 C) of the second section  720  is black, the resulting lower left-hand pixel of the pixel block ( 734 C,  732 C) of the decoded document  730  is black. Finally, because the lower right-hand pixel of one of the pixel block ( 714 C,  712 C) of the first section  710  and of the pixel block ( 724 C,  722 C) of the second  720  is black, the resulting lower right-hand pixel of the pixel block ( 734 C,  732 C) of the decoded document  730  is black.  
     [0052] It can be said that the decoded document  730  represents the document  700  against the background of the first section  710 . This is because for each pixel of the document  700  that is black, the corresponding pixel block of the decoded document  730  is made up of all black pixels. For example, the pixel ( 704 D,  702 B) of the document  700  is black, such that the pixel block ( 734 D,  732 B) is made up of all black pixels. However, for each pixel of the document  700  that is white, the corresponding pixel block of the decoded document  730  is identical to the corresponding pixel block of the first section  710 . For example, the pixel ( 704 E,  702 E) of the document  7000  is white. As a result, the pixel block ( 734 E,  732 E) of the decoded document  730  is identical to the pixel block ( 714 E,  712 E) of the first section  710 . That is, both the pixel block ( 734 E,  732 E) of the decoded document  730  and the pixel block ( 714 E,  712 E) of the first section  710  are the pixel block  350  of FIG. 2B.  
     [0053] In sum, the document  730  is a decoded representation of the document  700 . Each black pixel block of the decoded document  730  corresponds to a black pixel of the document  700 . Thus, the decoded document  730  is a larger but accurate representation of the document  700 . Although white pixels of the document  700  are not rendered as completely white pixel blocks in the decoded document  730 , neither are they rendered as completely black pixel blocks in the decoded document  730 . Therefore, the document  700  is discernible within the decoded document  730 . That is, the capital letter T of the document  700 , as rendered using the five pixels ( 704 B,  702 B), ( 704 C,  702 B), ( 704 D,  702 B), ( 704 C,  702 C), and ( 704 C,  702 D) in FIG. 7A, is discernible within the decoded document- 730 , as rendered using five pixel blocks ( 734 B,  732 B), ( 734 C,  732 B), ( 734 D,  732 B), ( 734 C,  732 C), and ( 734 C,  732 D) in FIG. 7D.  
     [0054] The term overlaying reflects the decoding process performed between the first section  710  and the second section  720  to yield the decoded document  730 . For instance, the first section  710  could be output on a first transparency sheet, and the second section  720  could be output on a second transparency sheet. Overlaying the first transparency sheet over or under the second transparency sheet, such that the pixel blocks of the first section  710  are aligned over or under their corresponding pixel blocks of the second section  720 , would then yield the decoded document  730 . Where one of the corresponding pixels of the transparency sheets is black, a black pixel would be revealed when the first transparency sheet is overlaid under or over the second transparency sheet. Only where corresponding pixels of both transparency sheets are white would overlaying the first transparency sheet under or over the second transparency sheet yield a white pixel.  
     [0055] Furthermore, as described in more detail earlier in the detailed description, the term overlaying as used herein can be performed electronically. That is, the overlaying of corresponding pixel blocks of the two sections to yield the decoded document can be performed by or at a computerized device. In such an instance, the background of the first section against which the decoded document is instantiated may be automatically cleared, to improve the viewer&#39;s discerning of the decoded document, as has also been explained in more detail earlier in the detailed description.  
     [0056] Conclusion  
     [0057] It is noted that, although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that any arrangement is calculated to achieve the same purpose may be substituted for the specific embodiments shown. This application is intended to cover any adaptations or variations of the present invention. Therefore, it is manifestly intended that this invention be limited only by the claims and equivalents thereof.