This paper describes some techniques for efficient coding of two‐tone (black and white) facsimile pictures. These techniques use the two‐dimensional correlation present in spatially close picture elements to change the relative order of transmission of elements in a scan line. This ordering increases the average length of the runs of consecutive black or white elements in the ordered line, making the data more amenable to one‐dimensional run‐length coding. We describe several variations of the ordering scheme, which differ in complexity and coding efficiency and evaluate their coding efficiency. For a variety of 8‐1/2 inch by 11‐inch typed documents, road maps, and circuit diagrams scanned with 200 lines/inch, these techniques reduce the bit rate by 30 to 50 percent over and above the one‐dimensional run‐length coding along a scan line; for single‐spaced typed material with 100 lines/inch, this reduction is about 25 percent. We compare one of our techniques with a two‐dimensional compression technique recently proposed by Preuss. We show that our technique results in an entropy about 10 to 18 percent lower than that obtainable through Preuss' technique.
We give simulation results using one of our ordering algorithms for the coding of eight ccitt test documents. These algorithms do not make any approximations and therefore can reproduce the documents exactly at the receiver. The code design is similar to the one‐dimensional modified Huffman code that has been proposed by the ccitt as a standard. One‐dimensional run‐length coding using the modified Huffman code results in 445,316 bits per document on the average, which can be transmitted in 92.77 seconds using a transmission rate of 4800 bits per second. Our ordering algorithm, which is two‐dimensional in nature, requires, on the average, 264,632 bits per document, or 55.13 seconds per document for the same transmission rate. Thus, the ordering scheme reduces the transmission time by approximately 41 percent, compared to one‐dimensional run‐length coding.
A new scheme for the reconstruction of dpcm‐coded signals is presented. In this scheme, instead of assigning one representative level to the prediction error whenever it is in a range determined by the decision levels of a dpcm quantizer, surrounding local picture structure is used to improve the reconstruction. No extra transmission is required. Mean‐absolute‐reconstruction error is decreased by over 20 percent, and the picture quality is significantly improved in flat, as well as high, detailed areas of still pictures and sequences of pictures containing motion.
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