328 IEEE SIGNAL PROCESSING LETTERS, VOL. 4, NO. 12, DECEMBER 1997

Hybrid Block Truncation CodingChih Shoung Huang and Yinyi Lin

Abstract—A hybrid block truncation coding (BTC) is presentedin this work. In the hybrid BTC, a universal codebook usingHamming codes and a differential pulse code modulation (DPCM)are employed, respectively, to the bit plane and the side infor-mation of BTC to reduce coding rate. Simulation results revealthat the performance of the proposed algorithm is only slightlyworse than that of the hybrid BTC using vector quantization (VQ)techniques, but with much lower computational or hardwarecomplexity.

Index Terms—Block truncation coding, differential pulse codemodulation, Hamming codes, vector quantization.

I. INTRODUCTION

BLOCK TRUNCATION coding (BTC) is a 1-b moment-preserving quantizer that preserves the edge information

of small blocks of original images [1]. Some hybrid BTCalgorithms such as BTC–VQ and BTC–VQ–DCT [2]–[3] wereproposed to reduce the bit rate of BTC, in which the vectorquantization (VQ) technique is applied to the bit plane and/orthe side information of BTC to reduce the rate. Although theVQ technique can achieve a nearly optimal performance, itis quite time consuming in learning procedure. In this letter,a novel hybrid algorithm is proposed, in which a universalcodebook using Hamming codes and differential pulse codemodulation (DPCM) scheme are, respectively, provided toreduce bit rates of both bit map plane and side informationof BTC. No learning and no codebook are required for theproposed algorithm.

II. HAMMING CODE AS A UNIVERSIAL CODEBOOK

The bit map data is determined by the mean value ofeach 4 4 subblock, in which a “0” and a “1” representthe level of a pixel below and beyond the mean value of asubblock, respectively. In the hybrid algorithm described byUdpikar and Raina [2] the vector quantization (VQ) techniqueis applied to both bit plane and side information of BTC. Alearning procedure and a large codebook are required for theVQ technique, although the technique is nearly optimal.

Here, a universal book using a Hamming code is providedto reduce the rate of the bit plane of BTC. Hamming codes

Manuscript received June 9, 1997. This work was supported by theNational Science Council, Taiwan, R.O.C., under Contract NSC 86-2221-E-008-012. The associate editor coordinating the review of this manuscript andapproving it for publication was Prof. R. M. Mersereau.

C. S. Huang is with the Department of Electrical Engineering, NationalCentral University, Chung Li, Taiwan 32054, R.O.C., and the AppliedTechnology Laboratory, Telecommunication Laboratories, ChunghwaTelecom Co., Ltd., Taiwan, R.O.C.

Y. Lin is with the Department of Electrical Engineering, NationalCentral University, Chung Li, Taiwan 32054, R.O.C. (e-mail:yilin@mbox.ee.ncu.edu.tw).

Publisher Item Identifier S 1070-9908(97)08944-X.

Fig. 1. Number of error bits versus bit rate for various coding techniques.

TABLE IPSNR FOR VARIOUS RATES

are originally used as data transmission codes to combatrandom errors occurred in communications channel. AnHamming code is perfect code (i.e., can correct exactly singleerror) with the following parameters [4].

• Code length:• Number of information digits:• Number of parity check digits:• Error correcting capability: (i.e., minimum Ham-

ming distance

1070–9908/97$10.00 1997 IEEE

HUANG AND LIN: BLOCK TRUNCATION CODING 329

TABLE IIPREDICTION GAIN FOR VARIOUS SIDE PARAMETERS

When an Hamming code is used as a data compres-sion code and applied to the bit plane of BTC, a data sequenceof length n in the bit plane of BTC is represented by (orencoded to) an index of length. The decoder and encoderof the Hamming transmission code are used as an encoderand a decoder of the code, respectively, when it is used as acompression code. As a result, no learning procedure and nocodebook are required during encoding and decoding, sincethe Hamming codes are linear codes. A compression ratio of

can be achieved and the bit error ineach data block is at most one bit since a Hamming code isa perfect code.

The 512 512 monochrome Lena image was used inthis experiment for performance comparison. The number ofbit errors for Hamming codes as a universal codebook withvarious rates and the upper bound of bit errors are depicted inFig. 1, in which the bound is given by (512 512)

Note that the code with is a (3,1) repetitivecode. The number of bit errors using line scan VQ andblock scan VQ based upon Hamming distance measurementis also shown in this figure for comparison. As shown,although the VQ technique can achieve a better performance,the computational complexity and a large codebook make itimpractical, especially for high rates.

The performance comparison of using Hamming code andVQ to the bit plane is also made by comparing peak signal-to-noise ratio (PSNR). The results are displayed in TableI, in which both side parameters (low mean and mean-lowmean in this experiment) were quantized using 8-b quantizers.As demonstrated, the performance of using Hamming codesas a universal codebook is only slightly worse than that ofusing block scan VQ technique with a comparable code rate.However, no learning procedure and no codebook are neededfor linear Hamming codes.

III. DPCM CODING FOR SIDE INFORMATION OF BTC

The DPCM coding includes a linear predicator and a scalarquantizer. Its performance depends on quantization error thatis determined by quantizer type, quantization bits, and thevariance of the differential signal [5]. For a given quantizertype and quantization bits, the prediction gain of DPCM isgiven by where and are the variancesof an input signal and its differential signal, respectively. Forsimplicity, the first-order linear predicator (i.e., one unit delay)

TABLE IIIPSNR FOR VARIOUS SIDE PARAMETER PAIRS

is considered here, and the prediction gains of various sideparameters with the first moment statistics are summarized inTable II. As shown, the gains of low mean and mean-lowmean are larger than others, and they are selected as the sideparameters of BTC. Table III compares the PSNR performancefor various combinations of side parameters in which each sideparameter pair is quantized using eight quantization bits withan optimal bit allocation. As demonstrated, at least a gain of0.4 dB can be obtained for low mean and mean-low mean asthe side parameter pair, as compared to others.

The optimal bit allocation is given by [6]

where and are the variation ranges of the two sideparameters, and is the total number of quantization bits.From histograms of both low mean and mean-low mean forthe first order differential Lena image, the optimal number ofquantization bits for low mean and mean-low mean are 5 band 3 b, respectively, with a total eight quantization bits (i.e.,the rate of the side information becomes 0.5 b/pixel).

A comparison of using both VQ and DPCM to the sideinformation (low mean and mean-low mean) of BTC is made,which indicates that, at the same bit rate of 0.5 b/pixel, theVQ technique achieves a gain of 0.3 dB only over that ofDPCM while with much higher computational or hardwarecomplexity.

IV. PERFORMANCE COMPARISION

The PSNR performance of the hybrid BTC algorithm us-ing Hamming codes as a universal codebook and DPCM iscompared with that of the hybrid BTC using VQ technique.The reconstructed Lena images together with the original Lenaimage are shown in Fig. 2. As shown, with a comparable bitrate, the hybrid BTC–Hamming–DPCM algorithm has only

330 IEEE SIGNAL PROCESSING LETTERS, VOL. 4, NO. 12, DECEMBER 1997

(a) (b)

(c)

Fig. 2. Lena image. (a) Original (34.32 dB, bit rate= 2 b/pixel). (b) Reconstructed by BTC-VQ (PSNR= 32.2 dB, bit rate= 1.0625 b/pixel). (c)Reconstructed by BTC–Hamming–DPCM (PSNR= 31.23 dB, bit rate= 1.071 b/pixel).

0.97 dB degradation compared to the BTC–VQ algorithm.However, the proposed algorithm has much lower computa-tional or hardware complexity. As an example, both algorithmswere realized in Sun SparcStation 10, and the computationaltime is 1 s using proposed algorithm, but 1 min using thehybrid BTC–VQ algorithm.

V. SUMMARY

A hybrid BTC using Hamming codes as a universal code-book and DPCM is proposed in this letter to reduce the rate ofBTC. A comparison with the hybrid BTC–VQ indicates thatthe performance of the proposed algorithm is only slightlyworse (within 1 dB) than that of the BTC–VQ algorithm,but with much lower computational or hardware complexity.

No learning procedure and no codebook are required for theproposed algorithm.

REFERENCES

[1] E. J. Delp and O. R. Mitchell, “Image compression using BTC,”IEEETrans. Commun., vol. COMM-27, pp. 1335–1342, Sept. 1979.

[2] V. R. Udpikar and J. P. Raina, “BTC image coding using vectorquantization,” IEEE Trans. Commun., vol. COMM-35, pp. 352–356,Sept. 1987.

[3] Y. Wu and D. Coll, “BTC-VQ-DCT hybrid coding of digital images,”IEEE Trans. Commun., vol. 39, pp. 1283–1287, Sept. 1991.

[4] S. Lin and D. J. Costello, Jr.,Error Control Coding: Fundamentals andApplications. Englewood Cliffs, NJ: Prentice-Hall, 1989.

[5] N. S. Jayant and P. Noll,Digital Coding of Waveforms—Principles andApplications to Speech and Video. Englewood Cliffs, NJ: Prentice-Hall, 1984.

[6] A. Gersho and R. M. Gray,Vector Quantization and Signal Compression.Boston, MA: Kluwer, 1992.