# An Enhanced Adaptive Block Truncation Coding with Edge Quantization Scheme +
## 1 Introduction  
Rapid improvements in the area of network and information technology increase the services of digital multimedia, especially digital image, in today's digitalized and information world. For example, consider storage and transmission. File compression reduces the amount of space needed to store data, and also speeds the time to send over the Internet. About compressing digital images, there are two main types of compressing digital images, lossless and lossy. In this paper, we deal with block truncation coding (BTC) and its variants [1; 2; 3; 4], which are lossy compression algorithms. Because of their stable compression rates and low computation efforts, BTC-like schemes are widely used in cryptography, e.g., data hiding [5; 6; 7; 8; 9], watermarking [10], secret image sharing, and visual cryptography [11; 12; 13; 14]. The BTC was first proposed by [PERSON] and [PERSON] [1]. It is a block-based lossy image compression technique for grayscale or color images, where a quantizer is adopted to reduce the number ofgray levels in each block. An image is subdivided into non-overlapping blocks. Then, each block is coded by the mean, the standard deviation, and the bit map consisting of 0's and 1's. Suppose that a block size has \((4\times 4)\) pixels, and then these 16 pixels (i.e., 128 bits) can be represented by a trio with \((8+8+16)=32\) bits. That is, 16 pixels are represented as two quantization levels and a bitmap. Therefore, the compression ratio (CR) of BTC is determined from CR = \((16\times 8)/32=4\) for this case. BTC provides a good compression ratio without degrading the visual quality of the reconstructed image much. However, the processing time for BTC algorithm has significant computational complexity, and thus it is not generally recommended for time-consuming applications. In [2], [PERSON] and [PERSON] proposed absolute moment BTC (AMBTC), a variation of BTC, which has a simple computation. AMBTC adopts bi-clustering approach, and thus still uses two quantization levels in a block like BTC. Afterwards the authors in [3] proposed a modified BTC (MBTC) to further enhance the visual quality of the reconstructed image by using the so-called max-min quantizer. Because of using the simple bi-clustering approach in AMBTC and MBTC, the details near edges will be removed from the reconstructed image. As we know, edges are important information for human visual perception. Moreover, the information of edges is also necessary for some image processing applications, e.g., pattern recognition and optical character recognition. Therefore, the loss of details near edges will compromise the availability of BTC-like compression, and this leads to motivation for designing an edge-based BTC compression algorithm. Recently, [PERSON] and [PERSON] proposed an adaptive BTC based on edge quantization (ABTC-EQ) [4]. The authors first use edge detector to divide an image into edge blocks and non-edge blocks. Afterward, by applying MBTC on non-edge blocks, and adopting tri-clustering algorithm to tackle edge blocks, ABTC-EQ may provide the better visual quality of the reconstructed image, but has the less compression ratio when compared with AMBTC or MBTC. This is because edge blocks have to use three pixels to represent the quantization values for three clusters. However, it is observed that ABTC-EQ uses 2 bits to represent the index of each cluster. Compared with existing ABTC-EQ [4], MBTC [3], and AMBTC [1], the proposed enhanced ABTC-EQ method takes full advantage of the image compression and achieves a higher image quality. The main contributions of this paper are as follows: (1) The proposed method improves the compression rate by using a variable-length code to represent the index of each cluster. As a result, we can only use an average of 5/3 bits. That is, our proposed method less compression ratio when compared with AMBTC or MBTC. (2) Increasing the number of quantization levels improves image quality, but degrades compression efficiency.