Aditya kumar et al, Int. J. Comp. Tech. Appl., Vol 2 - International ...

Aditya kumar et al, Int. J. Comp. Tech. Appl., Vol 2 (4), 1099-1117 

ISSN:2229-6093 

Image Compression by Moment Preserving 

Algorithms: A Scrutinization 

Aditya Kumar 

Department Of Computer Science & Engineering 

National Institute Of Technology, Hamirpur, India 

adi.bond.adi@gmail.com 

Pardeep Singh 

Department Of Computer Science & Engineering 

National Institute Of Technology, Hamirpur, India 

pardeep@nitham.ac.in 

Abstract-Block Truncation Coding is an image compression 

technique which is used globally in many online as well as offline 

graphical applications e.g. LCD overdrive etc. In this literature 

survey we will discuss many variants of Block Truncation coding 

and latest metamorphosed techniques which are introduced 

recently. These techniques are analyzed behalf on objective and 

subjective point of view. In this literature survey, simulation 

results are also provided for each technique. 

Keywords- Economical Block Truncation Coding, filtering, 

interpolation., LCD overdrive, transformation. 

I. INTRODUCTION 

Block Truncation Coding (BTC) [1] [2] [3] is a 

straightforward and accelerated lossy image compression 

technique for gray scale images invented by Delp and Mitchell 

[20]. The main conception of BTC is to execute moment 

preserving quantization for each blocks of each pixels by 

which the quality of the image will be remained endorse and at 

the same time the request for the storage space will be 

reduced. Even if the compression using Block Truncation 

Coding is inferior to the standard JPEG compression algorithm 

[21], BTC has achieved fame due to its experimental 

usefulness. Several variants related to the basic Block 

Truncation Coding have been discussed in this literature 

survey. 

Let us weigh up a digital gray-level immobile image of the 

size N pixels where every single pixel is represented by k bits. 

The motto of the image compression is to convert or transform 

the image to a space efficient (compressed) form so that the 

data of image is protect as far as possible when decompressing 

the encoded image. 

The goodness of compression techniques can be 

characterized by considering a set of quality. These qualities 

are included the bit rate which gives the average number of 

bits per stored pixel of the image. Bit rate is the excellent 

limiting factor [4] [5] [23] of a compression technique because 

it measures the efficiency of the technique. 

Another goodness of this method is the ability to safeguard 

the information data. A compression technique is lossless if 

the decompressed image is exactly the same as the original 

one. Otherwise the inherit method is lossy. The excellence of 

the reconstructed image can be measured by the mean square 

error (MSE) [6] [7], mean absolute error (MAE) [6] [7], signal 

to noise ratio (SNR) [1] [9], or it can be analyzed by a human 

photo analyst. Let x i stand for the i th pixel value in the original 

image and y i is the corresponding pixel in the reconstructed 

image (i=1,2,...,N). Here the row-major order of pixels of the 

image matrix is considered. The three quantitative measures 

are defined as 

MSE = ∑ 

|y − x 

| 

(1) 

MAE = ∑ 

|y − x | (2) 

SNR = −10log 

(3) 

These above limiting factor are globally used but 

calamitously they do not always occur simultaneously with the 

estimations of human expert [23] [27]. 

The third one characteristics of BTC is the processing 

speed of the compression and decompression algorithms. In 

on-line applications the response times are often serious 

parameter. In the extreme case a space productive 

compression algorithm is useless if its processing time causes 

an insufferable delay in the image processing related 

application. If image compression task work as a background 

process then it is tolerable. However, fast decompression is 

desirable [64]. 

The fourth one characteristics of BTC is robustness against 

data transmission errors. The compressed file is normally an 

object of a data transmission operation. The transmission is in 

the elementary form between primary storage and secondary 

memory but it can be between two remote sites via 

transmission lines. Visual comparison of the original and 

disturbed images gives a direct evaluation of the robustness. 

However, the data transmission systems commonly contain 

fault tolerant internal data formats so that this property is not 

always effective or valid. 

Another important features of the compression method we 

may mention the ease of implementation and the demand for a 

working storage space. Present time these measurement 

parameters are often of secondary importance. From the 

experimental point of view the last but often not least feature 

is running time of the algorithm itself. Certainty and 

IJCTA | JULY-AUGUST 2011 

Available online@www.ijcta.com 

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dependability of the software often to a high degree depends 

on the complexity of the algorithm. 

After this introduction we have given BTC algorithm in 

section II, variants of basic methods in section III, 

comparative analysis on recent BTC algorithm in section IV, 

comparison to JPEG in section V and finally the conclusion in 

last section VI. 

II. 

BTC ALGORITHM 

An image having N pixel is divided into non overlapping 

smaller blocks of the size m pixels and each individual block 

is processed separately [64]. A condensed representation is 

forage through locally for each block. While the decoding 

process metamorphoses the encoded blocks back into pixel 

values so that the decompressed image look like the original 

one as much as possible. The mean value (x̅) and standard 

deviation (σ) are enumerated and encoded for each block. 

x̅ = ∑ 

= ∑ 

x 

 

x 

(4) 

 

x 

(5) 

σ = x − x̅ 

 

(6) 

Then a two-level quantization is electrocuted. Pixels with 

values less than the quantization threshold ( x ≤ x ) are 

mapped to value a and pixels with values greater than or equal 

to the threshold (x > x ) are mapped to value b. Here the 

threshold x th is considered to be x and the value a and b are 

chosen so that the first and second sample moments (x̅, x ) are 

safe guarded in the encoding processes. This is the case for the 

selection 

a = x̅ − σ 

 

b = x̅ + σ 

 

where, q stands for the number of pixels x i >x th . 

A compressed block emerges as a triple (x̅, σ, B), where x̅ 

and σ give mean and standard deviation of the pixel values in 

the block and B stands for the bit plane, giving the 

quantization of the pixel values [64] . See Figure1. 

A direct encoding of x̅ and σ by k bits yields a bit rate of 

 

 

(7) 

(8) 

= 1 + 

 

bits per pixel (bpp) (9) 

 

The method is accelerated, to be deficient in extra space, is 

easy to carry out [23] [64], and has low computational 

demands. It conserved the quality of the reconstructed image 

and retains the edges. It also recovers excellently from 

transmission errors. One can still improve it in several 

different ways. 

III. 

VARIANTS OF BASIC METHOD 

Many techniques are related to basic Block Truncation 

Coding have been discussed in this section. They focus 

globally at a lower bit rate but other demerits of the method 

are also examined. The greatest deficiency of BTC is a 

relatively high bit rate as compared to other image 

compression methods, like DCT [9] [19], vector quantization 

[28] [31]. Other main demerits are ragged edges (staircase 

effect) regenerate in statue (image). 

Block Truncation Coding is divided into three separate 

steps, and each of these is analyzed separately. The overall 

structure of the algorithm is as follows: 

BTC algorithm for coding a single block 

1) Perform quantization 

- Select the threshold. 

- Select the quantization levels (a, b). 

2) Code the quantization data. 

3) Code the bit plane. 

In many variants, the choice of the threshold and the pair 

(a, b) are non dependable to each other, while some variants 

concern only one or the other. Most of the variants do not 

suppose a specific block size. Their instrumentations, 

however, are often planed for 4*4 blocks only. 

Original Bit Plane Reconstructed 

2 9 12 15 0 1 1 1 2 12 12 12 

2 11 11 9 0 1 1 1 2 12 12 12 

2 3 12 15 0 0 1 1 2 2 12 12 

3 3 4 14 0 0 0 1 2 2 2 12 

x=7.94 

σ=4.91 

q=9 a=2.3 

b=12.3 

Figure1. Block Truncation Coding by triplet (x̅, σ, B) [64] 

A. Performing the Quantization 

In commencement, choosing the threshold pixel value and 

choosing the quantization levels can be seen as two non 

corresponding stages. While most BTC techniques are 

encoded as safeguard certain sample moments, or to minimize 

some loyalty function. Therefore x th , a and b are in close 

documentation with each other [64]. 

Next part of this section will be included several variants, 

which can be characterized into three categories. The first 

category consists of the methods that will safeguard certain 

moments. The methods of the second category minimize the 

MSE-value, and the methods in the third one minimize the 

MAE-value. The remainders of the variants are intermediate 

between these three types. 

a) Moment Preserving Quantization 

A most number of the changes found in this portion are 

based on the original, two moments preserving quantization 

[20] [24] [25]. The following formulas must hold for this: 

mx̅ = (m − q). a + q. b (10) 



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mx = (m − q). a + q. b (11) 

This will be grasped by using x̅ as a threshold and 

choosing a and b according to equation 7. This option is not 

have optimal value according to MSE point of view. However, 

the base conception behind the technique has been a different 

loyalty measurement for example safeguarding the sample 

moments of the input [27]. A motivation for the method is that 

the human eye does not perceive small changes of intensity 

between individual pixels, but is sensitive to the average 

(mean) value and contrast in larger regions [27] [64]. 

b) Third Moment Preserving Quantization 

One can alter BTC so that it safe guard in addition to x 

and x the third moment x [20] [64], too. This can be gained 

by choosing x th, so that the parameter q attains the value 

where, 

q = . 1 + A 

 

A = 

(12) 

̅ ̅ 

(13) 

 

In distinction to the basic BTC the encoding phase is more 

necessitated. On the other hand, decoding is still fast. The 

point of the variant is that it upgraded some features (near 

edges) of the image. In fact, the third moment corresponds to 

the skewness of the distribution [23] [26]. Negative values 

indicate negative skewness and positive values positive 

skewness. Quantization levels (a,b) must be selected 

according to equation 7. 

c) Generalized Moment Preserving Quantization 

The BTC technique can be generalized to safe guard the r, 

2r and 3r th moments [15]. Here is the exact formulation of the 

method. Higher moments cause overflow problems and rarely 

good quality images. If one wants to preserve r and 2r th 

moments only, the threshold is 

x 

(14) 

 

Compared to the original first and second moments 

preserving quantization, the method imperceptibly upgrades 

the MSE-value [21]. 

d) Absolute Moment BTC 

Absolute moment block truncation coding (AMBTC) by 

Lema and Mitchell [23] [24] [25] preserves x̅ and the sample 

first absolute central moment 

α = ∑ 

|x 

− x̅| 

(15) 

Quantization levels are calculated from 

a = x̅ − 

. 

 

b = x̅ + 

. 

 

(16) 

(17) 

One can show that a=x (lower mean) and b=x (higher 

mean), where 

x = 

 

 

̅ (20) 

∗ ∑ |x | 

x 

= ∗ ∑ |x | 

 

̅ (19) 

After all, this selection decrease the MSE [22] value 

among the BTC-variants that use x as a quantization threshold 

[23]. It can, however, efficiently be shown in Table I and 

Table II that it is optimal for other selections of x too. The 

encoding and decoding tasks are very fast for AMBTC 

because square root and multiplication operations are omitted. 

e) MSE-Optimal Quantization 

The MSE-optimal choice for (a,b) is according to 

AMBTC, and it is non dependable of the quantization 

threshold. Therefore the MSE-optimal quantization can be 

obtained by choosing the quantization threshold so that it 

minimizes: 

 

MSE = ∑ x − a + ∑ 

x − b (20) 

The MSE-optimal quantization is also known as minimum 

MSE quantization (MMSE). 

f) MAE-Optimal Quantization 

The MAE loyality criterion (2) can be minimized by choosing 

a=median x 1 , x 2 ,…………………….,x m-q-1 (21) 

b=median x m-q , …………………….,x m (22) 

Now the optimal threshold is again found by an exhaustive 

search [20]. The MAE-optimal quantization is also known as 

minimum MAE quantization (MMAE). 

g) HEURISTIC CRITERION 

Goeddel and Bass [25] proposed a heuristic selection 

criterion for the threshold: 

x = 

 

(23) 

Where x min and x max stand for the minimal and maximal 

pixel values of a block. The criterion gives improved MSEvalues. 

The moments will not be safe guarded by the 

technique. However, if we use formulas (16-17) to select (a, b) 

instead of (7), this criterion can be considered as a practical 

estimation for the MSE-optimal quantization. 

Table I 

GB+mean Lyod MSE-opt. MAE-opt 

x th (x max+x min)/2 (a+b)/2 MSE-opt. MAE-opt 

(a,b) Mean values Mean values Mean values median 

MSE 37.05 36.83 35.54 40.21 

MAE 3.68 3.78 3.54 3.34 

SNR 32.44 32.47 32.62 32.09 

Table II 

GB+mean Lyod MSE-opt. MAE-opt 

x th (x max+x min)/2 (a+b)/2 MSE-opt. MAE-opt 

(a,b) Mean values Mean values Mean values median 

MSE 37.05 36.83 35.54 40.21 

MAE 3.68 3.78 3.54 3.34 

SNR 32.44 32.47 32.62 32.09 

h) Lloyd Quantization 

Another closely MSE-optimal quantization is obtained by 

an iterative algorithm proposed by Efrati and Lu [24]: 



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1. Let x th = x. 

2. Compute a and b according to (16) and (17). 

3. If x th = (a+b)/2 then exit. 

4. Let x th = (a+b)/2. Go to step 2. 

The algorithm produces the quantization levels and 

threshold of the Lloyd quantization [33]. 

i) Hopfield Neural Network 

A totally distinct approach to the quantization is proposed 

by Qiu. No direct quantization threshold is given, but instead a 

Hopfield neural network outputs for each input pixel, whether 

it should be quantized to a or b. This method gives near to 7 % 

better MSE-values compared to the method AMBTC. It has 

also been shown that the result is not optimal, but gives 

virtually similar outcome to the Lloyd quantization [34]. 

Simulation results and analysis [64] of different 

quantization methods are shown in Table I and Table II. 

Initially we encode the test images which mentioned in Table I 

and Table II by above discussed methods. Quantization levels 

(a,b) are encoded by 8+8 bits, and the bit plane is stored as 

such. The quality of the reconstructed images is shown in 

Table I and Table II. The results indicate that the difference 

between the original second moment preserving and the MSEoptimal 

quantization is remarkable. Magnifications of the 

reconstructed images are shown in Figure 2. The coding 

artifacts are clearly seen in the magnifications; however, it is 

almost impossible to observe any subjective quality 

differences between the quantization methods. 

The MSE-values are compared with the corresponding 

MSE-optimal quantization values in Figure 2. The methods 

that safeguard some set of moments are worst in the MSEsense. 

The best candidates aside MSE-optimal quantization are 

the Lloyd and the one which uses GB-heuristics as a threshold. 

The latter is also easy to calculate, and is thus a good 

alternative to the MSE-optimal quantization. In the following 

sections, the MSE-optimal quantization will be the point of 

comparisons, unless otherwise noted. 

The basic idea behind the original BTC was to preserve 

certain moments. Despite the fact that the moment preserving 

quantizers can be written in closed form, the resulting 

quantization levels are only integer approximations of the 

formulas, and thus distorted by rounding errors. Figure 4 and 5 

demonstrate how well the two first moments are actually 

preserved in different quantization systems (non black sections 

in the columns). 

The illustrations show that the moments are not preserved 

precisely in any method. In fact, the moment preserving 

quantization does not preserve the first moment (mean) any 

better than the other quantization methods (except the MAEoptimal 

quantization). It will, however, preserve the second 

moment somewhat better, but the difference is hardly 

significant. 

Moreover, if the quantization data and/or bit plane is 

further compressed, the moments are even less accurately 

preserved. In Figure 4 and 5, there are also errors originating 

from quantization of (a,b) to 6+6 bits (gray sections in the 

columns) and from 50 % interpolation of the bit plane (dark 

sections in the columns). Despite all of that, the greatest 

deficiency of the moment preserving quantization is that it 

does not even try to preserve the moments beyond the block 

boundaries. 

Figure 2(a).Original 

bpp=8.00 MSE=0 

Figure 2(c).3rd moment 

bpp=2.00 MSE=42.11 

Figure 2(e).GB+mean 

bpp=2.00 MSE=37.05 

Figure 2(g).MSE-optimal 

bpp=2.00 MSE=35.54 

Figure 2(b).2nd moment 

bpp=2.00 MSE=43.76 

Figure 2(d).Absolute moment 

bpp=2.00 MSE=40.51 

Figure 2(f).Lloyd 

bpp=2.00 MSE=36.83 

Figure 2(h).MAE-optimal 

bpp=2.00 MSE=40.21 

Figure2. MSE and bpp values for different moment preserving algorithms 



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compact representation for the block without any redundancy 

and cross correlations. 

In the original moment preserving BTC) the quantization 

data are represented by the pair (x̅, σ). This is not the case for 

the other quantization methods. For example AMBTC uses the 

mean and the absolute first central moment [30] [31]. If the 

heuristic threshold selection of [25] is applied, then one has to 

code the threshold and deviation corresponding to it:- 

σ = ∑ 

 

 

x − 

 

x 

(24) 

Figure3. MSE-deficiency compared to the MSE-optimal quantization [64]. 

Figure4. Error in the 1st moments of the reconstructed Lena [64] 

Figure5. Error in the 2nd moments of the reconstructed Lena [64] 

B. Coding the Quantization Data 

The second task in the structured BTC-algorithm is to 

encode the given quantization data of a block. Before this can 

be done, an important choice must be made, which data should 

be coded. There are two distinct approaches for sending the 

quantization data to the decoder. 

In the first approach the quantization data is expressed by 

two statistical values, representing the mid-value and variation 

quantity of a block (usually mean and standard deviation). It is 

known that the dispersion of the variation quantity is smaller 

than the dispersion of individual pixel intensities, and small 

values occur more frequently than large ones. This gives a 

A demerit to this approach is that the quantization levels 

are calculated at the decoding phase from the quantized values 

of (x̅, σ) containing rounding errors. Thus extra degradation is 

caused by the coding phase. 

The other approach is to calculate the quantization levels 

(a, b) already at the encoding phase and transmit them. In this 

way one can minimize both the quantization error and the 

computation needed at the decoding phase. They are also 

independent of the quantization method selected. The pair (a, 

b) contains redundancy, which can be easily removed by a 

suitable prediction and coding technique. 

Several methods for coding the quantization data will be 

presented next. 

a) Fixed Number of Bits 

The most straightforward approach is to code the 

quantization data by 8+8 bits as such. No extra computations 

are then needed and direct access to the coded file is retained. 

It has been observed [20], that the decrease in the quality of 

the image will be small if (x̅, σ) is quantized to 6+4 bits. Here 

one can simply allocate the values evenly within the ranges x̅∈ 

[0,255], and σ∈ [0,127] (or even truncate the standard 

deviation to the range σ∈ [0, 63]). In the same way, less than 

8+8 bits can be allocated for the pair (a, b). Our experiments 

indicate that the MSE-value of the test image Lena increases 

only circa 3 % when using 6+6 bits in the quantization. 

b) Joint Quantization 

Healy and Mitchell [32] [33] improved the 6+4 bits coding 

system by applying joint quantization to (x, σ) with 10 bits. 

Here the accuracy of x depends inversely on the value of σ. 

For example if σ=4 there are 10-3=7 bits left to code x. The 

technique still gives the same bit rate, but it has been argued 

that the quantization error is more visible to the human eye in 

the low variance regions, and a more accurate representation is 

needed in these. 

The concept joint quantization was originally introduced 

by Mitchell and Delp [35]. They used the method for 16- and 

32-level images by using 6 and 7 bits for the pair (x, σ), 

respectively. See Figure 6. 

c) Vector Quantization 

The use of vector quantization [28] [29] for coding the bit 

plane was first proposed by Udpikar and Raina [61]. They 

used a variant of AMBTC [32] that stores a compressed block 

in the form (x̅ , x , B). The decoder replaces each 0-bit of B by 

x and each 1-bit by x, 

 



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where 

x = x + . x̅ − x 

 

 

(25) 

By applying vector quantization (VQ) to the pair (x, x ), 

the bit rate can be reduces to 8 bits for (x, x) with the cost of 

increased MSE-value. The method, however, does not 

consider interblock correlations, i.e. the dependencies between 

neighboring blocks. 

Weitzman and H.B. Mitchell [46] apply predictive vector 

quantization for reducing the inter block redundancy. Instead 

of coding (a, b), they apply VQ to the prediction errors (ea i , 

eb i ):- 

ea = a − 2a + 2a + a /5 (26) 

eb = b − 2b + 2b + b /5 (27) 

Here a , a , and a refer to the a-values of 

the neighboring blocks that have already been coded. 

Figure6. Joint Quantization of x̅ and σ [64] 

Another approach was proposed by Alcaim and Oliveira 

[47]. They encode x and σ separately, making two subsample 

images, one from the x-values and another from the σ-values 

of the blocks. These subsample images are decomposed into 

2*2 blocks which are then coded by VQ. In this way one can 

reduce both the interblock and intrablock redundancy. 

d) DISCRETE COSINE TRANSFORM 

Wu and Coll [36] propose the compression of the pair (a, 

b) by the use of discrete cosine transform (DCT). Two 

subsample images are formed, one from the a-values and 

another from the b-values of the blocks. These subsample 

images contain one pixel per block of the original image. They 

are then coded by the adaptive DCT presented in [20] [31]. 

Details of the subsample images must be preserved as 

accurately as possible, since they have an influence on a large 

number of pixels in the reconstructed image. 

Here the second subsample image is not formed from the 

b-values, but from the (b-a)-differences instead. If one wants 

to retain the same MSE-level, the differences must be 

calculated at the coding phase by b-a', where a' is the 

reconstructed a-value after inverse DCT. 

The use of a computationally demanding algorithm like 

DCT is justified by the fact that the subsample images are only 

1/16 of size of the original image, for the block size 4*4. 

When the compression ratio of the DCT is predefined to 3:1, 

the total bit rate of a and b is 0.33 bpp at the cost of higher 

MSE. 

e) Lossless Coding 

The two subsample images can be compressed by several 

different image coding algorithms. As stated earlier, it is 

important that the information of the subsample images is 

preserved as far as possible. Therefore the use of a lossless 

image compression algorithm is apparently a good choice. 

Two variants of this type, and another related method. 

We consider next a new approach for coding the two 

subsample images. We apply FELICS coding (Fast and 

Efficient Lossless Image Compression System) by Howard 

and Vitter [25]. The method is highly applicable to BTC 

because of its practical usefulness, and it is also one of the 

most efficient lossless methods known. 

FELICS coding uses the information of two adjacent pixels 

when coding the current one. These are the one to the left of 

the current pixel, and the one above it. Denote the values of 

the neighboring pixels by L and H so that L is the one which is 

smaller. Howard and Vitter [25] have found that the 

probability of individual pixels obeys the distribution given in 

Figure 7. Our experiments show that the same distribution 

holds very well for the pixels of the subsample images, too. 

The coding scheme is as follows: A code bit indicates 

whether the actual value falls into the in-range. If so, an 

adjusted binary coding is applied. Here the hypothesis is that 

the in-range values are uniformly distributed. Otherwise the 

above/below-range decision requires another code bit, and the 

value is then coded by Rice coding [64] with adaptive k- 

parameter selection. For details of FELICS coding, see [64]. 

We can improve the coding of b if we remember that a is 

already known at the moment of coding b, and that b≥a. Thus, 

if a falls into the same interval as b, the actual range of b can 

be reduced so that only the potential values are considered. 

For example if a belongs to the in-range of b, the interval is 

reduced by changing the lower bound L to a. The 

improvement, however, remains marginal. 

The results of FELICS are quite similar compared to the 

results of the predictive entropy coding scheme, but it is fast 

and much less involved. 

Figure7. Probability distribution of intensity values 

C. Bit Plane Reduction 

In the basic BTC method, both quantization data and the 

bit plane of a block require 16 bits each. Several methods for 



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reducing the bits needed for the quantization data was 

presented in vector quantization. A larger reduction is still 

possible at the cost of decreased image quality. In this section, 

we will consider several attempts to reduce the size of the bit 

plane. 

a) Skipping the Bit Plane 

If the contrast of x i -values is very small one can except the 

storing of B and thus implicitly code all pixels by x̅ . The 

criterion for using this one-level quantization varies. Mitchell 

and Delp [35] omit the bit plane if σ

ISSN:2229-6093 


opening and roots of closing are adaptively used in the 

method. See Figure 10. 

Figure10. Roots of the Filtering [64] 

d) Vector Quantization 

Several approaches have been proposed for reducing the 

volume of the bit plane by the use of vector quantization or a 

similar ad hoc technique [48]. The basic idea of VQ is to 

select a small set of representative vectors (binary blocks) and 

to code all possible vectors by an index. The codebook is 

generated off-line on the basis of training vectors by using a 

suitable algorithm, like the generalized Lloyd algorithm [28]. 

Then the same codebook is used for whatever images are to be 

coded. Adaptive vector quantization [42] [43] was considered 

by Wu and Coll [34], but they prefer the non-adaptive, 

universal codebook VQ, because of the speed. 

The representative for a bit plane can be chosen by a total 

search, i.e. by testing each candidate code vector and selecting 

the one which minimizes the given distortion function. In this 

way, the result of the search is always optimal (corresponding 

to the distortion function) but it is impractical for large 

codebooks. The decoding, however, is always quick. 

A localized search was proposed by Weitzman and H.B. 

Mitchell [40]. They divide the codebook into several 

overlapping sub-codebooks. For each bit plane, its 

combination index is calculated. It determines the subcodebook 

in which the search is performed. Even if the search 

method is not extensive anymore, the correct code vector 

(corresponding to the extensive search) will still be found with 

a very high probability (> 99%) according to Michell [20]. 

The performance of a search method depends not only on 

the organization of the codebook, but also on the selected 

distortion function. MSE is the most obvious measure, 

however, it cannot be calculated independently from the 

quantization data (a, b) [17]. Most of the existing methods 

thus use Hamming distance, i.e. the number of positions in 

which the elements of the two binary vectors differ, as a 

distortion measure [48]. If there are two or more code vectors 

with the same Hamming distance from the original bit vector, 

the one with the same number of 1-bits is chosen. The 

advantage of Hamming distance is that it can be implemented 

by look-up table (LUT). 

Let’s suppose the size of the codebook was 256 and 128, 

so the bit rate of the bit plane was respectively 0.5 and 0.44. 

Weitzman and H.B. Mitchell [42] [43] proposed the use of 

several codebooks of different sizes. The size of a codebook 

depends on the contrast of a block (measured by b-a): the 

greater the contrast the larger the codebook. Nasiopoulos [48] 

coded only blocks whose contrast is between a given range 

(not too large but not too low either) by VQ. The codebook 

was formed so that edge blocks are well represented. This also 

reduces the so-called staircase effect, which is otherwise 

impaired by VQ. 

A classified VQ algorithm is proposed by Efrati et al. [52] 

for avoiding the staircase effect. BTC algorithm with VQ is 

used for the low contrast blocks, and a three-level quantizer is 

applied for the high contrast blocks. Thus, the algorithm uses 

two different codebooks, one for the low contrast and another 

for the high contrast blocks. 

e) Interpolation 

All the methods discussed above were based on the idea 

that the bit plane is only partially coded, thus omitting a part 

of it, or by selecting a representative for the bit plane (or for its 

rows) from a smaller subset, which can either be called a root 

signal set or a codebook. Therefore the reconstructed image 

contains pixels where an a-value has been changed to a b- 

value or vice versa. The cost of these errors may be high in the 

MSE-sense, if the contrast in the block is large. To avoid this 

problem, a totally different approach is taken in the following 

method. 

Zeng's interpolative BTC [41] [42] is similar to the 

prediction technique (method B) in the sense that half of the 

bit plane is omitted. At the decoding phase the partial image is 

first reconstructed and then the missing pixel values are 

interpolated on the basis of the existing ones. Zeng has 

proposed two variants of the method: one which codes 50 % 

(IBTC-1) and another which codes 25 % of the bits (IBTC-2). 

Figure11. Interpolation patterns of IBTC-1 and IBTC-2 [64] 

The interpolation is done by stack filters designed to be 

optimal in the MAE-sense [38] [41] or by using median filters 

[42]. The latter is recommended because of the ease of 

implementation. In the IBTC-1 four adjacent coded pixels are 

used to calculate the intensity of the current one. 

y , = median y , , y , , y , , y , , . y , + y , + 

y , + y , (29) 



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In the IBTC-2 a two-phase interpolation is used. At the 

first phase the following median filter is used, where each 

pixel is interpolated on the basis of the coded pixels. 

y , = median y , , y , , y , , y , , 1 4 . y , 

+ y , + y , + y , (30) 

Although the hierarchical decomposition seems to be an 

excellent idea, it has some drawbacks also. Several nonhierarchical 

methods are preserved direct access to the 

compressed file, but a straightforward implementation of 

HBTC does not. This also means that the fault tolerance has 

decreased. Moreover, large uniform areas may cause blocky 

appearance in the reconstructed image. 

At the second phase, the median filter of (2.30) is used. 

Note that the interpolation is a separate phase of the decoding 

process and therefore the block boundaries do not disturb the 

reconstruction of the missing pixels. 

f) Entropy Coding 

Since the bit plane can be considered as a binary image, 

one might expect that a binary image coding method could be 

used. On the other hand, the BTC-process ensures that the 

numbers of 0 and 1 bits are almost equal and the bits are 

relatively evenly distributed all over the bit plane. Therefore 

simple coding methods, like run length coding [44], are unlike 

to give any compression. 

In the entropy based bit plane compression, the image (the 

bit plane) is preceded in row major order from left to right. A 

high degree Markov model is applied for each pixel. The value 

of a pixel is predicted by the 7-bit context template and then 

coded by arithmetic coding according to its probability. QMcoder 

[45, 46] was used as the arithmetic coding component. 

The size and shape of the template have major effect on the 

coding efficiency when compressing binary images and better 

results can be achieved with larger templates. However, this 

does not necessarily apply to the block truncation coding. The 

problem here is the block wise quantization according to the 

mean x of each individual block. This destroys the correlation 

of neighboring bits belonging to two different blocks. 

D. Hierarchical Decomposition of the Image 

A natural extension of the single-level BTC is to use a 

hierarchy of blocks [44] [53]. In hierarchical block truncation 

coding (HBTC) the processing begins with a large block size 

(m 1 *m 1 ). If variance σ2 of a block is less than a predefined 

threshold vth the block is coded by a BTC-variant. Otherwise 

it is divided into four subblocks and the same process is 

repeated until the variance threshold criterion is met, or the 

minimal block size (m 2 *m 2 ) is reached. 

By adjusting the variance threshold v th , and the block sizes 

m 1 , m 2 , one can direct the benefit of the hierarchical 

decomposition to achieve a low bit rate or high image quality. 

The high MSE-values rarely originate from the largest 

blocks unless the variance threshold is too high. Therefore, if a 

low MSE-value is the primary criterion of the image quality, 

the maximal block size of 32*32 is recommended. The 

selection for the smallest block size m 2 causes a more dramatic 

change in MSE. If one wants to achieve very high quality 

images the smallest block size must be set to m 2 =2. The 

variance threshold v th can be considered as a fine tuning 

parameter. 

Figure12. Bit plane of Lena by BTC [64] 

Figure13. Bit plane of Lena by HBTC [64] 

Figure14. Bit plane of Lena by HBTC 



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E. Extensions of BTC 

This section are included, several external pre- and postprocessing 

techniques will be discussed. Some of them aim at 

an improved visual quality of the reconstructed image, while 

others simply strive for lower bit rates. BTC application to 

color images and video compression will be shortly discussed. 

a) Smoothing Filter 

A simple smoothing operation of the original image is 

proposed by Mitchell and Delp [35]. The purpose of the 

smoothing is to reduce noise in the original image which 

causes pixel values near the threshold to be quantized to the 

wrong value. Each pixel x i,j of a block is replaced by a 

weighted sum of itself and the four adjacent pixels. 

 

x , = 0.6 . x , + 0.1. x , + x , + x , + x , (31) 

b) Blocky Appearance 

Blocky appearance is a common feature of block coding 

techniques like BTC. The relatively small size of blocks (4*4) 

keeps the effect almost unnoticeable for human eyes. 

However, when large block sizes are applied in the 

hierarchical variant, the effect becomes more visible. 

this difference image. Both BTC and transform codes are sent 

to the decoder with bit rate 1.63 + 0.25 = 1.88 bpp. 

The hybrid method was argued for using the different 

properties of the methods. While BTC preserves edges, they 

tend to be ragged. On the other hand, transform coding usually 

produces smooth edges. In the hybrid formulation, the aim is 

to improve visual quality of the image. At the same time, 

MSE-value is reported to decrease [20]. 

Figure16. Image quality versus block size [64] 

d) Differential Pulse Code Modulation 

Differential pulse code modulation (DPCM) is a wellknown 

signal coding technique and it has been widely used in 

image compression [54] [55]. In DPCM, each pixel value is 

first predicted on the basis of previously coded pixels. The 

result of the prediction is then subtracted from the actual pixel 

values and the difference e ij =x ij -y ij is coded. 

Figure15. Bit Compression efficiency versus block size [64] 

For reducing the blocky appearance Nasiopoulos [48] 

proposed the use of smoothing filter as a post processing 

technique. The reconstructed image is scanned using an 8*8- 

window. If the contrast in the window is smaller than a 

predefined smoothness criterion, the area is smoothed by a 3*3 

averaging filter. Here each pixel y i,j of the window is replaced 

by the value y' i,j . 

 

= ∑ ∗ ∑ y , 

y , 

 

 

(32) 

The method takes care of the blocky appearance of the 

reconstructed image, but the smoothed regions now look flat 

and artificial. In order to give back to the image the lost 

texture, Gaussian random noise is added to the averaged areas. 

c) Discrete Cosine Transform 

A hybrid of BTC and DCT is proposed by Delp and 

Mitchell [20]. First a highly compressed image is obtained by 

taking the two-dimensional discrete cosine transform over 

16*16 pixel blocks. Only the eight non-dc coefficients in the 

low frequency section of each block are retained. A difference 

image is constructed by subtracting the transform coded image 

from the original. The basic BTC algorithm is then applied to 

Figure17. Differential Pulse Code Modulation 

Delp and Mitchell [56] propose a composite method of 

DPCM and BTC. First an open-loop prediction is performed to 

construct the mean value and standard deviation of the 

differences (e, σ e ). In this stage, quantization levels a and b are 

also calculated, because they are needed for the predictor. 

Then the quantization procedure is performed by applying 

DPCM with a closed-loop prediction. Prediction function is as 

follows. 

x̅ = 0.8. y , − 0.6. y , + 0.8. y , (33) 

Because the ranges of e and σ e are smaller than those of x 

and σ, they can be coded with fewer bits. With the block size 

8*8, Delp and Mitchell have found that 4+3 bits suffice; 

however, the detailed bit allocation table is not given. 



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e) N-Level Quantization 

The basic idea of block truncation coding, two-level 

quantization can be derived to a general n-level quantizer. 

Delp and Mitchell have proposed a moment preserving 

quantizer, which is shown to be related to the Gauss-Jacobi 

mechanical quadrature problem [33] [43]. MSE-optimal 

quantizer has been given by Max [35]. These quantizer, 

however, presuppose that the probability distribution of the 

signal is either uniform, Gaussian, or Laplacian. In Lloyd's 

quantizer [33] all quantization levels are given by an iterative 

algorithm. 

Monet and Dubois [58] have proposed a uniform 

quantization method in which the overhead information of a 

block is first coded, consisting of the pair (x min , x max ). The 

pixel values of a block are then scaled and normalized within 

this interval. They are finally quantized so that the number of 

quantization levels in a block is fixed regardless of the 

variance of the block. 

Quantizer 

TABLE III Properties of Different Quantizers [64] 

Quantization 

parameters: 

Quant. 

levels: 

Overhead 

Quant. Quant. 

param.: matrices 

BTC (a,b) 2 2 1 

3-level (a,b) 3 2 log 3 

BTC 

4-level (a,b) 4 2 2 

BTC 

n-level One value N N log N 

BTC 

Block AQ (x max, x min) N 2 log N 

Lyod Quan. level N N log N 

More specific approaches have been taken by several 

authors concentrating on the 3-level quantization [25] [52]. 

Goeddel and Bass [19] proposed a 3-level quantizer to be used 

along with the original BTC. For each block, both 

quantizations are determined, but only the one with the smaller 

MSE-value is sent to decoder. Ronsin and DeWitte [22] [28] 

use both 3- and 4-level quantization. They later developed 

another algorithm, in which the edge blocks are coded by a 3- 

level and the non-edge blocks by a 2-level quantizer [59]. 

Vector quantization of the quantization matrix is 

performed in all of these approaches. The codebook is 

designed to contain edge blocks [24]; or the end points of the 

edges are coded by an edge following algorithm [59]. Wang 

and Mitra proposed a more sophisticated algorithm by using 

block pattern models [60]. 

Ceng and Tsai [61] proposed the use of a 4-level quantizer 

without increasing the number of parameters. All four 

quantization levels can still be derived from the pair (a,b). Wu 

and Coll [62] have given a non-uniform n-level quantizer, 

where each of the quantization levels are iteratively 

determined aiming at minimal MAE. They also introduced a 

predictive entropy coding scheme for coding the overhead in 

the special case of a 4-level quantizer. Uhl [62] has extended 

the idea of multilevel quantization and proposed a hybrid 

algorithm. The blocks are classified and for each class, a 

different quantization is applied. They use 1, 2, 4, and 8-level 

quantizers, and a copy operation depending on the type of 

block. 

f) Color Images 

The most common representation of color images, RGB, 

divides the image into three separate color planes, namely red, 

green, and blue. This color system is based on the trichromatic 

nature of the human vision [6]. There exists a high degree of 

correlation between the planes R, G and B, and therefore a 

color space conversion from RGB to YUV (or YIQ) is usually 

performed [21]. Y represents the luminance of the image, 

while U, V (I,Q) consists of the color information, i.e. 

chrominance. 

Color images are considered as a three-component 

generalization of gray scale images, and thus they can be 

compressed by extending the existing algorithms. Lema and 

Mitchell [31] propose an algorithm in which the three 

components of the YIQ-space are separately coded by the 

absolute moment BTC. As the human visual system is most 

sensitive to the variations of Y, and less to I and least to Q, the 

chrominance planes are sub sampled. It means, that only the 

average value of each 2*2-block in the I-plane and the average 

value of each 4*4-block in the Q-plane are retained. In the 

decompression phase, the sizes of the planes are recovered by 

using bilinear interpolations. The method yields a bit rate of 

2.13 (1.62+0.41+0.10) bpp. 

Wu and Coll [67] proposed the use of a single bit map for 

all three components, given by the quantization of the Y- 

component. The quantization levels of each component are 

further compressed by DCT. High-frequency components of 

the DCT domain are discarded in the chrominance 

components so, that it correspond to a 3*3 averaging filter for 

the I-signal and a 5*5 averaging filtering for the Q-signal. 

Several variations of the basic idea are considered in [68], 

including both RGB and YIQ color space images. A bit rate of 

1.71 bpp has been reported for the latter. 

g) Video Images 

A straightforward application of BTC to video images 

proposed by Healy and Mitchell [69]. They extended the block 

to consist of pixels from consecutive frames by using block 

size of 4*4*3. A registration algorithm is used for detecting 

global translations, like camera movements. 2D-BTC is 

performed on movement blocks and edge regions. Bit rate can 

be reduced by coding only one 2D bit plane for the 3D-blocks. 

Further reduction is possible by skipping the coding of one or 

two frames, and coding only the blocks consisting of some 

activities. All of these ideas are applied adaptively so that 

more accurate representation is used whenever necessary for 

preserving the image quality. 

h) Block To Block Adaptive BTC 

In an adaptive compression scheme one can change the 

compression method from block to block. The adaptation may 

concern the quantization method, bit plane coding method, or 

both of them. In principle, one could even change the whole 

compression system, for example use BTC for one block and 

another coding system for the next block. Several attempts of 



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this kind apply multilevel quantizers along with the original 

BTC. 

Table IV 

Standard deviation Bit plane coding: Bit rate: 

High Full resolution 16 bits 

Medium Prediction technique 8 bits 

Low Uniform block 0 bits 

Griswold [70] vary the quantization system so that a 

different set of moments (r'th and 2r'th moments) is preserved. 

For each block, the BTC is tentatively applied with all values 

of r=1, 2, 3, 4, and the one with minimum MSE-value is 

selected. Quantization levels (a,b) are calculated already in the 

encoding phase, and therefore decoder does not need to know 

the choice of r. 

Adaptive compression coding (ACC) is proposed by 

Nasiopoulos [41]. If the range of a 4*4 block is smaller than a 

given smoothness threshold (2.18, 2.30, or2.42) it is 

represented by its average. Blocks that are above the threshold 

but below 120 are coded by absolute moment BTC. If the 

difference of quantization levels (b-a) is less than or equal to 

20, the bit plane is coded by vector quantization including 

only edge blocks. Hierarchical decomposition is applied to the 

remaining high activity blocks. Small blocks are either copied, 

or compressed by the one-level quantization. Overhead 

information is needed to inform the decoder of the coding 

system used. 

Figure17. Distribution of 4*4 blocks [64]. 

Figure18. Average MSE of different blocks 

Figure19. Additional MSE contributed by bit plane coding according to the 

block types 

IV. 

COMPARATIVR ANALYSIS ON RECENT BTC ALGORITHM 

In this section we discuss recently introduced algorithms 

which based on moment preserving criteria and uses in LCD 

overdrive like applications. 

A. FBTC ALGORITHM 

In this section, FBTC (Fast Pixel Grouping Technique) 

above mentioned current scheme is discussed. To clearly 

explain the FBTC technique, AMBTC is used here instead of 

MPBTC [49] because AMBTC provides better image quality 

and consumes less computational cost. Therefore, pixel 

grouping technique [48] can also be employed to improve the 

performance of AMBTC. 

In this scheme (FBTC), each grayscale image to be 

compressed is first partitioned into a set of non-overlapping 

image blocks of nxn pixels. Each image block x= 

{p 1 ,p 2 ,…..p nxn } is sequentially processed. Initially, the mean 

value x of is calculated and stored in x .All pixels with values 

smaller than x are classified into the first group G 0 . Otherwise, 

they are classified into the second group G 1 . Then, the mean 

value of pixels in each group is computed and taken as the 

quantization level. The quantization levels ql 0 and ql 1 in G 0 

and G 1 are calculated according to the following equations, 

respectively 

ql = 

ql = ∑ 

∑ x 

 

(34) 

x 

(35) 

In the traditional AMBTC scheme ql 0 and ql 1 are used to 

represent pixels in G 0 and G 1 , respectively. Theoretically, 

pixels in each group should be quite close to the corresponding 

quantization level. However, two confusing conditions may be 

happened. First, some pixels belonging to G 0 may have their 

pixel values closer to ql 1 than ql 0 . Second, some pixels in G 1 

may have their pixel values closer to ql 0 .than ql 1 . When either 

one of the two conditions is found, the following processing 

steps are iteratively executed in the proposed scheme. 

Step 1: Classify all the pixels in x into two groups 

according to their distances to ql 0 and ql 1 

Step 2: Calculate the mean values of pixels in each group 

to generate these two quantization levels ql 0 and ql 1 . 



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Figure 20(a).bridge512 

Figure 20(c).f16-512 

Figure 20(e).Pepper512 

Figure 20(g).Lena512 

Figure 20(i).Baboon512 

Figure 20(b).boat512 

Figure 20(d).elaine512 

Figure 20(f).zelda512 

Figure 20(h).goldhill512 

Figure 20(j).Barbarra512 

Step 3: If either one of the two conditions is held, go to 

Step 1. 

After the above steps are performed, all pixels in each 

block x are classified into G 0 and G 1 and the quantization 

levels are stored in ql 0 and ql 1 . The following rule is used to 

generate the 1-bit value b i in bit map BM for each pixel p i . 

b = 0, p ∈ G 

1, p ∈ G 

Now, the pixels in each block are portioned into two 

groups and the quantization levels are calculated. The 

compressed codes of one image block x comes out of a triplet 

(ql 0 , ql 1 , BM). 

a) Experimental Results 

Some experimental results are presented in this section to 

verify the performance of the FBTC algorithm. 

Results in Tables V-VII present the comparative 

performance of the traditional AMBTC [71] scheme, the 

optimal grouping AMBTC scheme (OBTC) [49], the 

economical AMBTC scheme (EBTC) [64], and the FBTC 

scheme when the block sizes are 4×4, 8×8, and 16×16, 

respectively. 

According to the experimental results in Table V, our 

FBTC has considerably reduced the execution time. An 

average execution time of 0.033 seconds is consumed in 

FBTC scheme [15] when the block size equal to 4×4. It is 

about 41.25% of the Performance of proposed scheme is 

further improved when the block size is 8×8. The consumed 

execution time of the FBTC [49] scheme is 38.7% and 5.4% 

of the execution times in Economical BTC and OBTC, 

respectively. 

Table V. Comparison of FBTC with others techniques when block size is 

4×4 

Images\Schemes AMBTC OBTC EBTC FBTC 

Airplane PSNR 33.253 34.044 33.981 33.838 

Time 0.017 0.233 0.067 0.033 

Baboon PSNR 27.754 28.199 28.137 28.056 

Time 0.017 0.233 0.117 0.033 

Barbara PSNR 29.105 29.445 29.384 29.321 

Time 0.017 0.250 0.083 0.033 

Boat PSNR 31.958 32.540 32.467 32.384 

Time 0.017 0.233 0.067 0.033 

Lena PSNR 33.643 34.200 34.147 34.020 

Time 0.017 0.233 0.067 0.033 

Average PSNR 31.143 31.686 31.623 31.524 

Time 0.017 0.236 0.080 0.033 

Meanwhile, the image quality of the proposed scheme is 

slightly worse than that of EBTC [12] and OBTC [12] [48]. 

An average image quality gain of 0.537 dB is obtained by 

using the proposed scheme compared to the conventional 

AMBTC scheme. 

According to the results in table 3.2, the image quality of 

the FBTC scheme is better than that of Economical BTC. In 

addition, the proposed scheme requires 35% and 1.8% of the 

execution times of EBTC [66] and OBTC [49], respectively. 

An average image quality gain of 0.655 dB is obtained by 

using the proposed scheme compared to the conventional 



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AMBTC scheme. Based on the results in Tables 3.1 to 3.3, the 

improvement of image quality increases as the block sizes 

increases in the proposed scheme. 

Table VI. Comparison of FBTC with others techniques when block size is 

8×8 

images\schemes AMBTC OBTC EBTC FBTC 

Airplane PSNR 30.153 31.036 30.998 30.978 

Time 0.017 0.650 0.083 0.033 

Baboon PSNR 25.841 26.156 26.127 26.114 

Time 0.017 0.683 0.117 0.050 

Barbara PSNR 26.653 27.067 27.032 27.025 

Time 0.017 0.667 0.100 0.033 

Boat PSNR 28.995 29.656 29.609 29.610 

Time 0.017 0.633 0.083 0.033 

Lena PSNR 30.216 30.883 30.847 30.816 

Time 0.017 0.650 0.083 0.033 

Average PSNR 28.372 28.960 28.922 28.909 

Time 0.017 0.657 0.093 0.036 

Table VII. Comparison of FBTC with others techniques when block size 

is 16×16 

images\schemes AMBTC OBTC EBTC FBTC 

Airplane PSNR 27.989 29.025 28.986 28.993 

Time 0.017 2.217 0.117 0.030 

Baboon PSNR 24.789 25.071 25.057 25.052 

Time 0.017 2.383 0.150 0.050 

Barbara PSNR 24.837 25.317 25.279 25.291 

Time 0.017 2.300 0.150 0.030 

Boat PSNR 26.802 27.547 27.508 27.519 

Time 0.017 2.233 0.083 0.050 

Lena PSNR 27.404 28.279 28.234 28.238 

Time 0.017 2.267 0.100 0.050 

Average PSNR 26.364 27.048 27.013 27.019 

Time 0.017 2.280 0.120 0.042 

PSNR than that of YCH can be achieved. Our three stage 

compressor gives a bit rate of 0.33 bpp at a PSNR value of 

33.21 for photos used for ID cards. This compression scheme 

may be useful for low cost handheld devices with low 

computational power which handles images. 

C. Parallel and Element-Reduced Error-Diffused BTC 

Block Truncation Coding (BTC) [1] [2] is an efficient 

compression technique for its inherent simple coding strategy. 

However, the annoying blocking effect and false contour 

accompanied in high coding gain configurations make the 

applications relatively limited compares to some up-to-date 

compression schemes. For this, in 2010, Jing-Ming Guo is 

provided Error-Diffused Block Truncation Coding (EDBTC) 

to solve these problems. Whole scenario of this scheme is 

shown in Figure 22 and Figure 23. 

D. Single Bit Plane based BTC for Color Image Compression 

In 2011, Jun Wang [1] introduced Single bit plane based 

BTC for color image compression in LCD overdrive. Single 

bit plane is used to represent the R, G and B bit planes and 

correct the two representative levels in this scheme. Outcome 

of this algorithm can improved the compression ratio of BTC 

form 4:1 to 6:1 with the limiting performance losing about 

0.297db. This algorithm is provided improved BTC such as 

VQ-BTC [1]. Figure 21 is used here for comparative analysis 

of different images with different methods. PSNR value of 

each image for different methods is shown in Figure 21. 

B. Low Computational Scheme based on AMBTC 

This scheme is introduced by K.Somasundaram and 

I.Kaspar Rajin in 2006 [74] which based on four techniques 

which combine used as compilation of current mentioned 

algorithm. The four techniques are listed below. 

‣ Quad Tree Segmentation 

‣ Bit plane Omission 

‣ Bit plane coding using 32 visual patterns 

‣ Interpolative bit plane coding 

The experimental results of this scheme is shown [72] that 

this scheme achieve an average bit rate of 0.46 bits per pixel 

(bpp) for standard gray scale images with an average PSNR 

value of 30.25, which is better than the results from the exiting 

similar methods based on BTC. 

Low computational complexity is two stage and three stage 

gray scale image compression scheme using quad tree 

segmentation. The three stage compressor starts with 16x16 

pixel block and the two stage compressor starts with 8x8 pixel 

blocks. Experimental results [74], by applying our schemes on 

standard images, show that an average bit rate of 0.46 bpp 

with an average PSNR value of 30.25 is for the three stage 

compressor and 0.4923 bpp with an average PSNR value of 

30.37 for two stage compressor which are better in bpp and 

Figure 21.PSNR results for different methods 

E. An Improved Algorithm using BSPS and GW 

This scheme is introduced by Garima Chopra and A. K. 

Pal in 2011 [4].Geometric wavelet is a recent development in 

This algorithm outperformed the EZW, the Bandelets and the 

GW algorithm. Current discussing algorithm reported a gain 

of 0.22 dB over the GW method at the compression ratio [4] 

of 64 for the Cameraman test image. Performance analysis of 

this scheme with traditional BTC is tabularized is Table VIII. 

Basically this table is provided the complexity comparison of 

traditional BTC and ODBTC. 

Table VIII. Complexity Comparisons between Traditional BTC and ODBTC 

(Total Operations in a Block of Size MXN) 

Operations Addition/ Multiplication/division Square root 

Subtraction 

BTC 2x(mxn)+3 Mxn+9 2 

Odbtc Mxn 0 0 



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Figure 22(a). 

Figure 22(c). Distribution of the two best diffused directions. 

Figure 22(b). 

Figure 22(d). Checkerboard pattern and serpentine scan. 

Figure 22. Optimization procedure and its final two diffused elements: (a) optimization procedure (b) element-reduced kernel. 

Figure23. 

F. VQ based BTC for Color Image Compression in LCD 

Overdrive 

This scheme is introduced in 2008 by Jong-Woo Han [3]. 

This scheme is described a novel block truncation coding 

based on the vector quantizer for the color image compression 

in LCD overdrive. Due to the constant output bit-rate and the 

low computational complexity, this method is suitable for the 

hardware implementation in LCD overdrive. Experimental 

results [3] are shown that current method achieves higher 

compression ratio as well as better visual quality as compared 

with the conventional methods. 

G. AM- BTC for Frame Memory Reduction in LCD Overdrive 

This scheme is introduced by Jun Wang in 2010 [2]. The 

AM-BTC firstly overcomes the limitation by adaptively 

selecting 2-level or 4-level BTC according to the edge 

property of the coding block. Then, to reduce the bit rate of 

AM-BTC he improves the 2-level and 4- level BTCs by using 

only luminance bit-map to represent three color bit-maps. As 

shown in simulation results [2], the AM-BTC successfully 

reduces the frame memory usage to 1/6 and significantly 

improved coding performance (up to 3.779 dB) as compared 

with other algorithms. When the AM-BTC is applied to LCD 

overdrive, it also improves overdrive performance up to 3.390 

dB as compared with other competitive method [2]. 

The whole scenario of this scheme is shown is Figure 24- 

26. Figure 24 is shown as the basic idea of algorithm and 

figure 24 represents the Block diagram of AM-BTC algorithm. 



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Figure24.Block diagram of overdrive in LCD[2] 

Figure25. Block diagram of AM-BTC algorithm [2]. 

Figure26. Gfig architecture of the AM-BTC encoder 

V. COMPARISON TO JPEG 

Next we will link together the best ideas of the BTC 

algorithm. Since the three phases of the BTC were studied 

separately, there is no guarantee that the combined algorithm 

is optimal in any sense, nor the best that could be constructed 

from these elements. In spite of that, we will compare it 

against JPEG. This is done by first fixing a certain bit rate and 

then comparing the MSE-values of these two methods. 

The combined BTC algorithm consists of the components 

given in Table IX. Hierarchical decomposition is fully 

utilized: The corresponding minimum and maximum block 

sizes are 2*2 and 32*32. Standard deviation (σ) is used as a 

threshold criterion and is set to 6 for other level transitions 

than 4*4->2*2, for which the threshold is left as an adjusting 

parameter. 

The bit plane is either stored as such, or its size is reduced 

by the interpolation technique. The level of interpolation is 

chosen according to the desired bit rate level. It will be 

referred by the proportion of coded bits which is 50, 75, or 100 

%. Bit planes of uniform blocks are skipped and the 1-bit 

quantization is applied to these blocks. The uniform block 

skipping threshold is used as a fine-tuning parameter. 

Figure 26 illustrates the performance of the combined BTC 

algorithm for Lena. The tests were performed by varying the 

threshold of the hierarchical decomposition from σ=0 to 50. 

Each curve represents one of the selected interpolation levels. 

In this way we are able to cover reasonably well the bit rates 

from 1.0 to 2.0 bits per pixel. Better image qualities are still 

possible at the cost of decreasing compression efficiency, but 

the increase of the bit rate serves the purpose only up to a 

limit. By the use of lossless image compression methods, such 

as lossless JPEG [46, 57] or FELICS [25], one can achieve bit 

rates of about 4.5 bpp (for Lena). At the other end, the image 

quality will decrease rapidly if very low bit rates are desired. 

A comparison of JPEG and the combined BTC is 

summarized in Figure 26-29. Here we use the same parameters 

that were used for the test results in Figure 26 with one 

exception: we performed two different tests. In the first one, 

we used the skipping threshold σ=0, and in the second σ=5. 

The final curves of Figure 26-29 are assembled from the 

results of these two so that they correspond to the best MSEvalues 

for each bits per pixel selection. The non-continuation 

of the curve in Figure 29 originates from the nature of the 

image Galaxy. It consists entirely of low contrast regions, and 

therefore the hierarchical decomposition cannot be used for 

adjusting its performance as much as is desirable. 

In our tests, JPEG clearly outperforms BTC (see Fig. 30). 

At the bit rate of 2.0, the MSE of JPEG is 65 % from the MSE 

of BTC (for Lena), and at the bit rate of 1.0 bpp, it is only 53 

%. The difference in the visual quality is yet unclear. Small 

differences in the MSE-value are not necessarily reflected in 

the visual quality and one must keep in mind, that the 

distortions caused by these two methods are not alike. 

Moreover, distortion is almost unnoticeable if one looks at the 

images in their natural sizes. Magnifications of Lena are 

shown in Fig. 31. We want to emphasize that there is a definite 

need for a better objective quality measure than MSE. 

Table IX 

PHASE 

METHOD 

BLOCK SIZE hierarchical (32→2) 

QUANTIZATION SYSTEM gb + means 

QUANTIZATION DATA (a,b) 

NUBER OF BITS 6+6 

coding the quant. data felics 

coding the bit plane 1 bpp 

interpolation 

skipping the bit plane 



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Figure26. Performance of the combined BTC algorithm for Lena 

Figure26. Comparison of JPEG versus BTC with test image Lena 

Figure28. Comparison of JPEG versus BTC with test image Lena 

VI. 

CONCLUSION 

Finally survey literature is concludes as background 

information of the variants of the block truncation coding. 

Motto of whole literature was that one can remarkably 

improve the overall performance of BTC by the use of 

hierarchical decomposition and interpolation coding. The most 

important change for improving the image quality was the use 

of 2*2-blocks in the high contrast regions. When compared to 

the performance of JPEG, the new combined block truncation 

coding is still weak if the image quality is measured by the 

mean square error. 

There are still other aspects which make BTC a useful 

alternative for JPEG in some practical applications. All the 

selected algorithms are quite simple and easy to implement. 

The integration makes the implementation somewhat more 

complicated, but it is nevertheless probably much simpler than 

the JPEG implementation. Since we did not perform any 

throughput analysis, we can only estimate the running times. 

The encoding phase of BTC is very fast, and the decoding 

phase is even faster. One can maximize the throughput at the 

decoding phase by the use of (a,b) as the quantization data. It 

could be further improved by the use of vector quantization 

instead of interpolation. This would load the encoding more, 

but the computational demands would be much less at the 

decoding phase. The hierarchical decomposition has only a 

small effect on the throughput, but is directly reflected in the 

number of blocks to be coded. 

By the use of hierarchical decomposition and FELICS 

coding, one can reduce the interblock redundancy. This will 

eliminate direct access to the decoded file and thus there is no 

longer guarantee of fault tolerance. 

Finally the literature survey on current algorithms which 

based on moment preserving algorithm is performed. Each 

algorithm which discussed in this literature are tried to 

enhance the performance of Block Truncation like algorithm 

directly or indirectly. All techniques are provided better visual 

quality (PSNR) and good bit rate. Many algorithms like 3.8 

and 3.9 are used in LCD overdrive for optimizing the 

performance of BTC algorithms. There is MSE, NAE and 

WPSNR values is also improved. 

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AUTHORS PROFILE 

Aditya Kumar received his B. Tech. degree 

from Ajay Kumar Garg Engineering College, 

Ghaziabad. He is currently pursuing M. Tech. at the 

Department of Computer Science & Engineering, 

National Institute of Technology, Hamirpur (HP) 

India. His research interests include Image 

compression and Digital Image processings. He is 

currently working on Image Compression 

Techniques. 

Pardeep Singh is working as Assistant 

Professor in the department of Computer Science & 

Engineering of National Institute of Technology, 

Hamirpur (HP) India. He is perusing PhD from the 

parent institute. His research area is speech 

processing. He is a member of International 

Association of Computer Science and Information 

Technology (IACSIT) and International Association 

of Engineers (IAENG). 



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