A predictive algorithm for multimedia data … PAPER A predictive algorithm for multimedia data compression Reza Moradi Rad • Abdolrahman Attar • Asadollah Shahbahrami Published

REGULAR PAPER

A predictive algorithm for multimedia data compression

Reza Moradi Rad • Abdolrahman Attar •

Asadollah Shahbahrami

Published online: 24 July 2012

� Springer-Verlag 2012

Abstract In lossless image compression, many prediction

methods are proposed so far to achieve better compression

performance/complexity trade off. In this paper, we con-

centrate on some well-known and widely used low-com-

plexity algorithms exploited in many modern compression

systems, including MED, GAP, Graham, Ljpeg, DARC,

and GBSW. This paper proposes a new gradient-based

tracking and adapting technique that outperforms some

existing methods. This paper aims to design an efficient

highly adaptive predictor that can be incorporated in

modeling step of image compression systems. This claim is

proved by testing the proposed method upon a wide variety

of images with different characteristics. Six special sets of

images including face, sport, texture, sea, text, and medical

constitute our dataset.

Keywords Image compression � Predictive coding �Multimedia � Lossless compression

1 Introduction

Nowadays, libraries, museums, and films are converting

more and more data into digital form especially into image

format. This needs large digital devices to store and a large

bandwidth to transmit through the networks. In order to

alleviate these requirements, compression techniques are

used. Image compression emerges to answer this essential

question: can we represent multimedia data with fewer

amounts of bits than the original data? Multimedia data

compression can be defined as ‘‘reducing the amount of

data required to represent the multimedia data’’. Many

compression techniques have been proposed in the litera-

ture, which can be classified into two groups: lossless and

lossy [24, 26]. In lossless compression, the quality of the

decoded multimedia data is the same as the original data.

The compression ratio of this category is generally limited.

In lossy compression, unnecessary data are deleted from

the original data. Therefore, the quality of the decoded

multimedia data is almost the same as the original data and

the compression ratio of this group is higher than the

previous one [29, 30, 31].

Predictive data coding is the most well-known technique

in lossless data compression for its efficiency, simplicity,

and robustness [1–3]. Prediction is a process to estimate the

unknown (future) values using the available and known

(past and present) values. In predictive coding, the essential

function is to extract the relationship and similarity of

neighboring values; for example, similarity of neighboring

pixels in an image; and reduce numbers of values that

should be known to represent a data. Most predictive data

compression techniques include two major steps [14]:

Modeling (prediction): In the first step, essential func-

tion is prediction of unknown values. An efficient mecha-

nism and predictor function are extracted to produce the

predicted data.

Coding: In the second step, essential function represents

errors (produced by subtracting original and predicted data)

in minimal form.

Researchers usually use Hoffman, Arithmetic, and some

other entropy coding schemas for the second step. While

R. M. Rad � A. Attar � A. Shahbahrami (&)

Department of Computer Engineering, Faculty of Engineering,

University of Guilan, P.O. Box: 3756-41635, Rasht, Iran

e-mail: [email protected]

R. M. Rad


A. Attar


123

Multimedia Systems (2013) 19:103–115

DOI 10.1007/s00530-012-0282-0

the story of first step differs, a lot of prediction schema and

functions have been proposed for this step. This work

concentrates on the first step, prediction or modeling, for

image data.

This paper is an extended and updated version of our

published conference paper [28] with more experimental

results and explanation than it. This paper is organized as

follows. Section 2 presents some background information,

predictive image compression and scan ordering. In Sect. 3

some related work are discussed. The proposed predictive

data compression is presented in Sect. 4. The benchmarks

and tested images are explained in Sect. 5. Experimental

results are presented in Sect. 6 followed by conclusions in

Sect. 7.

2 Background

In this section, some background information is presented.

2.1 Predictive image compression

In the prediction step we need a model to estimate the

unknown values to reduce the error as much as possible. A

simple schema of the prediction image compression is

depicted in Fig. 1.

Figure 2 shows different neighboring pixels in different

directions for unknown pixel of X. The symbols of W, NW,

N, and NE denote to West, North-West, North, and North-

East, respectively. Linear and non-linear are two types of

predictors that are used by various prediction methods.

Linear prediction is the simplest type of prediction algo-

rithms, while they cannot be efficiently used in some

applications. For example, in natural and sport images we

encounter abrupt changes in image intensity. The edge is

another example for non-stationary features of images.

The predictor must accurately work in non-stationary

situation according to local characteristics of an image.

Another way to address the non-linearity features of image

is to switch between linear predictors based on image local

information. In this case, final predictors constitute linear

functions, but the switching mechanisms make it similar to

non-linear performance. Predictor schemes can be

backward or forward, depending on whether they make

their decision on past or future pixels of images,

respectively.

In forward prediction, a few past pixels are known (for

example, one row and column) and the predictor estimates

unknown pixels. In backward prediction there is no hidden

information for predictor and the predictor tries to find the

best way to estimate and code each pixel regarding whole

image pixels. In other words, the predictor looks ahead and

finds how to estimate the unknown data to prevent the

worst prediction errors. Note that backward schema is a

trade-off between accuracy and overhead [18].

As a first look at backward and forward prediction, it is

obvious that backward schema is not desirable for trans-

mission, while forward schema is suitable for both storage

and transmission. Forward schema generally requires sin-

gle pass scanning, while backward schema requires at least

two pass scanning. That is why we concentrate on forward

schema in this work.

Another important feature for predictors is the level of

adaptivity. The predictors should be able dynamically

adjust and constitute final predictor according to local

information around current position. Adaptive predictor is

expected at least to be able to adaptively weigh specific

neighboring pixels.

2.2 Scan ordering

Scan ordering is the way of tracing the known image pixels

to estimate the unknown pixels [6, 25]. Predictive coding

algorithms employ various scan ordering. For instance,

history-based blending (HBB) [5] uses rain scan-ordering

and Jpeg uses zig-zag scan ordering, while MED, GAP

techniques use raster scanning. Although in [18] it has been

indicated that Hilbert space filling curve is the best scan

ordering technique in theory, in [27] it has been reported

that Hilbert space filling curve scan is impractical for gray-

scale lossless image compression. The researchers in [6]

investigate the effect of various scan ordering algorithms

such as raster scan, zigzag scan, Hilbert plane-filling scan,

block-wise scan, and resolution pyramid, or sub-sampling

scan on predictive image. The results showed that scan-

ordering has no special effect on the efficiency of predic-

tive coding. As pointed in [18, 25] most prediction schemas

employ raster scan ordering. In this paper, we used raster

scan ordering; scanning from left to right and top to down.Fig. 1 A simple schema of predicting image compression

Fig. 2 Neighboring pixels of predicted pixel X

104 R. M. Rad et al.

123

We tried just to focus on prediction mechanism. Figures 3,

4, 5 and 6 depict raster scan ordering, zig-zag scan order-

ing, rain-scan ordering, and Hilbert space filling curve scan

ordering for a block of size 8 9 8, respectively.

3 Related work

Many predictors such as Ljpeg, median edge detection

(MED), gradient adjusted prediction (GAP), differential

adaptive run coding (DARC), Graham, and gradient-based

selection and weighting (GBSW) for predictive image

compression have been presented by researchers [7, 12,

13, 19, 21]. In this section, some of them are briefly

discussed.

3.1 Ljpeg

Old lossless JPEG standard (Ljpeg) predictor [21] uses

three neighboring pixels (N, W, and NW) to estimate the

unknown pixels. Ljpeg exploits following predictors 0, W,

N, NW, W ? N-NW, W ? [(N-NW)/2], N ? [(W-

NW)/2], and (W ? N)/2 for prediction. Ljpeg predicts the

image using above-mentioned predictors and then chooses

the predictor which produces the lowest error (subtracting

the original image from predicted image) as a final

predictor.

It is considered as a global forward adaption predictor

[18], because first it should scan all image pixels (not

suitable for stream data) and select one predictor which is

fixed for an image.

Ljpeg performance is far from being flexible and pow-

erful enough to provide satisfactory prediction [18, 22]

because it has seven linear predictors and has to select one

of them for whole image pixels in different situations. For

example, an image probably has different characteristics

such as smooth, noisy, and edge region, so a fixed predictor

cannot have an acceptable prediction. We believe that lack

of adaptivity is one of the major reasons for Ljpeg failure.

3.2 MED

The MED [7] is a non-linear predictor that uses three

neighboring pixels to estimate unknown pixel. It detects

horizontal or vertical edges using three neighboring pixels

(N, W, and NW). The predicted pixel value is computed by

the following equation.

X ¼minðN;WÞ if NW � maxðN;WÞmaxðN;WÞ if NW � minðN;WÞN þW � NW Otherise

8<

:

where max(N, W) and min(N, W) are the functions which

return the maximum and minimum values of N and W,

respectively. MED algorithm according to the values of

function max, min, and pixel NW switches between three

conditions. In fact the predictor can be summarized to

medianSelector (N, W, N ? W-NW) where medianS-

elector is a function returning median value of N, W, and

N ? W-NW values [7, 17]. It is noted that MEDFig. 3 Raster scan ordering

Fig. 4 Zigzag scan ordering

Fig. 5 Rain scan ordering

Fig. 6 Hilbert space filling curve scan ordering

A predictive algorithm for multimedia data compression 105

123

algorithm output value always is limited on range [min(N,

W), max(N, W)] [15] and it can never predict out of this

range.

MED is also sometimes called median adaptive pre-

dictor (MAP), but MAP differs a bit, so that it produces the

median value for a set of predictors as output (not neces-

sarily predictors mentioned above) [18].

The MED algorithm is a simple algorithm and its com-

plexity is almost less than other algorithms [2, 4, 8–10].

3.3 Graham

Graham [19] is a non-linear predictor that uses three

neighboring pixels to estimate unknown pixels. Graham

algorithm estimates the gradient orientation by computing

vertical and horizontal gradient orientation parameters

named dv and dh, respectively.

dv ¼ W� NWj j dh ¼ N� NWj j

This simple predictor confines to only pixel N or pixel W

for final predictor without any weighting, and by

considering the values of dv and dh switches between one

of the northern pixel or western pixel.

X ¼ N dv [ dh

W dv� dh

�

In the Graham algorithm no new values are produced by

predictor, therefore it assigns existing values to unknown

pixels. It outperforms static predictors such as Ljpeg [4].

For vertical and horizontal edges, N and W are selected,

respectively.

3.4 Authors’ previous work

We have proposed a simple non-linear predictor which

switches between two predictor functions in [12, 13]. By

using three neighboring pixels, it considers two point of

views for prediction: aggressive view (v1) and conserva-

tive view (v2). The aggressive view can be considered an

inconsistent situation, so that the maximum change level

can be expected but in conservative view we encounter

consistent situation, so that minimum change level and

the most similar value to the neighboring pixels are

expected. So, when pixel NW does not have a value

between pixel N and W, average of v1 and v2 is esti-

mated for unknown pixel value, and otherwise v2 is

estimated. The predicted value is computed using the

following equations.

v1 = N + W� NW, v2 = average(N, W, NW)

X¼ðv1þv2Þ=2 if NW�maxðN,WÞ or NW�minðN,WÞv2 Otherwise

�

Its complexity is as low as MED and we believe it performs

well in noisy situations.

3.5 DARC

The DARC [20] is a non-linear adaptive predictor that uses

three neighboring pixels to estimate the unknown pixels.

DARC computes two parameters to weigh the pixels N and

W in the formation of final predictor. Parameters dh and dv

which represent the gradient orientation in vertical and

horizontal, respectively, are computed as following

equations:

dv ¼ W� NWj jdh ¼ N� NWj j

Then final predictor predicts the unknown pixel by the

following equation:

X ¼ dv

dv þ dh

� �

Wþ dh

dv þ dh

� �

N

The above equation shows that the weighting of the pixels

is according to dv and dh so that they try to keep gradient

orientation. Each of dv or dh, according to their values,

determines the importance and portion of pixel W or N in

predictor, because the sum of coefficients of pixels N and

W equals one. It means the unknown pixel is predicted in a

way that the more valuable pixel in a special situation

weighted more than other one in final predictor. DARC’s

complexity is as low as MED.

3.6 GAP

Gradient adjusted prediction (GAP) is a non-linear adap-

tive predictor that uses seven neighboring pixels to esti-

mate unknown pixel value [2, 6, 11]. The GAP algorithm

weighs the neighboring pixels according to local gradient

and classifies the edges to three classes namely, sharp,

normal, and weak. The GAP algorithm performs this

operation by computing dh and dv using the following

equations.

dh ¼ W�WWj j þ N� NWj j þ NE� Nj jdv¼W� NWj jþ N� NNj jþ NE� NNEj j

After computing the pixels orientation around the unknown

pixel, and according to their values it forms the final pre-

dictor by four neighboring pixels containing N, W, NW,

and NE with different weights. The predictor coefficients


123

and thresholds given in algorithm were empirically chosen.

The GAP algorithm is described as follows.

Clearly, GAP adapts itself to the gradients of horizontal

and vertical edges. Final predictor function predictive

values are adjusted by the gradients (dv and dh), hence the

predictor is named ‘gradient-adjusted predictor’ [17].

GAP’s complexity is not much but a bit higher than MED

and its output is not limited in such a range like MEDs’.

3.7 GBSW

The GBSW [4] is a non-linear adaptive predictor that uses

ten neighboring pixels to estimate unknown pixel. By

estimating the average gradients in four directions, it tries

to select the best predictor for predicting unknown pixels.

GBSW algorithm first computes four parameters to earn

the gradient orientation. Parameters are computed using ten

closest pixels as follows:

d1 ¼ 2 WW� NWj j þ 2 N� NNEj j þ W� Nj jþ NW� NNj j

d2 ¼ 2 N� NNj j þ 2 W� NWj j þ 2 NW� NNWj jþ 2 NE� NNEj j þ WW�WWNj jþ WWN � NNWWj j

d3 ¼ 2 W�WWNj j þ 2 N� NNWj j þ NW� NNWWj jþ NE� NNj j

d4 ¼ 2 W�WWj j þ 2 N� NWj j þ 2 NW�WWNj jþ 2 N� NEj j þ jNN � NNW þj jNN � NNEj

Then average gradients are estimated by the above

parameters in four directions: 45�, 90�, 135�, and 180�.

dNE ¼d1

6þ 0:5

� �

dN ¼d2

10þ 0:5

� �

dNW ¼d3

6þ 0:5

� �

dNE ¼d4

10þ 0:5

� �

After gradient estimation, GBSW produces the prediction

in a way that the neighboring pixel in the direction with the

minimal estimated gradient has the biggest contribution to

the formation of final prediction [4]. GBSW uses just two of

four neighboring pixels (N, W, NW, and NE) for final

predictor.

For example, if dW and dN (dW \ dN) are two minimum

estimated gradients around the current pixel X, then the

prediction for that pixel is computed as:

X ¼ dw � Nð Þ þ dN �Wð Þdw þ dN

GBSW’s complexity is not much but a bit higher than

MED. Please note that, as pointed before, all predictors

mentioned in related works section classify as low-

complexity predictors.

Table 1 provides summarizes information of all pre-

dictors of this section.

In Table 1 some information is provided as a single view

to compare predictors. In this table NANP means number of

all pixels needed for making decision and estimation by a

specific predictor. NPFP is the number of neighboring

pixels in final the predictor. NAV and NC are number of

auxiliary variables and clauses, respectively. In the last row,

the level of adaptivity for various predictors are given.

MED, PRV [14], and Graham classify as low level of

adaptivity because they use some specific configuration in

some conditions, for example three constant configuration

in MED. Note that the mentioned predictors switch between

linear predictors and try to simulate non-linear performance.

If the predictor is able to weigh the coefficients of final

predictors dynamically, it is considered as moderate

adaptivity level in this work, like DARC. A predictor

considered as high adaptivity level when it is able to make

decisions on which and how neighboring pixels contribute

in final predictor dynamically and regarding local infor-

mation, like NEW.

4 Proposed predictive data compression

The human visual system is more sensitive to important

features in an image. Edges are one of the most important

features that play a critical role in the presentation of an

image. Edges are revealing with jump in intensity, for

instance, Fig. 7 depicts the occurrences of edges for image

pixels. In this case, maximum intensity changes level

occurred in 45� direction. As can be seen, the image edge

exists in 135� angle.


123

Some predictors such as MED, DARC, and Graham

track edges in vertical and horizontal directions while

GBSW tracks and analyzes edges in four directions. GAP

also tracks edges in vertical and horizontal directions but

additionally classify edges to three classes namely, weak,

normal, and sharp. This paper proposes a new gradient-

based tracking and adapting method (GBTA) that tracks

edges in more directions precisely. Our goal is to design an

efficient and highly adaptive predictor that can be incor-

porated in the modeling step of image compression system.

By examining surrounding pixels of an unknown pixel

we try to find the maximum intensity change level to

determine edges. The new proposed algorithm uses 11

directions to predict the pixel value, as depicted in Fig. 8.

For the determination of more exact maximum-change

direction three simple steps are considered here. In the first

step, the main direction around each pixel among four main

directions (45�, 90�, 135�, and 180�) is selected as R. In the

second step, the sub-direction among R�-45� or R� or

R� ? 45� is selected, sub-directions are produced to be

more exact in determining the edges. In the third step, the

exact maximum-change direction calculated by the fol-

lowing equation is depicted in Fig. 8:

Direction ¼ 2�main directionð Þ þ sub-directionð Þ½ �=3

e:g: 2� 45�ð Þ þ 0�ð Þ½ �=3 ¼ 30�

To clarify the proposed algorithm, we give an example

here. Suppose that the main direction is 45� and the sub-

direction is 0�, then final direction (exact maximum-change

direction) is 30� as depicted in Fig. 9.

As shown in Fig. 9, two directions in terms of maximum

change level, main direction and sub-direction are con-

sidered. In other words, final direction not only relies on

the main direction but also relies on sub-direction. Sub-

Table 1 Summarized information about predictors

Ljpeg MED GAP PRV [14] DARC Graham GBSW NEW

NANP – 3 7 3 3 3 10 19

NPFP – 3 4 3 2 2 2 2

NAV – 0 2 0 2 2 4 0

NC 1 3 6 2 0 2 4 11

L-NL L NL NL NL NL NL NL NL

Switching No Yes Yes Yes No Yes No No

FW-BW BW FW FW FW FW FW FW FW

Adaptivity None Low Moderate–high Low Moderate Low Moderate–high High

NANP number of all needed pixels, NPFP number of pixels in final predictor, NAV number of auxiliary variables, NC number of clauses, L–NLlinear or non-linear, FW–BW forward or backward

Fig. 7 Details of edge occurrence

Fig. 8 Classification of edge directions

Fig. 9 Main direction = 45� and sub-direction = 0� so

direction = 30�

Table 2 Predictors which used when both main and sub-direction are

same

Main direction = sub-direction Direction Predictor

45 45 NW

90 90 W

135 135 NE

180 180 N


123

direction also affects final direction with less power than

main-direction.

Now it is time to introduce predictors regarding the

obtained final direction. For each pixel prediction just one

or two neighbor pixels participate in final predictor.

Regarding the final local gradient estimation, the predictor

performs dynamically. When the main direction and sub-

direction are the same, the predictor just uses one neighbor

pixel for prediction. When they are different, it uses two

neighbor pixels.

When the main direction and sub-direction are same,

then the predictor estimates the unknown pixel value to be

same as the pixel which keeps the intensity change level.

The whole predictors are used in a situation that both main

and sub-direction are the same as shown in Table 2.

Now, suppose that the main and sub-direction are dif-

ferent. In these circumstances predictor formation is a little

more complex than previous. In this situation, two pixels

participate to form the predictor. According to our algo-

rithm premises, the pixel which participates in order to

show the effect of main direction in keeping maximum

change level weighted two and the other one which par-

ticipates for effect of sub-direction weighted one and

divided by three to form a final predictor.

All of the predictors with details about direction are

shown in Table 3.

To clarify the mentioned explanations, an example is

presented here: the maximum change level occurred in 45�and it is the main direction. The predictor looks around it,

the maximum change level is selected among 45�, 90�, and

135� sub-direction. Sub-direction 90� is selected, while the

main direction is 45�. The NW value participates in

Table 3 Predictors which used when both main and sub-direction are

not same

Main direction = sub-direction Direction Predictor

45 0 30 (2NW ? N)/3

45 90 60 (2NW ? W)/3

90 45 75 (2W ? NW)/3

90 135 105 (2W ? NE)/3

135 90 120 (2NE ? W)/3

135 180 150 (2NE ? N)/3

180 135 165 (2N ? NE)/3

3/))*2((ˆ WNWX +=

Fig. 10 Formation of predictor for final gradient 60�

NW N NE

W X

75°60°

45°

30°

90°105°

135°

120°

150°

165°

180°

Angle selection

(According to local gradients)

Predictor Formation

(According to angle)

Computing of predicted pixel value

(According to predictors)

e=difference

Fig. 11 Snapshot of proposed

predictor


123

prediction that its weighted value is two. In addition, the

predictor uses the W value with weighted value of one. So

the predictor uses the following equation to estimate the

unknown pixel value (Fig. 10).

Complete steps in the proposed algorithm are shown in

Fig. 11.

5 Benchmarks

Now it is time to test the proposed method upon credible

datasets and analyze its performance in comparison with

related works. We believed that poor datasets cannot

reflect the real world of images. Proper datasets should

be able to show some important aspects of image world,

not just one ad hoc aspect of images. We select six

Fig. 12 Examples of image set:

face, sea, medical, texture,

sport, text

Table 4 Characteristics of images

Image properties Ranges

Width of images (pixel) 168–752

Height of image (pixel) 72–800

Resolution of image (dpi) 72–350


123

different groups of images which have a significant

contribution in file storage and transmission. Face, sea,

medical, texture, sport, and text constitute our six unique

datasets. Figure 12 shows some examples of each set.

These six groups of images inherently are different, and

each group has their own characteristics and features.

Table 5 Mean absolute error (MAE) upon face image set, including ten different face images

Image Dimension MED Graham Previous [13] DARC GAP GBSW GBTA

Face 0 344 9 400 6.79 7.46 7.68 6.65 6.99 7.01 5.20

Face 1 288 9 176 6.65 6.97 9.33 6.77 8.83 6.75 4.65

Face 2 368 9 360 5.13 5.86 5.53 4.99 5.46 5.40 4.28

Face 3 552 9 480 8.76 9.69 8.86 8.49 8.56 8.72 6.36

Face 4 248 9 264 4.41 5.12 6.53 4.36 4.79 5.04 3.27

Face 5 320 9 320 6.78 7.58 10.27 6.83 4.64 6.86 5.84

Face 6 680 9 512 4.57 5.30 5.15 4.48 5.11 5.03 3.79

Face 7 376 9 280 5.18 5.92 6.59 5.09 5.81 5.45 4.23

Face 8 256 9 256 10.24 10.84 12.93 10.06 10.67 10.42 7.38

Face 9 376 9 472 5.74 6.56 6.56 5.62 5.89 6.02 4.77

6.42 7.13 7.94 6.33 6.67 6.67 4.97

Bold values are average values

Table 6 Mean absolute error (MAE) upon medical image set, including ten different medical images


Medical 0 336 9 296 8.82 9.52 10.56 8.75 9.40 8.71 7.01

Medical 1 344 9 272 10.24 11.31 11.89 10.10 10.44 10.40 8.32

Medical 2 336 9 336 7.6 8.50 12.15 7.37 11.10 8.53 5.79

Medical 3 344 9 312 8.06 8.69 9.17 7.86 9.59 8.03 6.50

Medical 4 504 9 504 3.77 4.27 6.19 3.75 4.43 3.99 3.00

Medical 5 240 9 232 13.69 14.61 15.19 13.51 15.10 14.00 10.86

Medical 6 272 9 336 6.50 7.05 7.33 6.38 7.87 6.51 5.07

Medical 7 320 9 336 14.48 15.20 15.82 14.24 15.07 14.12 10.75

Medical 8 304 9 272 15.19 16.20 17.17 14.92 15.72 15.62 11.95

Medical 9 288 9 288 3.60 4.67 3.95 4.11 3.81 3.77 3.03

9.19 10.00 10.94 9.10 10.25 9.36 7.22


Table 7 Mean absolute error (MAE) upon sport image set, including ten different sport images


Sport 0 480 9 800 4.16 4.39 4.87 4.03 4.84 5.09 3.54

Sport 1 600 9 528 9.87 10.91 12.58 9.80 12.37 12.22 7.57

Sport 2 384 9 512 9.86 11.12 10.33 9.56 10.46 10.90 6.43

Sport 3 312 9 544 17.17 18.14 18.28 16.86 18.76 19.09 13.76

Sport 4 464 9 320 7.95 8.40 10.82 7.86 9.81 10.63 7.16

Sport 5 728 9 480 12.89 13.75 15.79 12.76 15.34 15.66 10.42

Sport 6 440 9 680 8.40 9.06 10.67 8.33 11.07 10.32 7.30

Sport 7 560 9 656 6.72 7.58 9.08 6.67 8.47 8.48 5.05

Sport 8 800 9 416 9.14 10.21 10.03 8.95 9.80 10.64 7.22

Sport 9 400 9 400 20.40 21.77 15.24 19.33 18.09 17.35 11.90

10.65 11.53 11.76 10.42 11.90 12.03 8.03



123

Each image has special histogram, and its size and

content completely differ from others. Table 4 indicates

the ranges of height, width, and resolution for all these

images.

6 Experimental results

In order to measure the accuracy of the proposed technique

we have implemented all predictors which have been

Table 8 Mean absolute error (MAE) upon texture image set, including ten different texture images


Texture 0 336 9 512 10.92 10 96 16.69 11.06 11.24 16.74 10.79

Texture 1 336 9 512 21.22 22.21 21.04 20.45 21.11 20.79 17.35

Texture 2 168 9 256 33.62 35.90 34.78 32.40 35.64 33.90 27.47

Texture 3 336 9 512 18.06 19.55 20.00 17.89 21.73 17.52 15.47

Texture 4 256 9 384 24.79 26.66 23.97 23.87 25.02 25.10 20.45

Texture 5 336 9 512 12.24 13.12 14.66 12.10 15.49 13.38 10.50

Texture 6 256 9 384 24.41 25.26 22.62 24.00 21.12 23.80 15.90

Texture 7 336 9 512 6.11 6.52 6.72 5.98 6.41 6.62 4.94

Texture 8 256 9 384 16.74 18.09 17.75 16.47 19.16 16.15 10.98

Texture 9 200 9 512 11.67 12.35 13.41 11.43 14.43 13.05 10.79

17.97 19.06 19.16 17.57 19.13 18.70 14.46


Table 9 Mean absolute error (MAE) upon sea image set, including ten different sea images


Sea 0 384 9 512 7.15 7.67 8.14 6.99 8.65 8.77 6.16

Sea 1 384 9 512 2.95 3.12 4.22 2.88 4.71 4.40 2.83

Sea 2 296 9 400 3.14 3.37 5.28 3.01 5.79 5.35 3.45

Sea 3 448 9 600 2.24 2.36 3.25 2.16 3.44 3.35 1.92

Sea 4 320 9 512 5.15 5.44 7.13 5.18 7.29 7.47 5.18

Sea 5 256 9 400 7.67 8.21 8.23 7.50 8.33 8.14 6.60

Sea 6 296 9 400 5.60 5.93 5.92 5.33 6.32 7.16 4.61

Sea 7 296 9 400 7.01 7.37 8.20 6.88 8.02 8.81 5.66

Sea 8 368 9 512 5.14 5.55 5.87 5.02 6.07 6.31 4.64

Sea 9 336 9 512 2.28 2.27 5.24 2.42 5.61 4.91 2.79

4.83 513 6.14 4.74 6.42 6.46 4.38


Table 10 Mean absolute error (MAE) upon text image set, including ten different text images


Text 0 416 9 312 13.06 13.31 21.75 13.18 18.39 15.15 11.35

Text l 624 9 600 8.95 9.03 10.70 8.84 12.11 9.38 6.76

Text 2 744 9 584 16.83 16.90 19.40 17.06 17.46 21.24 13.70

Text 3 752 9 72 15.54 15.05 23.86 15.50 24.93 20.95 12.33

Text 4 600 9 624 7.49 7.5 9.28 7.42 8.69 22.38 6.44

Text 5 424 9 336 12.20 12.23 15.67 12.05 14.47 16.68 8.75

Text 6 456 9 232 16.38 16.35 20.68 16.78 18.41 27.28 14.09

Text 7 472 9 88 31.54 32.49 26.51 31.81 26.83 33.66 21.46

Text 8 296 9 576 24.51 24.50 28.57 24.38 24.28 28.75 16.83

Text 9 384 9 648 18.41 18.89 18.65 18.47 17.37 20.01 14.84

16.49 16.62 19.50 16.54 18.29 21.54 12.65



123

discussed in related work section and the proposed algo-

rithm using Matlab tool programming. We have tested the

predictors upon our specific corpus explained in the dataset

section. Our criterion for comparison different algorithms

is the measurement of the similarity between predicted

image and the original image.

Fig. 13 a Original, b MED, c previous, d GAP, e DARC, f Graham, g GBSW, and h GBTA

Fig. 14 a MED, b previous, c GAP, d DARC, e Graham, f GBSW, g GBTA


123

Some papers exploit math-based statistical tables for

comparison [1–8, 10, 11, 14–17, 22], but this work does not

confine such statistical tables. Hence, we separate the

comparison into two parts, mathematical comparison and

visual comparison.

6.1 Mathematical comparison

Since mean absolute error (MAE) is widely used by

researchers in image compression field, MAE is picked up

for mathematical comparison in this work. MAE is the

average of the absolute errors ei;j ¼ Xi;j � Xi;j, where X is

the true pixel value and X is the predicted pixel value.

MAE equation is shown for an image of size N 9 M in the

following formula.

MAE ¼PN

i¼1

PMj¼1 ei;j

N �M

Tables 5, 6, 7, 8, 9 and 10 present the MAE for all

predictors discussed before upon the six-image set.

6.2 Visual comparison

For further illustration of the performance of the proposed

method over other predictors discussed before, we present

those predictive error values as an image, similar to [23].

As image Lena is the most famous image in image pro-

cessing field, it is selected by the authors for this exami-

nation. These images obtained by subtracting the original

Lena from predicted Lena. The brighter pixels show the

errors produced by the predictors, so that the distribution of

the errors can be observed all over the predicted image.

As shown by Fig. 13a–h the bright pixels in an image

predicted by NEW predictor is less than the others. In

addition, for showing the dispersion of produced errors by

predictors, histograms of each predictor for Lena are pre-

sented. X-axis shows the possible value of errors (on range

0–255) and Y-axis shows the number of pixels which have

error corresponding to x. So it is expected that the better

predictor has the most aggregation near the zero because

the smaller produced error is desirable for a better

predictor.

Histograms in Fig. 14 show that the number of produced

errors near the zero for GBTA predictor is more than the

others.

7 Conclusions

Predictive coding has many applications in digital image

processing such as image compression. Predictive algo-

rithms estimate the unknown pixel value using the past and

present pixel values. In this paper, a new gradient-based

tracking and adapting predictor algorithm were proposed. It

evaluates and uses the values of the known pixels in dif-

ferent directions to estimate the value of the unknown

pixel. The proposed algorithm and other predictive algo-

rithms such as MED, GAP, GBSW, Graham, DARC, and

the proposed algorithm in [13] were implemented using the

Matlab programming tool. The implemented algorithms

were tested on different images with different contents and

sizes. The obtained experimental results show that the

prediction error of the proposed algorithm is much less

than the other algorithms. This means that the quality of the

obtained predicted image using the proposed algorithm is

better than the quality of the obtained predicted images

using other algorithms.

References

1. Baligar, V.P., Patnaikb, L.M., Nagabhushana, G.R.: High com-

pression and low order linear predictor for lossless coding of

grayscale images. Image Vis Comput J 21(6), 543–550 (2003)

2. Knezovic, J., Kovac, M., Mlinaric, H.: Classification and

Blending Prediction for Lossless Image Compression. IEEE

Melecon, Benalmadena, (2006)

3. Estrakh, D.D., Mitchell, H.B., Schaefera, P.A., Mannb, Y.,

Peretzb, Y.: Soft median adaptive predictor for lossless picture

compression. J. Signal. Process. 81(9), 1985–1989 (2001)

4. Knezovic, J, Kovac, M.: Gradient based selective weighting of

neighboring pixels for predictive lossless image coding. In: 25th

International Conference on Information Technology Interfaces

(2003)

5. Seemann, T., Tischer P., Meyer, B.: History-based blending of

image sub-predictors. In: Proceedings of the International Picture

Coding Symposium (PCS’97), pp. 147–151. VDE-Verlag, Ger-

many (1997)

6. Memon, N., Wu, X.: Recent development in context-based pre-

dictive techniques for lossless image compression. Comput J

40(2/3), 127–136 (1997)

7. Martucci, S. A. Reversible compression of HDTV images using

median adaptive prediction and arithmetic coding. In: IEEE

International Symposium on Circuits and Systems, USA,

pp. 1310–1313 (1990)

8. Memon, N., Sippy, V., Wu, X.: A comparison of prediction

schemes proposed for a new lossless image compression stan-

dard. Appl Comput Harmon Anal 5(3), 332–369 (1998)

9. Yua, U.H., Changa, C.C., Hu, Y.C.: Hiding secret data in images

via predictive coding. Pattern. Recogn. 38(5), 691–705 (2005)

10. Deng, G., Ye, H.: Lossless image compression using adaptive

predictor combination, symbol mapping and context filtering. In:

International Conference on Image Processing, vol. IV (1999).

ISBN: 0-7803-5467-2

11. Wu, X.: An algorithm study on lossless image compression. In:

IEEE Conference on Data Compression, pp. 150–159 (1996)

12. Shahbahrami, A., Moradi Rad, R., Attar, A.: A study of predictive

method and presentation of an improvement. In: Local Workshop

in Department of Computer Engineering, Faculty of Engineering,

University of Guilan, Rasht, Iran (2010)

13. Seyed Danesh, A., Moradi Rad, R., Attar, A.: A novel predictor

function for lossless image compression. In: 2nd IEEE Interna-

tional Conference on advanced computer control, China (2010)


123

14. Shukla, J., Alwani, M., Kumar Tiwari, A.: A survey on lossless

image compression methods. In: 2nd International Conference on

Computer Engineering and Technology, China (2010)

15. Seemann, T., Tischer, P.: Generalized locally adaptive DPCM’’.

In: Proceedings of the Conference on Data Compression, USA

(1997)

16. Shamardan1, H. M., El-Azim, S. A., Fikri, M.: New prediction

technique for lossless compression of multispectral satellite

images. In: International Conference on Graphics, Vision and

Image Processing, GVIP 05 Conference, Egypt (2005)

17. Chang, C., Chen, G.: Enhancement algorithm for nonlinear

context-based predictors. In: IEEE Proceedings Vision, Image

and Signal Processing (2003)

18. Penrose, A. J.: Extending lossless image compression. Technical

report no. 526, University of Cambridge, computer laboratory,

UK (2001)

19. Graham, R.E.: Predictive quantizing of television signals. IRE

WESCON Conv. Rec. 22(Pt. 4), 147–157 (1958)

20. Gandhi, B., Honsinger, C., Rabbani, M., Smith, C.: A proposal

submitted in response to call for contributions for JTC 1.29.12

[JTC1/SC29/WG1 N41] ISO working document ISO/IEC JTC1/

SC29/WG1 N204 (1995)

21. Wallace, G. K.: The JPEG still picture compression standard. In:

IEEE Transactions on Consumer Electronics, vol. 38, no. 1,

Arlington, VA (1992)

22. Wang, S., Cheung, C., Cheung, K., Po, L.: Lossless wavelet coder

with adaptive orientational prediction. In: Proceedings of the

IEEE Region 10 Conference TENCON 99, Cheju Island (1999)

23. Jiang, J., Guo, B., Yang, S.: Revisiting the JPEG-LS prediction

scheme. In: IEEE Proceedings Vision, Image and Signal Pro-

cessing (2000)

24. Ponomarenko, N., Krivenko, S., Lukin, V., Egiazarian, K. Astola,

J. T.: Lossy compression of noisy images based on visual quality:

a comprehensive study. J. Adv. Signal Process (EURASIP), vol.

2010, article ID 976436 (2010)

25. Sayood, K.: Lossless compression handbook. Academic Press,

Elsevier Science, USA (2003)

26. Solomon, P D.: Data compression the complete reference, 4th

edn. Springer, New York (2006)

27. Memon, N., Sayood, K.: Lossless image compression: a com-

parative study. In: Proc. SPIE Still-Image Compression (1995)

28. Attar, A., Rad, R. M., Shahbahrami, A.: An accurate gradient-

based predictive algorithm for image compression. In: The 8th

International Conference on advances in mobile computing and

multimedia (MoMM2010), Paris, France (2010)

29. Jiang, J., Armstrong, A., Feng, G.C.: Web-based image indexing

and retrieval in JPEG compressed domain. Multime. Syst. 9,

424–432 (2004)

30. Zadeh, M.H., Wang, D., Kubica, E.: Perception-based lossy

haptic compression considerations for velocity-based interac-

tions. Multime. Syst. 13, 275–282 (2008)

31. Winkler, T., Rinner, B.: User-centric privacy awareness in video

surveillance. Multimedia Syst. 18(2), 99–121 (2012)


123

A predictive algorithm for multimedia data … PAPER A predictive algorithm for multimedia data compression Reza Moradi Rad • Abdolrahman Attar • Asadollah Shahbahrami Published

Documents