Bit-inverted Gray Coded Bit-plane Matching for Low Complexity

Motion Estimation

Changryoul Choi and Jechang Jeong

Department of Electronics and Computer Engineering, Hanyang University, Seoul, Korea

Keywords: Block Matching, Motion Estimation, Bit-Plane Matching.

Abstract: In this paper, a bit-inverted Gray coded bit-plane matching algorithm is proposed for low complexity

motion estimation. Unlike the typical Gray coded bit-plane matching algorithms, the proposed algorithm

uses bit-inverted Gray codes for transforming image frames and a corresponding extended matching

criterion to enhance the motion estimation accuracy. Experimental results show that the proposed algorithm

outperforms other bit-plane matching based motion estimation algorithms while preserving the binary

matching characteristic.

1 INTRODUCTION

Motion estimation (ME) plays a key role in reducing

the total video data efficiently by exploiting the

correlation among neighbouring frames. The block

matching algorithm (BMA) is the most popular and

is deployed in many video compression standards

due to its simplicity and effectiveness. Although the

full search BMA (FSBMA) can find an optimal

motion vector according to some matching criterion

such as the sum of the absolute differences (SAD) or

the sum of the squared differences (SSD), it is not

suitable for real time applications due to the heavy

computational complexity. Therefore, many

techniques have been proposed to relieve the high

computational complexity of the FSBMA in the

literature (Li and Salari, 1995, Choi and Jeong,

2009). Among these techniques, there proposed

some algorithms that use different matching

criterion instead of the classical SAD or SSD to

make the faster computation of the matching

criterion itself exploiting the bit-wise operations.

These algorithms are called as bit-plane matching

(BPM) based ME. The advantages of these

techniques over the matching algorithms using the

classical SAD or SSD are two-fold: fast computation

of the matching criterion and reduced memory

bandwidth in the interim of ME process.

Natarajan et al. first proposed the one-bit

transform (1BT) based ME, where the reference

frames and the current frames are transformed into

one-bit representations by comparing the original

image frame with filtered output (Natarajan et al,

1997). A two-bit transform (2BT) based ME was

proposed to enhance the ME accuracy of the 1BT-

based ME algorithms (Erturk and Erturk, 2005). The

2BT-based ME shows some improvement especially

in small block sizes. Gullu proposed to use a two-bit

constraint mask according to the difference between

a pixel and its 1BT threshold value (Gullu, 2011).

Although this algorithm, weighted constrained 1BT

(WC1BT), shows some improvement in terms of the

ME accuracy, the binary matching characteristic

doesn’t hold due to a two-bit constraint mask.

Ko. et al. proposed Gray-coded BPM based ME

(Ko et al, 1999), which is also called truncated Gray-

coded BPM (TGCBPM) (Celebi et al, 2009). And its

variation weightless TGCBPM (WTGCBPM)

(Celebi et al, 2010) were also proposed. Both

TGCBPM and WTGCBPM use Gray-code mapping

as transforming image frames into bit-planes, which

is very simple compared to other bit-plane

transformation algorithms using complex filtering

operations. Let the gray-level of the pixel at location

(i, j) be represented as follows:

1210

12 10

(, ) 2 2 2 2

ij a a a a



 

(1)

where a

(0 ≤ k ≤ K-1) takes on either 0 or 1. Then

the corresponding Gray-code representation is given

11KK





,0 2

kk k

gaa kK







(2)

where



denotes the Boolean XOR operation and

230

Choi C. and Jeong J..

Bit-inverted Gray Coded Bit-plane Matching for Low Complexity Motion Estimation.

DOI: 10.5220/0005323902300234

In Proceedings of the 5th International Conference on Pervasive and Embedded Computing and Communication Systems (PECCS-2015), pages

230-234

ISBN: 978-989-758-084-0

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

is the k-th bit representation. After this

transformation, TGCBPM and WTGCBPM use

respective number of non-matching points (NNMP)

as matching criteria which are given as:

11 1

(,)

2{(,) ( , )}

TGCBPM NTB

NN K

kNTB t t

ijkNTB

NNMP m n

ij g i mj n

 







 

)

11 1

(,)

(, ) ( , )

WTGCBPM NTB

NN K

ijkNTB

NNMP m n

ij g i mj n

 







 

where K represents the pixel-depth and NTB is the

number of truncated bits, the motion block size is

NN, and –s ≤ m, n ≤ s is the search range. The kth

most significant bit of the Gray-coded image pixel

frame of time t is represented as g

(i, j). Compared

with the previous BPM based ME algorithms,

TGCBPM and WTGCBPM based ME show

significant gains in terms of the ME accuracy.

Since all the matching criteria of BPMs try to

replace the SAD or SSD with the bitwise operations

for reduction of computational complexity, their

output must be similar to the SAD or SSD in order

to find a more accurate motion vector. Therefore, if

one can find a matching criterion (using only the

bitwise operations) whose output is similar to the

SAD or SSD between two image bit-planes, its ME

accuracy increases substantially. In this paper, a

transformation method which is a slight

modification of the typical Gray-code mapping is

proposed. And together with a transformation

method, a corresponding extended bitwise

operation-only matching criterion shows similar

characteristics with the output of the SSD.

Experimental results demonstrate that the proposed

algorithm outperforms other BPM based ME

algorithms while preserving the binary matching

characteristic.

The rest of this paper is organized as follows: In

Section II, the proposed algorithm is presented.

Experimental results and analyses are given in

Section III. Finally, Section IV provides conclusions.

2 PROPOSED ALGORITHM

Since the Gray-coded BPMs use only some of the

first most significant bits of pixels, they are very

similar to the quantized frame based ME except the

way of handling the quantized pixels and the

matching criterion (Choi and Jeong, 2013). For

example, when 2 bit-planes are used, their symbols

for respective matching criteria are in Table 1.

Table 1: Symbols for the quantized frame based ME and

the Gray-coded BPM based ME when using 2 bit-planes.

Quantized Symbol Quantized Frame Gray Coded

Note that the Gray-coded BPM based ME uses one

of the metrics of (3) and the quantized frame based

ME uses the metric of SAD. The metric distribution

of Gray-coded BPMs in terms of the absolute

difference between two quantized symbols is in

Table 2.

Table 2: Metric distributions of TGCBPM and

WTGCBPM when using 2 bit-planes.

Absolute Difference TGCBPM WTGCBPM

0 0 0

1 1 or 2 1

2 3 2

3 2 1

For TGCBPM, when two Gray-coded symbols

are (00, 01) or (11, 10), their distances are 1. And

when two symbols are (01, 11), their distance is 2.

Note that when the absolute difference between two

quantized symbols is k (0 ≤ k ≤ 3), its expected true

absolute difference between two pixels is 64k

(when the pixel bit-depth is 8). That is, the actual

distortion between two pixels in terms of the SAD is

proportional to the absolute difference between these

quantized symbols. Therefore, it would be better for

a matching criterion if the absolute difference

between two quantized symbols be small, its

matching criterion output be small, and vice versa.

To this end, the Gray coded bit-planes are inverted

as follows:

~, 1

hgNTBkK



 

(4)

where K represents the pixel-depth, ~ represents the

Boolean NOT operation, NTB is the number of

truncated bits and g

is the k-th Gray bit

representation. Note that when NTB = 6, this code

allocation is that of the typical 2BT. And note also

that this inversion process does not violate the

property of the typical Gray codes that consecutive

codewords differ only in one bit position no matter

what NTB is. A corresponding matching criterion of

the bit-inverted Gray coded BPM (BGCBPM) is

proposed as follows:

Bit-invertedGrayCodedBit-planeMatchingforLowComplexityMotionEstimation

231

11 1

(,) (,) ( , )

NN K

gram k k

ijkNTB

NNMP m n h i j h i m j n

 







 

211

(,)

2 [ (, ) { (, ) ( , )}]

gram

KNTB t t t

KKK

NNMP m n

hijhijhimjn







  



211

(,)

2 [ (, ) { (, ) ( , )}]

gram

KNTB t t t

KKK

NNMP m n

hijhijhimjn



 





  



(,) (,)

BGCBPM gram i

NNMP m n NNMP m n





)

where • denotes the Boolean AND operation, K

represents the pixel-depth, NTB is the number of

truncated bits, the motion block size is NN, and –s

≤ m, n ≤ s is the search range. The kth most

significant bit of the bit-inverted Gray-coded image

frame of time t is represented as h

(i, j). Note that

this matching criterion is a generalized version of

(Choi and Jeong, 2013) by allowing the number of

bit-planes from 2 to (K-NTB).

To check whether the proposed bit-inversion of

Gray coded bit-planes and the corresponding

matching criterion reflect the properties of the

discussed above, the metric distributions of

BGCBPM in terms of the absolute difference are

calculated. Table 3 and Table 4 show the results

when 2 bit-planes and 3 bit-planes are used.

Table 3: Metric distributions of BGCBPM when using 2

bit-planes.

Absolute Difference BGCBPM

0 0

1 1

2 6

3 9

Table 4: Metric distributions of BGCBPM when using 3

bit-planes.

Absolute Difference BGCBPM

0 0

1 1

2 2

3 1 or 11

4 10

5 11 or 17

6 18

7 17

When using 2 bit-planes, the proposed matching

criterion of BGCBPM gives a small value when the

absolute difference is small and gives relatively

large value in the opposite case. Since these values

are much bigger than their absolute differences, the

proposed algorithm can prune out the bad motion

vectors effectively. Unlike the metric distributions of

2 bit-planes, those of 3 bit-planes show some

multiple metric outputs (when absolute difference is

3 or 5) and some metric output gives relatively small

value when their absolute difference is large (when

the absolute difference is 3). However, as can be

seen from the tables, these cases are relatively rare

and the metric distributions clearly show the

tendency that the proposed matching criterion of

BGCBPM gives a small value when the absolute

difference is small and vice versa.

Note that from (5), it appears that transforming

the image frames into bit-inverted Gray codes

requires (K-NTB) Boolean NOT operations more for

each pixel compared with the typical Gray-coded

BPMs. However, since the output of the XOR

operation between two binary vectors x and y is the

same as that of the XOR operation between ~x and

~y (where ~ means the component-wise NOT

operation), the following identity is easily derived:

(, ) (~ ,~ )

wwxy x y

(6)

where w

denotes the Hamming weight. Therefore,

the bit-planes which only the Boolean XOR

operations are involved with need not to be inverted.

Table 5: Computational complexity comparison of

transformations (per pixel).

TGCBPM WTGCBPM WC1BT BGCBPM

XOR K-NTB-1 K-NTB-1 - K-NTB-1

NOT - - - 1

Shift - - 1 -

Addition - - 16 -

Subtraction - - 1 -

Comparison - - 8 -

Table 6: Computational complexity comparison of

matching (per pixel).

TGCBPM WTGCBPM WC1BT BGCBPM

XOR



(K-NTB)



(K-NTB)

NN



(K-NTB)

AND - - -

2N



Shift (K-NTB-1) - - 2

Addition



(K-NTB)



(K-NTB)

NN

3NN

K-NTB)+3

Compari-

son

- -

NN

Multipli

-cation

- -

NN

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Only the (K-2)th Gray coded bit needs to be inverted,

since only this bit-plane is involved with the

Boolean AND operation in (5). The total operations

of BGCBPM required for transformation of image

frames and for matching compared with other

recently proposed BPMs are in Table 5 and Table 6.

3 EXPERIMENTAL RESULTS

To demonstrate the superiority of the proposed

algorithm, several experiments were carried out by

comparing the ME accuracy of other BPM ME

algorithms including WC1BT, TGCBPM,

WTGCBPM, and the FSBMA using the measure of

SAD. For WC1BT, the thresholds were set to T

10, T

= 30, T

= 50. The first 100 frames of 17 CIF

(352  288) sequences are used as test sequences.

All the searching processes were in spiral order.

Table 7 shows the average peak-to-peak signal to

noise ratio (PSNR) results of the proposed

BGCBPM algorithm with varying NTBs compared

with other BPM based ME algorithms when the

motion block size is 1616 and the search range is

±16. We highlighted the PSNR values showing the

best performance (except the FSBMA) in each

sequence. The PSNR performances of the proposed

algorithm with varying NTBs clearly show that the

extension of the number of bit-planes from 2 to (K-

NTB) enhances the ME accuracy. And compared

with other BPM based ME algorithms, the proposed

BGCBPM shows the best ME accuracy in terms of

the PSNR. Compared with the recently proposed

WC1BT, although they use multiplications in

matching calculations and non-binary matching

characteristic, their PSNR performances are worse

than that of the proposed algorithm. And the PSNR

difference between the proposed BGCBPM and the

FSBMA is only 0.26dB, which is very small.

4 CONCLUSIONS

In this paper, a bit-inverted Gray coded BPM

algorithm is proposed for low complexity motion

estimation. Since the Gray-coded BPMs use only

some of the first most significant bits of pixels, they

are very similar to the quantized frame based ME

and the actual distortion between two pixels in terms

of the SAD is proportional to the absolute difference

between these quantized symbols. To incorporate

these facts into a BPM based ME, a transformation

method which is a slight modification of the typical

Gray-code mapping is proposed. And together with

a transformation method, a corresponding extended

bitwise operation-only matching criterion shows

Table 7: Average PSNR performance comparison of the algorithms when the motion block size is 1616.

WC1BT

TGCBPM

(NTB=5)

WTGCBPM

(NTB=5)

BGCBPM

(NTB=6)

BGCBPM

(NTB=5)

BGCBPM

(NTB=4)

FSBMA

stefan 25.42 25.47 25.46 25.60 25.71 25.68 25.75

football 23.36 23.68 23.55 23.59 23.95 23.87 24.00

akiyo 42.66 42.37 42.56 42.09 42.61 42.70 42.84

foreman 32.43 32.51 32.68 31.99 32.83 33.11 33.43

mobile 23.77 23.78 23.68 23.81 23.87 23.86 23.92

hall 34.09 33.81 33.84 33.16 34.03 33.95 34.34

coastguard 29.40 29.37 29.40 28.09 29.49 29.54 29.62

container 38.27 37.66 37.66 37.67 37.70 37.99 38.33

bus 24.48 24.66 24.53 24.62 24.84 24.84 24.90

dancer 30.07 30.96 30.77 30.48 31.16 31.66 32.14

mother 39.55 39.25 39.48 37.48 39.49 39.76 40.12

tempete 27.38 27.51 27.46 27.44 27.61 27.61 27.70

table tennis.

28.27 28.18 28.37 28.32 28.62 28.71 28.87

flower 25.88 25.93 25.92 25.84 25.98 25.98 26.03

children 28.72 28.93 28.68 29.04 29.17 29.11 29.24

paris 30.50 30.52 30.48 30.49 30.67 30.65 30.71

news 36.68 36.92 36.89 36.79 37.04 37.07 37.33

Average 30.64 30.68 30.67 30.38 30.87 30.95 31.13

Bit-invertedGrayCodedBit-planeMatchingforLowComplexityMotionEstimation

233

similar characteristics with the output of the SSD.

Experimental results show that the proposed

algorithm outperforms other BPM based ME

algorithms while preserving the binary matching

characteristic.

ACKNOWLEDGEMENTS

This research was supported by the MSIP (Ministry

of Science, ICT & Future Planning), Korea, under

the "Establishing IT Research Infrastructure

Projects" supervised by NIPA (National IT Industry

Promotion Agency) (I2221-14-1005).

REFERENCES

Li, W., Salari, E., “Successive elimination algorithm for

motion estimation,” IEEE Trans. Image Process., vol.

4, no.1, pp. 105-107, Jan. 1995.

Choi, C., Jeong, J., “New sorting-based partial distortion

elimination algorithm for fast optimal motion

estimation,” IEEE Trans. Consumer Electron., vol. 55,

no. 4, pp. 2335-2340, Nov. 2009.

Natarajan, B., et al, “Low-complexity block-based motion

estimation via one-bit transforms,” IEEE Trans.

Circuits Syst. Video Technol., vol. 7, no. 5, pp. 702-

706, Aug. 1997.

Erturk, A., Erturk, S., “Two-bit transform for binary block

motion estimation,” IEEE Trans. Circuits Syst. Video

Technol., vol. 15, no. 7, pp. 938-946, July 2005.

Celebi, A., et al, “Truncated Gray-coded bit-plane

matching based motion estimation method and its

hardware architecture,” IEEE Trans. Consumer

Electron., vol. 55, no. 3, pp. 1530-1536, Aug. 2009.

Celebi, A., et al, “Bit plane matching based variable block

size motion estimation method and its hardware

architecture,” IEEE Trans. Consumer Electron., vol.

56, no. 3, pp. 1625-1633, Aug. 2010.

Choi, C., Jeong, J., “Enhanced two-bit transform based

motion estimation via extension of matching

criterion,” IEEE Trans. Consumer Electron, vol. 56,

no. 3, pp. 1883-1889, Aug. 2010.

Gullu, M., “Weighted constrained one-bit transform based

fast block motion estimation,” IEEE Trans. Consumer

Electron., vol. 57, no. 2, pp. 751-755, May 2011.

Ko, S.-J., et al, “Fast digital image stabilizer based on

Gray-coded bit-plane matching,” IEEE Trans.

Consumer Electron., vol. 45, no. 3, pp. 598-603, Aug.

1999.

Baek, Y., et al, “An efficient block matching criterion for

motion estimation and its VLSI architecture,” IEEE

Trans. Consumer Electron., vol. 42, no. 4, pp. 885-

892, Nov. 1996.

Choi, C., Jeong, J., “Constrained two-bit transform for low

complexity motion estimation,” International

Conference on Consumer Electronics, ICCE 2013, Las

Vegas, USA, Jan. 2013.

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