A Levy Flight Firefly Optimizer based Piecewise

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I. INTRODUCTION. Remotely sensed digital imagery when captured in presence of ..... [20] R. C. Gonzalez and R. E. Woods, Digital Image Processing, 4th ed.
A Levy Flight Firefly Optimizer based Piecewise Gamma Corrected Unsharp Masking Framework for Satellite Image Enhancement Himanshu Singha, Anil Kumarb and L. K. Balyanc Indian Institute of Information Technology Design and Manufacturing, Jabalpur-482005, India a [email protected], [email protected] and [email protected] Abstract—In this paper, an efficiently modified lévy-flight based biologically inspired firefly optimizer is employed in association with a novel optimally weighted piecewise gamma corrected unsharp masking framework for imparting overall quality improvement of remotely sensed dark satellite images. The key intelligence is to utilize a weighted summation of intensity as well as texture based enhancement along with an efficiently defined cost function. The cost function is framed such that more and more intensity span can be explored in a positive manner. Here, the unsharp masking takes care for enhancing the high frequency content of the images. In association with it, piecewise gamma correction is also imparted to enhance the intensity channel of the input image. Rigorous experimentation is executed by employing the performance evaluation and comparison with pre-existing recently proposed and highly appreciated quality enhancement approaches. Keywords—Remotely sensed images; intensity span maximization; unsharp masking; piecewise gamma correction; Lévy-flight firefly optimization; image quality enhancment.

I.

INTRODUCTION

Remotely sensed digital imagery when captured in presence of unfavorable and poorly illuminated circumstances usually requires a lot of optimal and highly adaptive pre-processing for enhancing the intrinsic quality of the captured image. Usually, such images are categorized as remotely sensed dark images, and hence, conventionally proposed quality enhancement approaches sometimes do not supports the reliable and robust quality enhancement especially for dark images [1]. The importance of remotely acquired data is always very high irrespective of the domain of application. Most of the technological human welfare advancements in various domains of geoscience, astronomy, defense applications, agriculture, mining, weather forecasting, vegetation density analysis, etc., usually rely on remotely acquired captured information in one form or the other [2]. In addition to the other kind of constraints, dynamic capturing range limitation of the image acquisition device as well as other kind of hardware limitations of the imaging devices, also lead to the poorly captured images. Wide variety of histogram based as well as transform-domain based methodologies has been already available in literature for general images [3-19]. Initially, general histogram equalization (GHE) approach [20] has been introduced, and later onwards, its various variants have been proposed by various researchers. In the same

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context, necessity of localized processing seems more aspiring and hence various sub-equalization inspired histogram based enhancement approaches have been also proposed. A detailed literature analysis in this context is also available in [1]. Significant contributions like contrast-limited adaptive HE also dragged the core attraction of the researchers. Statistical segmentation based sub-equalization like median-mean based sub-image clipped HE (MMSICHE) [21] has been also introduced. Later on, the averaging histogram equalization (AVGHEQ) [22]; HE based optimal profile compression (HEOPC) [23] method for color image enhancement followed by HE with maximum intensity coverage (HEMIC) [24] have been also proposed. Also, the adaptive gamma correction with weighting distribution (AGCWD) [25] and its efficient variations [26-28] have been also proposed for dark images. Afterwards, the intensity and edge based adaptive unsharp masking filter (IEUMF) [29] based enhancement has been also proposed by employing the unsharp masking filter for edge augmentation. Recently, a piecewise gamma corrected HE (PGCHE) [1] is also proposed for dark image enhancement. Here, the piecewise gamma correction is optimally associated with unsharp masking, and consequently an efficiently improved intensity as well as texture based quality enhancement approach is presented with proper restoration of the high frequency content of the images. The rest of the content is organized as: Section II deals with the problem formulation followed by the proposed methodology in Section III. Experimentation is discussed in Section IV and finally, conclusion is drawn in Section V. II. PROBLEM FORMULATION In spite of conventionally embraced histogram sub-division approaches, here, an optimally framed highly robust, weighted distributed methodology is applied is this work. Although cumulative distribution based gamma correction is highly appreciated, but for dark images and to resolve the oversaturation, over enhancement and non-uniform or unbalanced enhancement type issues, piecewise gamma corrected HE approach is found more suitable. Also, high frequency content of the image like edges are not supported in AGCWD as well as PGCHE; and hence unsharp masking can be integrated in an optimal fashion by employing an intensity span maximization inspired entropy based cost function when associated with an efficiently framed lévy-flight firefly optimizer [30].

III.

PROPOSED METHODOLOGY

Parallel band processing is generally required for multiband images, but for enhancing equivalent color images, HueSaturation-Intensity (HSI) model can be applied to decouple the chromatic and non-chromatic information content, as [1]: HSI [ H ( m,n) ,S ( m,n ) ,I ( m,n )]T = TRGB [ R ( m,n ) ,G ( m,n ) ,B ( m,n )]T , (1)

HSI Here, TRGB is RGB to HSI transformation process. The color image enhancement can be done by enhancing only the luminance intensity values, keeping rest (hue and saturation) values preserved, followed by linear stretching. The gamma compressed interim intensity channel can be evaluated as [1]:

γ

I gcp = ( I in ) ,

γ >1,

(2) The corresponding gamma expanded interim intensity channel can be evaluated as [1]: 1γ

I gex = ( I in )

γ >1,

(3) The unsharp masking filter based sharpened interim intensity channel (UMF) can be evaluated as: (4) I umf = I in + η .ξ .I f , ,

analytically is [α , β ,γ ,η ] ← [( 0 ,1) , ( 0 , 5 ) , (1, 5 ) , ( 0 , 2 )] . Following the fundamental bio-luminance based signaling behavior behind fire-flies and consequently for analogous optimal idealized formulation of the flashlight, the prime objective can be resolved easily. The core idealization rules when integrated with levy flight (due to its heavy-tailed probability distribution behavior) results into more efficient and highly converging approach due to randomization approach. The luminance intensity variation and consequent mutual attraction among the flies mainly decides the core efficacy of the FA; both of these issues are inter-separation distance dependent. Attractiveness ( β ) and luminance are highly correlated and hence minimization problem can be framed choosing relative β as a monotonically reducing expression as [30]:

Here, I f mainly comprises of edges, obtained by convolutional filtering with mask ( H ) as follows: I f = Iin ⊗ H , § −1 −1 −1· 1¨ ¸ H= ¨ −1 8 −1¸ , 8¨ ¸ © −1 −1 −1¹

m

( m ≥ 1) ,

β (r ) = β0 e−τ r ,

(11)

→ 1 as k → ∞ , if τ is kept fixed Characteristic length, Γ = τ and initial value can be typically taken as τ = Γ − m , Considering the locations xi , x j for flies i, j , the spatial distance can be evaluated as [30]: −1 k

(5)

rij  x i − x j =

d

(x δ − x δ ) ¦ δ i,

2

j,

(12)

,

=1

(6)

Here, xi ,δ is the δ th element of the i th firefly’s spatial-position

In addition, η stands for augmentation constant here, while the

x i . Drifting of i th fly towards more attractive j th fly can be characterized as [30]:

hyperbolic gain curve profile (ξ ) can be framed as: ξ = 0.5 ª¬1 + tanh ( 3 − 6 ( Iin − 0.5 ) ) º¼ ,

(7) Later on, weighted summation input intensity channel with uniformly equalized intensity channel ( Iˆ en ) can be obtained as: § α · § 1−α · § β · Iˆen = ¨ ¸ I gcp + ¨ ¸ I gex + ¨ ¸ Iumf , © 1+ β ¹ © 1+ β ¹ © 1+ β ¹

(8)

Here, while evaluating I umf , unfortunately over-ranging may get resulted, and it should be minimized efficiently without affecting the resulted enhancement and hence it can be included as a penalty term in the cost function framed here, as: §σ 2 · § n · J = H .Δσ 2 .¨ ¸ .¨1 − ov ¸ , (9) © μ ¹ © M*N¹ Here, μ ,σ 2 , Δσ 2 and H stands for output brightness, contrast, relative contrast, and output Shannon entropy, respectively for an L-bit, M * N image. Here, nov is the count of the normalized over-ranged pixels, which can be evaluated as: (10) nov = ¦ {imn < 0 * imn > 1}, Cost-function is devised here, so that the relative variance along with maximal information restoration can be imparted with proper check on relative mean brightness. Biologically inspired and later on efficiently modified Lévy-flight Firefly Algorithm (LFA) is employed here for optimal enhancement for dark images by efficient exploration, followed by generous exploitation in a four-dimensional search space so that the required optimal values for α , β ,γ , and η can be obtained. The efficient parametric variation for framing search space derived

xi = xi + β 0e−τ r ( x j − xi ) + ξ .sign ª¬rand ( 0,1) − 0.5º¼ ⊕ Le′vy, (13) 2

Here, attraction and randomization (ξ ) collectively constitutes the updating expression. Last term directs the randomly directed, random step size decided by Le′vy distribution (with mean and variance → ∞ ) as [30]: (14) Le′vy  u = t − λ , (1 < λ ≤ 3 ) , Hence, finally the above mentioned heavy tailed power-law intuitively adds the more efficient random walk process in firefly motion. Finally, optimally enhanced channel is obtained and hence, correspondingly enhanced color image can be derived as [1]: 





[ R ( m,n ) ,G ( m,n ) ,B ( m,n )]T = T

RGB HSI

T

ª H ( m,n ) ,S ( m,n ) , I ( m,n ) º¼ , ¬

(15)

RGB Here, THSI is HSI to RGB transformation process.

IV.

EXPERIMENTATION AND RESULT ANALYSIS

A. Assessment Criterion Experimentation and comparison is done qualitatively for resultant images [31-32] and for further quantitative assessment, performance metrics such as brightness (B), contrast/variance (V), entropy (H), sharpness (S), and colorfulness (C) for comparison among state-of the-art methods are employed, here.

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(1i) (2i) (3i) (4i) (5i) (6i) Fig. 1. Visual evaluation with comparison among 1a-6a: input images [31-32]; 1b-6b: GHE [20]; 1c-6c: MMSICHE [21]; 1d-6d: AVGHEQ [22]; 1e-6e: AGCWD [25]; 1f-6f: HEOPC [23]; 1g-6g: HEMIC [24]; 1h-6h: IEUMF [29]; and 1i-6i: the proposed approach.

Table I. Quantitative evaluation with comparison among input images [31-32], GHE [20], MMSICHE [21], AVGHEQ [22], AGCWD [25], HEOPC [23], HEMIC [24], IEUMF [29], and the proposed approach using metrics termed as Brightness, Contrast, Entropy, Sharpness and Colorfulness. S. No.

1.

2.

3.

4.

5.

6.

INDICES

INPUT

GHE

MMISCHE

AVGHEQ

AGCWD

HEOPC

HEMIC

IEUMF

OURS

Brightness Contrast Entropy Sharpness Colorfulness

0.2573 0.0304 6.8359 0.299 0.1264

0.5004 0.0859 7.2603 0.513 0.267

0.2955 0.0596 7.0938 0.3982 0.1352

0.3193 0.0492 7.0964 0.3803 0.156

0.4243 0.063 7.1282 0.4353 0.2267

0.3220 0.0461 6.9724 0.3694 0.1600

0.3849 0.052 7.2701 0.4034 0.2016

0.3237 0.0501 7.0812 0.4620 0.1592

0.4170 0.0781 7.3812 0.6123 0.2203

Brightness Contrast Entropy Sharpness Colorfulness

0.1060 0.0076 5.5645 0.2513 0.0489

0.5019 0.0846 6.7583 1.0145 0.2549

0.1573 0.0408 6.0061 0.4821 0.0652

0.1253 0.0120 5.7490 0.3180 0.0572

0.3337 0.0655 6.5470 0.8437 0.1586

0.1294 0.0102 5.7736 0.2956 0.0602

0.2186 0.015 6.3054 0.4060 0.1113

0.1400 0.0191 5.8876 0.4206 0.0619

0.4113 0.0753 6.9112 0.9817 0.2265

Brightness Contrast Entropy Sharpness Colorfulness

0.2232 0.0440 5.9635 0.6581 0.1328

0.5260 0.0669 6.3469 0.8567 0.3077

0.2581 0.0723 6.3378 0.8033 0.1481

0.2893 0.0421 7.2381 0.5041 0.1615

0.3759 0.0855 6.1279 0.9919 0.2414

0.2651 0.0355 7.1482 0.5082 0.1497

0.3477 0.0485 7.3685 0.5637 0.1984

0.3006 0.0621 7.2859 0.7700 0.1827

0.4318 0.1402 7.3754 1.2567 0.3098

Brightness Contrast Entropy Sharpness Colorfulness

0.3519 0.0094 6.8800 0.2415 0.2126

0.5010 0.0859 7.2077 0.7182 0.3204

0.3787 0.0339 7.0756 0.4474 0.2288

0.6367 0.0544 7.6275 0.5638 0.3684

0.5218 0.0345 7.2984 0.4524 0.3169

0.4485 0.0183 7.2257 0.3370 0.2687

0.528 0.0294 7.4517 0.4254 0.3135

0.4671 0.0573 7.5047 0.8688 0.2950

0.5240 0.0687 7.5411 1.0021 0.4848

Brightness Contrast Entropy Sharpness Colorfulness

0.0612 0.0071 3.0107 0.2812 0.0875

0.6079 0.0322 3.8806 0.6202 0.5103

0.1259 0.0542 3.2498 0.6980 0.2138

0.2692 0.1188 3.3540 1.1706 0.3768

0.1820 0.0415 3.2902 0.7130 0.2425

0.1235 0.0281 3.8289 0.5694 0.1658

0.4127 0.0433 4.4715 0.6471 0.4550

0.1234 0.0305 3.3400 0.5945 0.1703

0.3021 0.0624 4.6812 0.9678 0.3427

Brightness Contrast Entropy Sharpness Colorfulness

0.1446 0.0320 5.2964 0.4526 0.1228

0.5260 0.0668 6.1069 0.8683 0.3483

0.1752 0.0569 5.6815 0.5610 0.1602

0.1939 0.0570 5.4922 0.6203 0.1672

0.3186 0.0765 5.7146 0.9196 0.2513

0.1811 0.0489 5.5860 0.5558 0.1521

0.4248 0.0501 6.3627 0.6105 0.2781

0.1871 0.0569 5.4880 0.6660 0.1618

0.3919 0.0766 6.3654 0.9751 0.3694

B. Qualitative Assessments For explicit analysis, reimplementation for various recent state-of-the-art methodologies (namely, GHE, MMSICHE, AVGHEQ, AGCWD, HEOPC, HEMIC, and IEUMF) has been done. Visual results for all enhanced images are shown in Fig. 1. C. Quanitative Assessments For explicit quantitative comparison and evaluation, relevant image performance metrics have been evaluated and listed in Table I.

V.

CONCLUSION

As a concluding remark, it can be explicitly identified that the proposed approach is highly suitable for overall quality enhancement for remotely sensed dark images. The edge sharpening along with piecewise gamma correction using the complementary dual-inverse optimally evaluated gamma values. The entire weighted summation framework leads to optimal involvement of exponential, linear, convolutionalfiltering and statistical operations for mapping which is intuitively governed by highly efficient exploration as well as

exploitation following the biologically inspired Lévy-flight Firefly Algorithm (LFA). Although the approach is some-how iterative, but the associated robustness and it’s highly adaptive behavior counter-balances for that. Highly relevant performance metrics are evaluated for proper image quality evaluation and consequently the outperformance of the proposed framework can be easily highlighted in addition to the qualitative evaluation through visual results. REFERENCES [1]

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