Cuckoo Search Optimizer based Piecewise Gamma

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Satellite digital imagery along with its sister applications related to remotely sensed ..... [20] R. C. Gonzalez and R. E. Woods, Digital Image Processing, 4th ed.

Cuckoo Search Optimizer based Piecewise Gamma Corrected Auto-clipped Tile-wise Equalization 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—An efficient optimally weighted framework for piecewise gamma corrected adaptively clipped sectional equalization for overall quality improvement of remotely sensed dark satellite images, is proposed here. In association with it, cuckoo search based biologically inspired optimizer is employed here due to its remarkably attractive exploration and exploitation policies. Tile-wise equalization and associated optimal clipping leads to adaptively equalized interim intensity channel. Piecewise gamma correction using reciprocal gamma values those are derived optimally. Entire allowable intensity span must be exploited so that the count of the void bins can be reduced and hence, cost function is framed by introducing this void-bin count as a penalty term along with desired assurance for entropy as well as contrast enhancement. Rigorous experimentation is executed by employing the performance evaluation and comparison with pre-existing recently proposed and highly appreciated quality enhancement approaches. Keywords—piecewise gamma correction; tile-wise equalization; optimal clipping; cuckoo search optimization; remotely sensed images; image quality enhancment.



Satellite digital imagery along with its sister applications related to remotely sensed imagery such as scientific anthropological innovations in various sectors of geoscience, astronomy, defense applications, agriculture, mining, weather forecasting, vegetation density analysis, etc., usually rely on the quality and reliability of the captured images so that they can be further relevantly processed [1]. Due to the hardware challenges of the capturing circuitry along its desirable position and unfavorable climatic circumstances, most the times, the acquired images are not up to mark and hence preprocessing is essentially required so that desired quality enhancement can be imparted [2]. Various histogram-based, transform-domain based as well as spatial-domain based strategies [3-19] (involving various kinds of intelligence) have been suggested till date for enhancing the visual intensity and gradient based features of the image. Earlier, general histogram equalization (GHE) [20] based enhancement is initially coined for imparting uniform probability distribution. Later onwards, multiple histogram sub-division and local equalization based methods have been also proposed for enhancement of general images. A complete descriptive analysis for these methods is already mentioned in the literature [1]. Various significant contributions like contrastlimited adaptive HE [21] also fascinated the researchers.

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Intensity level based segmentation and consequently subequalized approaches like median-mean based sub-image clipped HE (MMSICHE) [22] has been also suggested. In the same sequence, the averaging HE (AVGHEQ) [23] and later onwards, HE based optimal profile compression (HEOPC) [24] has been proposed for color image enhancement. Focusing on allowable intensity span expansion through count reduction of void intensity bins for color image enhancement has been proposed under the head of histogram equalization with maximum intensity coverage (HEMIC) [25]. For general images, these techniques seem sound; but without imparting gamma correction, it is very tough to impart quality improvement for dark images. Earlier, the adaptive gamma correction with weighting distribution (AGCWD) [26] is introduced, but sometimes leads to the regional over-saturation due to nature of its transformation curve and hence, improved versions [27-29] also came to the existence. Other better proposals have been also drafted like the intensity and edge based adaptive unsharp masking filter (IEUMF) [30] by employing the unsharp masking filter which can be further utilized as edge augmentation for imparting overall enhancement. Recently, a piecewise gamma corrected HE (PGCHE) has been also proposed for dark image enhancement. In this paper, a cuckoo search optimizer [31] based piecewise gamma correction is optimally associated with tile-wise equalization followed by adaptive clipping. Remaining content is organized as: Section II presents the core problem formulation. The proposed methodology is available in Section III. Experimentation is discussed in Section IV and finally, conclusion constitutes the Section V. II. PROBLEM FORMULATION Unlike the conventionally appreciated histogram-division based image enhancement methods, here, the authors have drafted an optimal weighted summation framework for imparting an efficient improvement over their self-proposed PGCHE which is a competent way for imposing gamma correction for remotely sense dark images, by employing an intensity span maximization inspired entropy based cost function when associated with an efficient cuckoo search optimizer. In spite of involving the GHE based uniformly distributed interim intensity channel, here, in this work, the contextually clipped and tile-wise adaptively equalized interim intensity channel is efficiently incorporated. In this way, more adaptive and a very robust mechanism is suggested, here.

An L-bit image (with histogram hi , j ( k ) containing M × N pixels having 2 L − 1 intensity levels can be equalized and mapped using its corresponding CDF as: ( 2 L − 1) . n h k ,where,k ∈ ª 0 , 2 L − 1º , (2) fi , j ( n ) = ¦ i, j ( ) ¬ ¼ M * N k =0 This uniformly distributed output fi , j ( n ) suffers from nonuniform regional contrast enhancement; and therefore, histogram clipping is required so that high frequency bins may not influence their nearby intensity bins. Normalized clipping limit (η ) in range (0.01, 0.5) is to be optimally evaluated.

Fig. 2. (a) IR region along with its corresponding nearest neighborhood, (b) Inter-spatial relationship for neighborhood modeling of first quadrant.

Fig. 1. Tile-wise symmetric distribution pattern.



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:

[ H ( m,n ) ,S ( m,n ) ,I ( m,n )]T HSI TRGB

= TRGB [ R ( m,n ) ,G ( m,n ) ,B ( m,n )] , HSI



Here, stands for typical RGB to HSI transformation. Enhancement for color images is usually planned through intensity values transformation, by keeping rest of the (hue and saturation) channels preserved as such. After employing linear stretching, the entire intensity matrix is divided into various uniformly sized matrices. In other words, multiple uniformly sectioned non-overlapping tiles are obtained from the main image. This partition is governed by image division into three kinds of regions: corner regions ( CRs ) , border regions ( BRs ) , and inner regions ( IRs ) , and hence, any M × N image, can be sectioned into 4 similar CRs; 2 × ( M + N − 4 ) similar ERs and remaining ( M − 2 ) × ( N − 2 ) similar IRs. Aforementioned division can be explicitly identified from Fig. 1. Subsequently, histogram evaluation followed by optimal clipping, and then separate histogram equalization is performed. Later on, individual cumulative distribution functions ( CDF ) have been evaluated, so that the mapping curves can be derived. Here, mapping curves are derived by a linear combination of nearest four surrounding regions. Here, mapping approach for IR regions, is typical and straight forward, while for CR and BR regions, special approaches have to be employed. Further, the contrast enhancement has to be imparted; and hence, intensity values can be non-linearly mapped to enhance the average standard deviation along with positive mean shift.

Fig. 3. (a) BR region along with its corresponding nearest neighborhood, (b) Inter-spatial relationship for neighborhood modeling of second quadrant.

Fig. 4. Inter-spatial relationship for neighborhood modeling of extreme CR.

For IR regions as shown in Fig. 2, each quadrant region has been mapped based on its four nearest neighboring regions; and hence, mapping function for pixels in ( i, j ) region is

represented by f ( .) , then new pixel p can be evaluated as [21]: i, j

pIR =

· s § y x fi −1, j −1 ( pold ) + fi , j −1 ( pold ) ¸ ¨ r+s© x+ y x+ y ¹

· r § y x fi −1, j ( pold ) + fi , j ( pold ) ¸ , + ¨ r+s© x+ y x+ y ¹


Following similar and analogous approach for BR group, where neighborhood structure is slightly different due to obvious reasons as shown in Fig. 3. Similar kind of mapping transformation can be designed for corner regions as shown in Fig. 4. The mapping relation can be derived as [21]: s r (4) pBR = f i , j −1 ( pold ) + f i , j ( pold ) , r+s r+s In context of IR and BR groups, 4th quadrant’s neighborhood structure is exactly similar to IR regions, and similarly 2 nd and 3rd quadrants have similar kind of neighborhood same as BR group. Remaining pixels in first quadrant region can be mapped in simple way as conventional mapping; and hence, can be simply transformed as [21]: pCR = f i. j ( pold ) , (5) Hence, finally optimally clipped sectionally (tile-wise) equalized interim image ( I SEQ ) can be derived as a collective constructive contribution of (4-6) as: I SEQ = pIR * pBR * pCR ,


The gamma compressed interim intensity channel can be evaluated as [1]: γ (7) I GCP = ( I IN ) , γ >1, The corresponding gamma expanded interim intensity channel can be evaluated as [1]: 1γ (8) I GEX = ( I IN ) , γ >1, 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 + ¨ ¸ I SEQ , 1 β 1 β + + © ¹ © ¹ © 1+ β ¹


Here, while evaluating IˆEN , the count of void bins 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 · § k0 · J = H .Δσ 2 .¨ ¸ .¨ 1 − L ¸, © μ ¹ © 2 −1¹ 2


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, the count of empty bins in the enhanced image can be obtained as: (11) k 0  ¦ {hˆ ( i ) = 0}, Here, hˆ ( i ) stands for histogram of the processed image. Costfunction 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 optimal enhancement for dark images, by efficient exploration followed by generous exploitation in a threedimensional search space so that the required optimal values for α , β , and γ can be obtained. The efficient parametric variation for framing search space derived analytically is [α , β ,γ ] ← [( 0 ,1) , ( 0 , 5 ) ,(1, 5 )] . Aggressive psychology of the

cuckoo bird, and its interesting breeding behavior (more specifically, its brood parasitism) of the cuckoo bird fascinated various researchers to frame an analogously designed population oriented metaheuristic optimization algorithm. CSOA is highly appreciable for resolving multimodal, multiobjective, and highly non-linear optimization issues deprived of any kind of exhaustive search. Core structure for CSOA and its problem solving strategy in its original form has been already elaborated in [27]. Following the Lévy distributed quasi-random flight; a suitable intelligence has been also introduced, where the succeeding step has to be decided by keeping “current location” and “next-state transition probability” in the mind. This type of step flight pattern is highly compatible and profitable with CSOA behaviour. Simplified analogous behavioural modelling has been done by imposing three rules, as already existed in the relevant literature. Lévy distributed flight is generally for both local as well as global exploration of the corresponding search space. Lévy flight for iterative new solution xt +1 for the i th cuckoo can be drafted as [27]: (12) xit +1 = xit + ∂ ⊕ Lévy ( β ) , where, ∂ > 0 , Here, entry-wise walk during multiplications can be indicated through product operation ⊕. Random exploration follows Lévy distributed (having both first as well as second moment infinite) random step size, as [27]: (13) Lévy  u = t − λ , ∀ λ ∈ (1,3] , This power law step-flight distributed random walk leads to debut for a few new solutions in the vicinity of best solution (identified so far), and in this manner local search can be speed up. In addition, a generous share of new solutions should be created through far-field randomization, so that the local trapping can be avoided and global exploration can be encouraged. Finally, enhanced channel is obtained and hence, correspondingly enhanced color image can be derived as: 

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



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


RGB Here, THSI is HSI to RGB transformation process.



A. Assessment Criterion Experimentation and comparison is done qualitatively for resultant images [32-33] 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. B. Qualitative Assessments For explicit analysis, reimplementation for various recent state-of-the-art methodologies (namely, GHE, MMSICHE, AVGHEQ, AGCWD, HEOPC, HEMIC and IEUMF) is followed by comparative evaluation. Visual results for all enhanced images are shown in Fig. 1.

















































(1i) (2i) (3i) (4i) (5i) (6i) Fig. 1. Visual evaluation with comparison among 1a-6a: input images [32-33]; 1b-6b: GHE [20]; 1c-6c: MMSICHE [22]; 1d-6d: AVGHEQ [23]; 1e-6e: AGCWD [26]; 1f-6f: HEOPC [24]; 1g-6g: HEMIC [25]; 1h-6h: IEUMF [30]; and 1i-6i: the proposed approach.

Table I. Quantitative evaluation with comparison among input images [32-33], GHE [20], MMSICHE [22], AVGHEQ [23], AGCWD [26], HEOPC [24], HEMIC [25], IEUMF [30], and the proposed approach using metrics termed as Brightness, Contrast, Entropy, Sharpness and Colorfulness. S. No.

















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

0.3994 0.0779 7.3601 0.5112 0.2301

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

0.3909 0.0721 6.8232 0.8747 0.1965

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

0.4316 0.1329 7.3112 1.2421 0.2821

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

0.4784 0.0631 7.5132 0.9103 0.9112

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

0.2196 0.0559 4.6070 0.8997 0.3135

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

0.3912 0.0721 6.1742 0.8457 0.3732


C. Quanitative Assessments For explicit quantitative comparison and evaluation, relevant image performance metrics have been evaluated and listed in Table I. V.




At last, while framing a concluding note, it can be easily noticed that the optimally weighted piecewise gamma correction explicitly outperforms over the other state-of-the-art methodologies, when applied through deriving adaptively clipped tile-wise equalized, interim intensity channel. Conventionally, the globally equalized, interim intensity channel is proposed for the same purpose, but based on this experimentation; adaptively clipped tile-wise equalization has its noteworthy implications especially when employed in association with the cuckoo search optimizer which itself is also very well appreciated in the literature. A very relevant set of performance metrics is utilized here for sketching the quantitative as well as qualitative evaluation and comparison for various remotely sensed dark satellite images.






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