An Image Retargeting Scheme with Content-based Cropping and Local Significance Aware Seam Carving

Transcription

1 Proceeding of APSIPA Annual Summit and Conference December 2015 An Image Retargeting Scheme with Content-baed Cropping and Local Significance Aware Seam Carving Po-Chyi Su, Yung-Chieh Chou Dept. of Computer Science and Information Engineering National Central Univerity, Jhongli, Taiwan Abtract Thi reearch preent an image retargeting cheme coniting of two main operation, the content-baed cropping and eam carving, to modify the width/height of imagery data. The eam carving i firt employed to remove inignificant pixel in the middle part of image. The election of eam i baed on the gradient in one direction and local energy to avoid obviou ditortion. When the background tend to be uniform, ome eam can be inerted in a imilar way to make the apect ratio cloer to the target one. The content-baed cropping that conider the viual aliency i then applied to remove boundarie. The final image i formed by caling directly if neceary. The experimental reult will demontrate the advantage of the propoed method. I. INTRODUCTION iual media retargeting draw a lot of attention in recent year becaue of it ability to adapting the reolution of image or video frame to the diplay facilitie in a flexible manner. Unlike directly caling the imagery data to obtain the target apect ratio, content-baed retargeting method can proce the region of an image in different way uch that the nonuniform caling can be achieved to make the image fit the required ize. The methodologie of retargeting can be claified into four categorie: content-baed cropping, eam carving, warping, and the ue of multi-operator. The contentbaed cropping can determine the region of interet in an image by content analyi to remove inignificant boundarie [3][9][10][11]. The method of warping impoe a et of grid on the image and adjut the grid non-uniformly to achieve the global optimization baed on certain ditortion meaurement [4][17]. The gradient, viual aliency, face detection and even motion can be ued to evaluate the importance of grid and different kind of warping can be applied accordingly. Avidan and Shamir [13] propoed the idea of eam carving for till image. By ucceively removing the eam with the minimum energy or aliency in the image, important area can be better preerved. Mot of the change are made in uniform area o that le evere ditortion will be introduced. Rubintein et al. propoed an improved eam carving method and extended the technique to video [5]. The lookingforward energy help to reduce the dicontinuou eam. Grundmann et al. propoed a dicontinuou eam carving method to prevent the moving object in conecutive frame from being affected by the eam carving proce [8]. Domingue et al. propoed the idea of tream carving to remove multiple eam at the ame time [2]. The reulting hole will be fixed by image inpainting. The face and line detection are employed to further reduce poible ditortion. Multi-operator method combine different approache to purue more atifactory reult. Hua et al. employed Scale Invariant Feature Tranform (SIFT) to evaluate the difference between the quality before and after retargeting o that a more uitable termination of eam carving can be decided [14]. Rubintein et al. defined Bi-Directional Warping to evaluate the quality [6]. The propoed method chooe one operator from cropping, eam carving and caling baed on the evaluation to achieve good retargeting reult. The drawback i the peed ince the quality evaluation ha to be applied in each tep. Luo et al. propoed Accumulated Energy Seam Carving to improve the ingle-direction modification o that the reulting image can maintain a cloer reolution to the targeted one [15]. Dong et al. combined eam carving and caling baed on the difference meaurement and dominating color decriptor [7]. Dong et al. further propoed an energy function to peed up the proce but the complexity will till be increaed if more operator are ued [16]. It hould be noted that cropping i alway an effective way to remove inignificant boundarie of image ince mot of the region of interet are located at the center. The viual aliency in an image ha to be evaluated to determine the area to be cropped off. If the aliency can be calculated efficiently, content-baed cropping can be applied without a lot of computation. The rik of cropping i that important object located near the boundarie may be affected. The technique of eam carving can help to compenate the deficiency of cropping to remove inignificant pixel in the middle part of an image. If taking them off in an imperceptible way i achievable, the cropping, which follow the operation of eam carving, can have a better chance of preerving the important viual content. However, eam carving i often criticized for it negative impact on image quality. The reulting ditortion may appear in everal part of an image when eam carving i the only tool for retargeting. Thi reearch propoe an image retargeting cheme employing both cropping and eam carving to exploit their advantage. The eam carving i applied according to the meaurement of pixel energy, which i calculated baed on the gradient in one direction and the dicontinuity of adjacent pixel. The global eam energy will help to elect a eam to carve while the local energy decide whether a eam i kept or the whole operation ha to be terminated. The trategy of checking the local energy i to avoid generating obviou ditortion, which may appear at mall pot of an image but caue unpleaant viual effect. Some eam can be further added or inerted in the uniform background in a imilar way to make the apect ratio cloer to the target one. After the APSIPA 643 APSIPA ASC 2015

2 Proceeding of APSIPA Annual Summit and Conference December 2015 viual aliency i evaluated, the content-baed cropping i then applied accordingly to preerve region of interet in the image. The final tep i the normalization tep that directly cale the image to the required ize. The ret of the paper i organized a follow. Sec. II will detail the propoed algorithm and ome experimental reult are demontrated in Sec. III, followed by the concluion in Sec. I. II. THE PROPOSED SCHEME A. Seam Carving To apply eam carving, an energy function i defined for identifying the importance of pixel. Given a required image or frame reolution, if the apect ratio i maintained, caling with delicate interpolation yield good reult. The conidered cenario i thu the change of apect ratio and only one direction, either width or height, will be modified. Without lo of generality, the modification of width i taken into account in thi paper. Given an image, I, with N row and M column, the vertical eam i defined a S v N = { y ( x)} = 1, y ( x) y ( x 1) 1, (1) x A vertical eam i thu an eight-neighbor connected path of pixel in the image from top to bottom, containing only one pixel in each row of the image. Removing the pixel of a eam will make the pixel on the right-hand ide hift left by one poition to compenate for the miing path. The pixel on a eam in an image can be expreed a N I { I( y ( x))} x= 1 = (2) When a eam i carved, only a mall portion in an image will be affected. The election of eam to carve i baed on the importance of pixel. Given the energy of a eam i E(I ), we will elect the bet eam S* uch that the energy from uch a eam carving i the minimum, i.e., S = min{ E( I )} (3) * The calculation i performed via the dynamic programming. From the econd row to the lat row of an image, all the energy value are accumulated by M ( x 1, y 1) M = e( + min M ( x 1, (4) M ( x 1, y + 1) where e( i the energy of the pixel ( and M i the cumulative minimum energy. After calculating all the energy value according to (4), we trace back from the lat row with the minimal energy and then elect the recorded path. The reulting eam i choen and removed. There are a few way of calculating the energy function. Some complicated calculation may include advanced aliency etimation, egmentation or face detection. In [13], a very imple energy function meaured by the magnitude of derivative i adopted, i.e., e ( I ) = I + I = G R + G C. (5) x y It i worth noting that computing the gradient i efficient and the reulting eam can alo perform quite naturally in image. On the other hand, advanced energy function conidering viual aliency certainly help the elected eam to avoid important object in an image. However, according to our obervation, viual aliency in an image uually how uniform area or region. Adjacent eam may travere along the ame direction to ecape a certain important object, which can make the adjacent area around the object look abnormal. Therefore, the propoed cheme till adopt the magnitude of gradient a the energy function but trie to achieve the balance between the number of carved eam and the image quality. Since only the modification of width i conidered and vertical eam are needed, the energy function for eam carving in the propoed cheme i the column gradient, i.e., e ( I ) = I = G C. (6) y On the other hand, when the horizontal eam are required, the conidered energy function will be e H, taking account of the row gradient only. The reaon of uch a choice i to try increaing the number of eam that are allowed to form without eriouly affecting the image quality. An obviou example i to accept a vertical eam to pa through a horizontal line, which ha a trong e H but a weak e. Seriou ditortion eldom appear ince taking a pixel away till reult in a traight line after hifting other pixel horizontally. In addition to the gradient, the continuity between pixel value i alo conidered in meauring the energy. Aume that I(, I(y+1) and I(y+2) are the concatenated pixel in the ame row and I(y+1) i a pixel of a choen eam. After I(y+1) i taken off, I( and I(y+2) are adjacent to each other. The energy of I( will be increaed by S C, which i conidered a penalty for linking the pixel that were not neighbor. S C can be divided into S H (horizontal penalt and S (vertical penalt. In the previou example, S H of I( or I(y+2) i equal to I(-I(y+2). For S, if I( remain in the image but it upper or lower neighbor i removed due to the eam carving proce, the energy of I( ha to be adjuted. If the upper neighbor become I(x-1,y-1) (or I(x- 1,y+1)), intead of I(x-1,, the additional penalty will be I(-I(x-1,y-1) (or I(-I(x-1,y+1) ). Similarly, the lower neighbor will be checked to ee if additional penalty ha to be impoed. The um of both penaltie will be S. The energy function aociated with ( i then equal to APSIPA 644 APSIPA ASC 2015

3 Proceeding of APSIPA Annual Summit and Conference December 2015 e = e + ScF( S + S ), (6) ( H where ScF i a weighting factor. A larger ScF will make the poition ( have a maller chance to be choen in the future o that the elected eam will not be alway tangled together. The reult of uing eam carving only are uually ued a the reference or comparion in exiting work ince noticeable ditortion appear quite often. In our opinion, eam carving ha the advantage of removing pixel directly to reduce the ize of image but ha to be applied with care without being overued. It hould be noted that the proce of dynamic programming mentioned above enure that a vertical eam with the length N ha the lowet energy. Neverthele, noticeable ditortion can occur in local area o a global meaurement cannot reflect the real ituation. Thi problem become more eriou in eam carving ince the ditortion are not additive noie but twit of content. The propoed cheme trie to avoid viible local ditortion by defining ome alient point and requiring that a elected eam hould not contain any uch alient point. To be more pecific, ( i identified a a alient point if it energy function e( i larger than a threhold calculated by T S = 1 M N N M 2 e x= 1 y= 1. (7) e can be calculated by Prewitt operator to find vertical edge and T S i a common threhold to identify edge pixel. One may think that thee alient point can be determined firt and aigned with a very large energy o that the dynamic programming proce will automatically kip thee alient point. Neverthele, it i oberved that thee point may appear along the edge o the elected eam will alo extend along/near the edge and may caue unpleaant reult. Our trategy i thu to employ the dynamic programming to elect the eam with the mallet energy. During the invere tracing to find the route, we check whether any alient point i paed. If ye, we give up thi eam and turn to find the econd bet one and o on. Thi eam carving proce will be topped if we have examined all the eam (M eam at the beginning) and cannot find any eam that doen t contain any alient point. The adaptive threhold T S i quite important but cannot guarantee an excellent reult. If T S i too mall, we will have fewer eam, which will be le reaonable ince eam carving cot a large amount of computation, compared with cropping or caling. If T S i too large, ome eam may pa through harp edge and the quality can be affected. From our obervation, the eam paing through harp edge are the major caue of quality degradation. In the propoed cheme, a maller threhold i adopted, i.e., T S/D, o more point will be viewed a edge pixel of foreground. The labelling of connected component i calculated and the point with the number of four-neighbor component maller than K will be removed from thee foreground edge. The energy of the remaining foreground edge will be caled, e.g., by D, to make thee point more ignificant. Some ubtle line, which may not have tronger energy, can thu be better preerved. However, thi method alo increae the energy of textural area where the eam hould be allowed to go acro. An order filtering with a mall upport area (n by n) i calculated and the caled e ranked the Q% mallet value i ued a the divior to decreae e. i.e., e ( A) ( S ) e =, (8) ( S ) 1+ ord( e { X, Y}, Q%) { X, Y } A where e (S) i the caled energy and ord(.) find the value ranked a the mallet Q% and A i the et {x-n X x+n, y-n Y y+n }. e (A) i the adjuted energy to replace e in (6). If Q i equal to 25, then the denominator i the quantile value plu one. We tend to chooe a maller Q to modify e (S) in a more conervative way to reduce the effect on harp edge. When a eam i elected to carve, partial updating i applied to adjut the energy function of affected pixel only. Since the pixel of a eam are eight-neighbor connected, when I( i choen, at leat two out of I(x+1,y-1), I(x+1, and I(x+1,y+1) are examined. Beide, if the energy function of a pixel i changed, the three pixel in the next row will be checked too. The propoed cheme compute the energy function only once and applie the updating on pixel if neceary. The pixel that i choen in a eam will be aigned with a large energy value o that it will not be elected again. In fact, we can draw the eam on the image directly and then carve thee eam to reduce the width of the image. Fig. 1 how an example with Fig. 1 demontrating an Eagle image with the uperimpoed eam and Fig. 1 illutrating the image proceed by the propoed eam carving. Fig. 1 An example of eam carving the Eagle image with the carved eam and the reulting eam-carved image. Fig. 2 An example of adding eam the eam carved image uperimpoed with inerted eam and the reulting image. When the background i not complex and further change of width i till neceary, we can chooe to inert horizontal eam. The procedure i imilar to the eam carving algorithm. Baically, we determine the eam baed on G R and the APSIPA 645 APSIPA ASC 2015

4 Proceeding of APSIPA Annual Summit and Conference December 2015 penalty mentioned before. The eam are copied, intead of being carved. A long a the threhold i et lower, ay T S /F, the copying i imilar to the interpolation ince the conidered area are uually uniform. Fig. 2 how an example of eam adding, with the inerted eam in flat area. B. iual Saliency for Content-baed Cropping After the eam carving, if the width ha to be reduced further, content-baed cropping will be applied. The viual aliency, intead of the energy function mentioned before, will be needed to determine the boundarie of region of interet. The method propoed by Montabone et al. [12] i ued to calculate the viual aliency. Thi method make ue of the property that the human perceive the viual information by the on-center and off-center ganglion cell in eye; on-center ganglion cell repond to bright area urrounded by a dark background while off-center ganglion cell repond to dark area urrounded by bright area. The aliency map i then calculated a follow. After converting the image into graycale value, the 3 by 3 Gauian filter i employed to mooth the graycale image twice and then the integral image i calculated. The integral image G( repreent the um of the value above and to the left of (, i.e., G = g( x', y' ), (9) y' y, x' x where g i the filtered pixel. The um of any rectangular area defined by two point, (x1,y1) and (x2,y2), can be calculated by G( in contant time, i.e., Sum( x1, y1, x2, y2) (10) = G( x2, y2) G( x1, y2) G( x2, y1) + G( x1, y1) The on-center and off-center difference with two urrounding value, 3 and 7, and three cale, 2, 3 and 4, can be computed efficiently to acquire ix intenity ubmap: 3 2 2, 3 2 3,3 2 4, 7 2 2, and 7 2 4, o the et of cale q i {12, 24, 48, 28, 56, 112}. The urrounding pixel are defined a Sum( x q, y q, x + q, y + q) g( urround y, q) = (11) (2q + 1) 2 1 The intenity ubmap are then calculated by Int Int = max{ g( urround y, ),0}, (12) ( On, q) q = max{ urround y, q) g( ),0}, (13) ( Off, q) y The aliency image P( i formed by ( ( On, q) ( Off, q) q q P = max{ Int, Int } (14) Fig. 3 how an example, in which the eagle i apparently the main object of the image and higher aliency value are aigned correctly to the area where the eagle i located. Although thi method doe not include complex algorithm uch a image egmentation or object detection, the detected aliency can reaonably reflect the region of interet and alo preerve the advantage of image gradient. In contrat, ome advanced viual aliency method do uccefully identify a large object in an image and view all other area a the background. However, if thee background pixel are all removed, the image will look quite trange. We found that thi imple viual aliency tend to preerve more area and can be quite uitable to the cropping operation. Fig. 3. A aliency example: the original image and the aliency map. C. Content-baed Cropping The cropping i applied on both ide of an image until a meaningful foreground i touched according to the aliency map. We calculate the average value of the aliency pixel in m by m block. If the average value i larger than the threhold ε, the block i conidered a foreground block. The block ize m can be related to the image ize. The threhold ε i decided uing Otu algorithm. All the pixel in the block will be et either 255 (foreground) or 0 (background). The foreground image will be proceed by the eight-connected-component labeling and we will determine whether a component i important baed on the number of connected foreground block. Next, we employ the property of Rule of Third in digital photography [1], which tate that the central 1/3 of the image i uually the region of interet. Two contraint are impoed: 1) The foreground object located around the two ide of the image are eldom important o they hould be viewed a the background and can be cropped off. We thu trace the ignificant component tarting from the two ide toward the center. When a foreground pixel i found following a background one during the trace, an object i aid to be encountered and hould be kept. 2) Since the top/bottom 1/3 of an image may not be important according to the property of Rule of Third, we conervatively ignore top/bottom 1/9 of the image, which will not be traced to find the foreground area. Fig. 4 how an example. The white pixel in Fig. 4 are identified a the foreground. The mall red block generated during the tracing help to determine the location of edge o the cropping can be applied efficiently a hown in Fig. 4. Comparing Fig. 2 and 4, one may think that we hould analyze the cropping boundarie after the eam carving. Neverthele, the eam carving operation may change the content at the boundarie and the firt contraint mentioned above may be affected. The propoed cheme thu determine the boundarie from the original image firt. The boundary pixel are recorded for the ubequent content-baed cropping, after the eam carving proce. By doing o, it eem that we hould apply cropping before the eam carving ince the APSIPA 646 APSIPA ASC 2015

5 Proceeding of APSIPA Annual Summit and Conference December 2015 neceary number of line can be removed by cropping. The remaining image with a maller ize can be proceed more efficiently in the eam carving. However, it hould be noted that cropping will more or le loe image content near the boundarie, where many people may have different opinion on whether certain part hould be preerved or not. Therefore, we till prefer to employ the eam carving firt to remove ome imagery data and help preerve more content near the ide of an image. 30, 45, 29 and 19 for thee four image and we can ee that the eam are inerted in a more conervative way to prevent poible ditortion. The number of cropped line are 94, 409, 53 and 106 for Eagle, Butterfly, Wine and Ski repectively. In Fig. 6, the eagle wing on the right-hand ide ha been ditorted in SC and MO. In Fig. 7, the butterfly i perfectly preerved in the propoed method a the cropping achieve mot of the width reduction. In contrat, the hape of butterfly i modified in SC and MO. In Fig. 8 and 9, the detailed comparion are alo illutrated in Fig. 8(d) and Fig. 9(d). The feet of chair are trimmed too much in SC and MO. For the peron on the left-hand ide in Ski, hi leg are ditorted eriouly in SC and hi body become too lim in MO. Fig. 4. A cropping example: the determination of the foreground and uitable cropping poition and the reult of cropping. (c) Fig. 6. Comparion of Eagle: SC (0.68) MO (0.7) (c) Our (0.76). (c) (d) Fig. 5. Tet image. Eagle, Butterfly, (c) Wine and (d) Ski III. EXPERIMENTAL RESULTS The etting of the propoed cheme i decribed a follow. ScF in (6) i et a 4. The factor D for finding weak line or curve i 2. The number of connected component K for determining the meaningful line i 128. In the order filtering, the ize n ued in the upporting area i 13 and the parameter Q i The factor F for determining the threhold in adding eam i 4. The block ize m for cropping i empirically et a the image height divided by 24. We compare the reult with Seam Carving (SC) [5] and Multi-Op (MO) [6]. The tet image and target reolution are et according to [7] with the width being reduced by half. The original image are hown in Fig. 5, including Eagle (402x600), Butterfly (700x1024), Wine (697x1024) and Ski (661x1003). Fig. 6 to 9 how the comparion. The core of quality aement uing [18] are alo lited in the caption of Fig. 6 to 9 a the reference. In the propoed cheme, the number of carved eam are 71, 71, 135 and 113 for Eagle, Butterfly, Wine and Ski repectively. A reaonably large number of eam are carved and thi i reaonable and even required ince the proce of eam carving doe take ome time. The number of added eam are (c) Fig. 7. Comparion of Butterfly: SC (0.79) MO (0.78) (c) Our (0.8). (c) (d) Fig. 8. Comparion of Wine: SC (0.6) MO (0.61) (c) our (0.76) (d) cloe-up comparion of the chair (SC,MO, Our). (c) (d) Fig. 9. Comparion of Ski: SC (0.61) MO (0.75) (c) our (0.75) (d) cloe-up comparion of the man (SC,MO, Our) APSIPA 647 APSIPA ASC 2015

6 Proceeding of APSIPA Annual Summit and Conference December 2015 It hould be noted that the numerical etting may have different effect on image. The deign principle i to enure that a larger number of eam can be carved and the eam hould not pa through clear or harp edge. Therefore, image with varying characteritic are collected, epecially thoe containing harp line or curve, to help determine uitable parameter. The objective of cropping i to preerve the viually ignificant object. Neverthele, different uer may have varying opinion about the ame content. Fig. 10 how two example. In Fig. 10, DKNYgirl, cropping more help to maintain the hape of girl well but the taxi in the background may not be included. In Fig. 10, Umdan, if the two peron on the left-hand ide are cropped off, we can prevent the other five peron from being queezed horizontally, but ome uer may prefer to keep all the even peron intead. In the propoed cheme, we try to crop more background in Fig. 10 but keep all the peron in Fig. 10. Fig. 10(c) and Fig. 10(d) demontrate the reulting image by reducing the width by half uing the propoed method. (c) (d) Fig. 10. The example for determining the parameter in cropping: DKNYgirl, Umdan, (c) retargeted DKNYgirl and (d) retargeted Umdan. I. CONCLUSION AND FUTURE WORK Thi reearch preent an image retargeting cheme that combine the eam carving and content-baed cropping. The eam carving i deigned to avoid poible ditortion in local area. Carving and adding eam can be applied in a imilar way. The content-baed cropping can remove inignificant boundarie efficiently according the viual aliency. The experiment how that, the propoed method outperform [6] in everal image. The propoed method can be further improved by conidering more advanced aliency detection, uch a the incluion of face detection, to avoid generating perceptible ditortion when the human face occupie larger area. The algorithm can certainly be extended to video proceing, e.g., on the key frame of a video egment or tatic cene without obviou camera motion. ACKNOWLEDGMENT Thi reearch i upported by the Minitry of Science and Technology in Taiwan, R.O.C., under Grant MOST E and MOST E REFERENCES [1] A. Santella, M. Agrawala, D. DeCarlo, D. Salein, and M. Cohen, Gaze-baed interaction for emi-automatic photo cropping, Proceeding of the SIGCHI conference on Human Factor in computing ytem. pp , ACM, [2] D. Domingue, A. Alahi, and P. andergheynt, Stream carving: an adaptive eam carving algorithm, IEEE International Conf. on Image Proceing (ICIP), pp , [3] F. Stentiford, Attention baed auto image cropping, The 5th International Conf. on Computer iion Sytem, Bielefeld, [4] L. Wolf, M. Guttmann, and D. Cohen-Or, Non-homogeneou contentdriven video retargeting, IEEE 11th International Conference on Computer iion, [5] M. Rubintein, A. Shamir, and S. Avidan, Improved eam carving for video retargeting, ACM Tran. on Graphic. vol. 27. no. 3, [6] M. Rubintein, A. Shamir, and S. Avidan, Multi-operator media retargeting, ACM Tran. on Graphic, vol. 28, no. 3, [7] W. Dong, N. Zhou, J. C. Paul, and X. Zhang, Optimized image reizing uing eam carving and caling, ACM Tranaction on Graphic (TOG), vol. 28, no. 5, p125, [8] M. Grundmann,. Kwatra, M. Han, and I. Ea, Dicontinuou eamcarving for video retargeting, IEEE Conference on Computer iion and Pattern Recognition (CPR), IEEE, June [9] M. Zhang, and L. Zhang, Auto cropping for digital photograph, IEEE International Conf. on Multimedia and Expo. p. 4-pp, [10] M. Nihiyama, T. Okabe, Y. Sato, and I. Sato, Senation-baed photo cropping, bproceeding of the 17th ACM international conf. on Multimedia, pp , [11] P. Cheatle, Automatic image cropping for republihing, IS&T/SPIE Electronic Imaging. International Society for Optic and Photonic, pp O-75400O-9, [12] S. Montabone, and A. Soto. Human detection uing a mobile platform and novel feature derived from a viual aliency mechanim, Image and iion Computing, vol. 28, no. 3, [13] S. Avidan, and A. Shamir. Seam carving for content-aware image reizing, ACM Tranaction on graphic, vol. 26. no. 3. Aug [14] S. Hua, G. Chen, H. Wei, and Q. Jiang, Similarity meaure for image reizing uing SIFT feature, EURASIP Journal on Image and ideo Proceing, pp. 1-11, Jan [15] S. Luo, J. Zhang, Q. Zhang, and X. Yuan, Multi-operator image retargeting with automatic integration of direct and indirect eam carving, Image and iion Computing, vol. 30, no. 9, Sep. 2012, pp [16] W. M. Dong, G. B. Bao, X. P. Zhang, and J. C. Paul, Fat Multi- Operator Image Reizing and Evaluation, Journal of Computer Science and Technology, vol. 27, no. 1, pp , [17] Y. S. Wang, C. L. Tai, O. Sorkine, and T. Y. Lee, Optimized caleand-tretch for image reizing, ACM Tranaction on Graphic, vol. 27, no. 5, [18] Chih-Chung Hu,Chia-Wen Lin,Yuming Fang,Weii Lin, Objective Quality Aement For Image Retargeting Baed On Perceptual Ditortion And Information Lo, iual Communication and Image Proceing (CIP), APSIPA 648 APSIPA ASC 2015