由於不同螢幕的解析度和長寬比例上的差異，如傳統電視、數位電視和手持電話，近年來圖片與影片縮放的研究變得愈來愈熱門。傳統的做法是內插圖片中的內容來改變解析度。然而這種將全部內容做單一縮放的方法，很容易改變圖片中的人或是一些具有結構性物體的比例，產生縮放上的失真。於是，有一些學者利用裁切的方法，移除圖片週圍一些比較不重要的區域來改變圖片的大小。他們利用一些自動的方法偵測每一個區域的重要性，然後尋找一個可以包含最多資訊的裁切視窗，將內容的損失降至最低。

然而這種裁切的方法是有其限制的，如果重要的物體都緊鄰著圖片的週圍，那不論怎麼裁切都會將這些重要的物體移除。因此，基於內容為主的圖片縮放技術接著被提出來了。這些方法利用移除或擠壓圖片中比較不重要的內容，來隱藏不等比例縮放所產生的瑕疵。例如壓扁天空中的雲就不會產生視覺上的不適。基於這項論點，我們的目的是將圖片中的每個區域作不等比例的變形，達到減少瑕疵的目的。與前人的方法相比，我們對每一個區域的大小與長寬比例作最佳化，使得縮放後的圖片更加自然。

此外，我們還將這樣的技術應用到影片上。除了維持住重要物體的比例外，我們還必需維持相同的物體在不同的時間點的縮放是一致的。否則物體會忽大忽小，產生另一種時間上的瑕疵。為了達成這個目的，我們偵測物的運動軌跡，找出每個物體在不同時間點的關連性，然後限制這些套用在相關物體的變形是一致的。最後，我們利用最佳化技術，在時間和空間上尋找一個平衡點，將視覺上的失真降至最低。

Research on automatic resizing of images and videos is becoming ever more important with the proliferation of display units, such as television, notebooks, PDAs and cell phones, which all come in different aspect ratios and resolutions. To achieve full presentation of images and videos, we introduce a content aware technique which considers the interior pixels while resizing the images and videos. Specifically, we represent an image/frame with a grid mesh and then warp the mesh based on the saliency measure. Unlike the previous methods, which strove to preserve the prominent objects untouched, our method allows them to be scaled uniformly, enabling the distortion propagation in multiple directions. In addition to the resizing of static images, we extend our resizing technique to videos. The most important issue on this extension is the temporal coherence since the interior contents keep changing when the video is played. Due to the camera and object motions, simply preserving consistent resizing of temporally adjacent pixels cannot achieve temporal coherence and thus, resulting in flickering or waving artifacts. To solve this problem, we detect the camera motion based on the SIFT features and then decompose the scene into foreground and background regions. Obviously, the background motions depend on the camera while the foreground motions are arbitrary. We introduce different constraints to preserve their temporal coherences due to their different natures. All the criteria are formulated into energy terms and we solve for the resized images and videos by minimizing the objective function.

S.~Avidan and A.~Shamir, ``Seam carving for content-aware image resizing,'
{em ACM Trans. Graph.}, vol.~26, no.~3, p.~10, 2007.

M.~Rubinstein, A.~Shamir, and S.~Avidan, ``Improved seam carving for video
retargeting,' {em ACM Trans. Graph.}, vol.~27, no.~3, 2008.

R.~Gal, O.~Sorkine, and D.~Cohen-Or, ``Feature-aware texturing,' in {em
Proceedings of Eurographics Symposium on Rendering}, pp.~297--303, 2006.

L.~Wolf, M.~Guttmann, and D.~Cohen-Or, ``Non-homogeneous content-driven
video-retargeting,' in {em Proceedings of IEEE ICCV}, pp.~1--6, 2007.

Y.-F. Zhang, S.-M. Hu, and R.~R. Martin, ``Shrinkability maps for content-aware
video resizing,' in {em PG '08}, 2008.

T.~A. Keahey and E.~L. Robertson, ``Nonlinear magnification fields,' in {em
INFOVIS '97: Proceedings of the 1997 IEEE Symposium on Information
Visualization (InfoVis '97)}, p.~51, IEEE Computer Society, 1997.

T.~A. Keahey and E.~L. Robertson, ``Techniques for non-linear magnification
transformations,' in {em INFOVIS '96: Proceedings of the 1996 IEEE
Symposium on Information Visualization (INFOVIS '96)}, p.~38, IEEE Computer
Society, 1996.

T.~A. Keahey, ``The generalized detail-in-context problem,' in {em INFOVIS
'98: Proceedings of the 1998 IEEE Symposium on Information Visualization},
pp.~44--51, IEEE Computer Society, 1998.

M.~S.~T. Carpendale, D.~J. Cowperthwaite, and F.~D. Fracchia, ``Distortion
viewing techniques for 3-dimensional data,' in {em INFOVIS '96: Proceedings
of the 1996 IEEE Symposium on Information Visualization (INFOVIS '96)},
p.~46, IEEE Computer Society, 1996.

M.~S.~T. Carpendale, D.~J. Cowperthwaite, and F.~D. Fracchia, ``Extending
distortion viewing from 2d to 3d,' {em IEEE Comput. Graph. Appl.}, vol.~17,
no.~4, pp.~42--51, 1997.

E.~LaMar, B.~Hamann, and K.~I. Joy, ``A magnification lens for interactive
volume visualization,' in {em PG '01: Proceedings of the 9th Pacific
Conference on Computer Graphics and Applications}, p.~223, IEEE Computer
Society, 2001.

L.~Wang, Y.~Zhao, K.~Mueller, and A.~E. Kaufman, ``The magic volume lens: An
interactive focus+context technique for volume rendering,' in {em IEEE
Visualization}, p.~47, 2005.

L.~Q. Chen, X.~Xie, X.~Fan, W.~Y. Ma, H.~J. Zhang, and H.~Q. Zhou, ``A visual
attention model for adapting images on small displays,' {em ACM Multimedia
Systems Journal}, vol.~9, no.~4, pp.~353--364, 2003.

H.~Liu, X.~Xie, W.-Y. Ma, and H.-J. Zhang, ``Automatic browsing of large
pictures on mobile devices,' in {em Proceedings of ACM International
Conference on Multimedia}, pp.~148--155, 2003.

A.~Santella, M.~Agrawala, D.~DeCarlo, D.~Salesin, and M.~Cohen, ``Gaze-based
interaction for semi-automatic photo cropping,' in {em Proceedings of CHI},
pp.~771--780, 2006.

B.~Suh, H.~Ling, B.~B. Bederson, and D.~W. Jacobs, ``Automatic thumbnail
cropping and its effectiveness,' in {em Proceedings of UIST}, pp.~95--104,
ACM, 2003.

P.~Viola and M.~J. Jones, ``Robust real-time face detection,' {em Int. J.
Comput. Vision}, vol.~57, no.~2, pp.~137--154, 2004.

L.~Itti, C.~Koch, and E.~Niebur, ``A model of saliency-based visual attention
for rapid scene analysis,' {em IEEE Trans. Pattern Anal. Mach. Intell.},
vol.~20, no.~11, pp.~1254--1259, 1998.

D.~DeCarlo and A.~Santella, ``Stylization and abstraction of photographs,'
{em ACM Trans. Graph.}, vol.~21, no.~3, pp.~769--776, 2002.

T.~S. Cho, M.~Butman, S.~Avidan, and W.~T. Freeman, ``The patch transform and
its applications to image editing,' in {em CVPR '08}, 2008.

D.~Simakov, Y.~Caspi, E.~Shechtman, and M.~Irani, ``Summarizing visual data
using bidirectional similarity,' in {em CVPR '08}, 2008.

V.~Kraevoy, A.~Sheffer, D.~Cohen-Or, and A.~Shamir, ``Non-homogeneous resizing
of complex models,' {em ACM Trans. Graph.}, vol.~27, no.~5, p.~111, 2008.

Y.-S. Wang, T.-Y. Lee, and C.-L. Tai, ``Focus+context visualization with
distortion minimization,' {em IEEE Trans. Visualization and Computer
Graphics}, vol.~14, no.~6, 2008.

F.~Liu and M.~Gleicher, ``Video retargeting: automating pan and scan,' in {em
Multimedia '06}, pp.~241--250, 2006.

C.~Tao, J.~Jia, and H.~Sun, ``Active window oriented dynamic video
retargeting,' in {em Workshop on Dynamical Vision, ICCV '07}, 2007.

M.~Rubinstein, A.~Shamir, and S.~Avidan, ``Multi-operator media retargeting,'
{em ACM Trans. Graph.}, vol.~28, no.~3, p.~23, 2009.

I.~Viola, A.~Kanitsar, and M.~E. Groller, ``Importance-driven volume
rendering,' in {em VIS '04: Proceedings of the conference on Visualization
'04}, pp.~139--146, IEEE Computer Society, 2004.

J.~Zhou, M.~Hinz, and K.~D. Tonnies, ``Focal region-guided feature-based volume
rendering.,' in {em 3DPVT}, pp.~87--90, IEEE Computer Society, 2002.

M.~J. McGuffin, L.~Tancau, and R.~Balakrishnan, ``Using deformations for
browsing volumetric data,' in {em VIS '03: Proceedings of the 14th IEEE
Visualization 2003 (VIS'03)}, p.~53, IEEE Computer Society, 2003.

E.~A. Bier, M.~C. Stone, K.~Pier, W.~Buxton, and T.~D. DeRose, ``Toolglass and
magic lenses: the see-through interface,' in {em SIGGRAPH '93: Proceedings
of the 20th annual conference on Computer graphics and interactive
techniques}, pp.~73--80, ACM, 1993.

H.~Fang and J.~C. Hart, ``Detail preserving shape deformation in image
editing,' {em ACM Trans. Graph.}, vol.~26, no.~3, p.~12, 2007.

R.~Szeliski, ``Image alignment and stitching: a tutorial,' {em Foundations
and Trends in Computer Graphics and Vision}, vol.~2, no.~1, pp.~1--104, 2006.

B.-Y. Chen, K.-Y. Lee, W.-T. Huang, and J.-S. Lin, ``Capturing intention-based
full-frame video stabilization,' {em Computer Graphics Forum}, vol.~27,
no.~7, pp.~1805--1814, 2008.

M.~L. Gleicher and F.~Liu, ``Re-cinematography: Improving the camerawork of
casual video,' {em ACM Trans. Multimedia Comput. Commun. Appl.}, vol.~5,
no.~1, pp.~1--28, 2008.

D.~G. Lowe, ``Distinctive image features from scale-invariant keypoints,' {em
Int. J. Comput. Vision}, vol.~60, no.~2, pp.~91--110, 2004.

M.~A. Fischler and R.~C. Bolles, ``Random sample consensus: a paradigm for
model fitting with applications to image analysis and automated
cartography,' {em Commun. ACM}, vol.~24, no.~6, pp.~381--395, 1981.

T.~Deselaers, P.~Dreuw, and H.~Ney, ``Pan, zoom, scan - time-coherent, trained
automatic video cropping,' in {em CVPR '08}, 2008.

O.~Sorkine, Y.~Lipman, D.~Cohen-Or, M.~Alexa, C.~R"{o}ssl, and H.-P. Seidel,
``Laplacian surface editing,' in {em SGP '04}, pp.~179--188, 2004.

H.-W. Kang, Y.~Matsushita, X.~Tang, and X.-Q. Chen, ``Space-time video
montage,' in {em CVPR '06}, 2006.

Z.~Rasheed and M.~Shah, ``Scene detection in hollywood movies and tv shows,'
in {em CVPR '03}, vol.~2, pp.~II--343--8, 2003.

Y.-S. Wang, C.-L. Tai, O.~Sorkine, and T.-Y. Lee, ``Optimized scale-and-stretch
for image resizing,' {em ACM Trans. Graph.}, vol.~27, no.~5, p.~118, 2008.

P.~Kr"ahenb"uhl, M.~Lang, A.~Hornung, and M.~Gross, ``A system for
retargeting of streaming video,' {em ACM Trans. Graph.}, vol.~28, no.~5,
2009.

T.~Ju, S.~Schaefer, and J.~Warren, ``Mean value coordinates for closed
triangular meshes,' {em ACM Trans. Graph.}, vol.~24, no.~3, pp.~561--566,
2005.

K.~Madsen, H.~Nielsen, and O.~Tingleff, ``Methods for nonlinear least squares
problems,' {em Tech. rep., Informatics and Mathematical Modelling}, 2004.

K.~Madsen, H.~Nielsen, and O.~Tingleff, ``Optimization with constraints,' {em
Tech. rep., Informatics and Mathematical Modelling}, 2004.

S.~Toledo, D.~Chen, and V.~Rotkin, ``Taucs: A library of sparse linear solvers,
version 2.2.,' {em Tel-Aviv University, Available online at
http://www.tau.ac.il/~stoledo/taucs/}.