ACM Reference Format Wu, H., Wang, Y., Feng, K., Wong, T., Lee, T., Heng, P. 2010. Resizing by Symmetry-Summarization. ACM Trans. Graph. 29, 6, Article 159 (December 2010), 9 pages. DOI = 10.1145/1866158.1866185 http://doi.acm.org/10.1145/1866158.1866185. Copyright Notice Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or direct commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701, fax +1 (212) 869-0481, or permissions@acm.org. © 2010 ACM 0730-0301/2010/12-ART159 $10.00 DOI 10.1145/1866158.1866185 http://doi.acm.org/10.1145/1866158.1866185 Resizing by Symmetry-Summarization Huisi Wu 1,3 Yu-Shuen Wang 2 Kun-Chuan Feng 2 Tien-Tsin Wong 1 Tong-Yee Lee 2 Pheng-Ann Heng 1,3 1 The Chinese University of Hong Kong 2 National Cheng Kung University 3 SIAT, China (a) Original (b) Multi-Operator (c) Shift-Map (d) Warping (e) Ours [Rubinstein et al. 2009] [Pritch et al. 2009] [Wang et al. 2008] Figure 1: By summarizing the symmetry structure in (a) the input image, our method (e) can preserve the original curved lattice structure without breaking, over-squeezing or cropping the lattice. Input resolution is 999×820. Target resolution is 516×820. Abstract Image resizing can be achieved more effectively if we have a better understanding of the image semantics. In this paper, we analyze the translational symmetry, which exists in many real-world images. By detecting the symmetric lattice in an image, we can summa- rize, instead of only distorting or cropping, the image content. This opens a new space for image resizing that allows us to manipulate, not only image pixels, but also the semantic cells in the lattice. As a general image contains both symmetry & non-symmetry regions and their natures are different, we propose to resize symmetry re- gions by summarization and non-symmetry region by warping. The difference in resizing strategy induces discontinuity at their shared boundary. We demonstrate how to reduce the artifact. To achieve practical resizing applications for general images, we developed a fast symmetry detection method that can detect multiple disjoint symmetry regions, even when the lattices are curved and perspec- tively viewed. Comparisons to state-of-the-art resizing techniques and a user study were conducted to validate the proposed method. Convincing visual results are shown to demonstrate its effective- ness. Keywords: image resizing, summarization 1 Introduction Image resizing techniques fit an input image to the target resolution by reducing or replicating the image content. Image seamlessness is the key. Existing methods [Wang et al. 2008; Rubinstein et al. 2009; Dong et al. 2009] rely on the importance or saliency map to prevent the modification from being over-aggressive. However, the importance or saliency may not confirm to the true semantics, since mainly local and low-level features (such as gradient and/or entropy) are considered. Without higher-level understanding of the image content, the image seamlessness is hard to maintain. Although computational understanding of general image content is infeasible in the near future, analysis of certain high-level seman- tics is feasible. One of them is symmetry. It exists everywhere, from windows on the buildings to soldiers in marching. The sym- metry structure and the repetitive elements (or cells) reinforce the visual importance. Previous resizing techniques attempt to modify without preserving the symmetry structure, and may easily result in apparent visual artifacts, such as the obvious seam (Figure 1(c)) or over-squeezing (1(b) and 1(d)). By considering the knowledge of symmetry, resizing can then be achieved via summarization, which removes or replicates the cells with respect to the semantics (Fig- ure 1(e)). Note that we extend the original meaning of summa- rization to include both reduction and repetition of cells. In other words, symmetry opens an additional space for resizing. Instead of squeezing or stretching the image pixel-wisely, we can now remove or replicate it cell-wisely. In this paper, we propose a novel summarization operator for im- age resizing that handles one common type of symmetry, the trans- lational symmetry [Liu et al. 2004]. Existing symmetry detection methods are usually too slow for practical resizing applications. In- stead, we propose a real-time and automatic method to detect sym- metry over arbitrary surfaces (planar or non-planar) with arbitrary viewing perspective, and to extract the corresponding lattice in im- age space without reconstructing the underlying 3D geometry. By trimming and extending the lattice, we can resize the content with more respect to the semantics. By smoothing the transformation and intensity of cells across the lattice, we can maintain the seam- lessness in both geometry and illumination respectively. In contrast, most existing resizing techniques do not consider the seamlessness of illumination. However, a general image normally contains both symmetry region (S-region) and non-symmetry region (NS-region), leading to com- plication. While the S-region can be resized with our summariza- tion operator, the NS-region can be resized with carving or warping operators. But most importantly, there is no guarantee that both resultant regions can be seamlessly combined, due to the different natures of resizing strategies. In this paper, we propose a frame- ACM Transactions on Graphics, Vol. 29, No. 6, Article 159, Publication date: December 2010.