Skip to main content
Log in

New progress in geometric computing for image and video processing

  • Review Article
  • Published:
Frontiers of Computer Science Aims and scope Submit manuscript

Abstract

In recent years, geometry-based image and video processing methods have aroused significant interest. This paper considers progress from four aspects: geometric characteristics and shape, geometric transformations, embedded geometric structure, and differential geometry methods. Current research trends are also pointed out.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Cheng M M, Zhang G X, Niloy J M, Huang X L, Hu S M. Global contrast based salient region detection. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition. 2011, 409–416

  2. Huang T J, Tian Y H, LI J, Yu H N. Salient region detection and segmentation for general object recognition and image understanding. Science China Information Sciences, 2011, 54(12): 2461–2470.

    Article  MathSciNet  Google Scholar 

  3. He X, Jing H Y, Han Q, Niu X M. Salient region detection combining spatial distribution and global contrast. Optical Engineering, 2012, 51(4): 3194–3201

    Article  Google Scholar 

  4. Pan B, Zhong F, Wang S, Chen W, Peng Q S. Salient structural elements based texture synthesis. Science China Information Sciences, 2011, 54(6): 1199–1206

    Article  Google Scholar 

  5. Radhakrishna A, Francisco E, Patricia W, Sabine S. Salient region detection and segmentation. In: Proceedings of the 6th International Conference on Computer Vision Systems. 2008, 66–75

  6. Wu K K, Zhang J W. A new method for salient regions detection and segmentation under noisy condition. In: Proceedings of Fourth International Conference on Machine Vision. 2011, 83501S: 1–8

    Google Scholar 

  7. Gao W, Ai H Z, Lao S H. Adaptive contour features in oriented granular space for human detection and segmentation. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition. 2009, 1786–1793

  8. Yang B, Huang C, Nevatia R. Segmentation of objects in a detection window by nonparametric inhomogeneous CRFs. Computer Vision and Image Understanding, 2011, 115(11): 1473–1482

    Article  Google Scholar 

  9. Zhuang Y T, Han Y H, Fei WU, Yang J C. Stable multi-label boosting for image annotation with structural feature selection. Science China Information Sciences, 2011, 54(12): 2508–2521

    Article  MathSciNet  Google Scholar 

  10. Cheng M M, Zhang F L, Mitra N J, Huang X L, Hu S M. RepFinder: finding approximately repeated scene elements for image editing. ACM Transactions on Graphics, 2010, 29(4): 83: 1–8

    Article  Google Scholar 

  11. Chen T, Cheng M M, Tan P, Shamir A, Hu S M. Sketch2Photo: internet image montage. ACM Transactions on Graphics, 2009, 28(5): 124: 1–10

    Google Scholar 

  12. Eitz M, Richter R, Hildebrand K, Boubekeur T, Alexa M. Photosketcher: interactive sketch-based image synthesis. IEEE Computer Graphics and Applications, 2011, 31(6): 55–66

    Article  Google Scholar 

  13. Eitz M, Hildebrand K, Boubekeur T, Alexa M. Sketch-based image retrieval: benchmark and bag-of-features descriptors. IEEE Transactions on Visualization and Computer Graphics, 2011, 17(11): 1624–1636

    Article  Google Scholar 

  14. Szanto B, Pozsegovics P, Vamossy Z, Sergyan S. Sketch4Match — content based image retrival system using sketches. In: Proceedings of the 9th IEEE International Symposium on Applied Machine Intelligence and Informatics. 2011, 183–188

  15. Cho T S, Butman M, Avidan S, Freeman W. The patch transform and its applications to image editing. In: Proceedings of IEEE Conference on Computer Vision and Pattern Recognition. 2008, 1–8

  16. Barnes C, Shechtman E, Finkelstein A, Goldman D B. PatchMatch: a randomized correspondence algorithm for structural image editing. ACM Transactions on Graphics, 2009, 28(3): 24: 1–10.

    Article  Google Scholar 

  17. Darabi S, Shechtman E, Barnes C, Goldman D B, Sen P. Image melding: combining inconsistent images using patch-based synthesis. ACM Transactions on Graphics, 2012, 31(4): 82: 1–10

    Article  Google Scholar 

  18. James F O B, Hany F. Exposing photo manipulation with inconsistent reflections. ACM Transactions on Graphics, 2012, 31(1): 4: 1–11

    Google Scholar 

  19. Eduardo S L G, Manuel MO. Domain transform for edge-aware image and video processing. ACM Transactions on Graphics, 2011, 30(4): 69: 1–11

    Google Scholar 

  20. HaCohen Y, Shechtman E, Goldman D B, Lischinski D. NRDC: nonrigid dense correspondence with applications for image enhancement. ACM Transactions on Graphics, 2011, 30(4): 70: 1–9

    Article  Google Scholar 

  21. Huang C, Ai H Z, Li Y, Lao S H. High-performance rotation invariant multiview face detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2007, 29(4): 671–686

    Article  Google Scholar 

  22. Timo Ahonen, Jiri M, Chu H, Matti P. Rotation invariant image description with local binary pattern histogram fourier features. Lecture Notes in Computer Science, 2009, 5575: 61–70

    Article  Google Scholar 

  23. Xiang S J, Kim H J, Huang J W. Invariant image watermarking based on statistical features in the low-frequency domain. IEEE Transactions on Circuits and Systems for Video Technology, 2008, 18(6): 777–790

    Article  Google Scholar 

  24. Shao Z F, Li D R, Zhu X Q. A multi-scale and multi-orientation image retrieval method based on rotation-invariant texture features. Science China Information sciences, 2011, 54(4): 732–744

    Article  MATH  Google Scholar 

  25. Wang Y P, Hu S M. A new watermarking method for 3D model based on integral invariant. IEEE Transactions on Visualization and Computer Graphics, 2009, 15(2): 285–294

    Article  Google Scholar 

  26. Zhang G X, Cheng M M, Hu S M, Martin R R. A shape-preserving approach to image resizing. Computer Graphics Forum, 2009, 28(7): 1897–1906

    Article  Google Scholar 

  27. Wang D, Li G Q, Jia W J, Luo X N. Saliency-driven scaling optimization for image retargeting. The Visual Computer, 2011, 27(9): 853–860

    Article  Google Scholar 

  28. Zhang Y F, Hu S M, Martin R R. Shrinkability maps for content-aware video resizing. Computer Graphics Forum, 2008, 27(7): 1797–1804

    Article  Google Scholar 

  29. Xu K, Li Y, Ju T, Hu S M, Liu T Q. Efficient affinity-based edit propagation using K-D tree. ACM Transactions on Graphics, 2009, 28(5): 118: 1–6

    Google Scholar 

  30. Lai Y K, Hu S M, Martin R R. Automatic and topology-treserving gradient mesh generation for image vectorization. ACM Transactions on Graphics, 2009, 28(3): 85: 1–8

    Article  Google Scholar 

  31. Li X M, Zhang C M, Yue Y Z, Wang K P. Cubic surface fitting to image by combination. Science China Information Sciences, 2010, 53(7): 1287–1295

    Article  MathSciNet  Google Scholar 

  32. Thakoor N, Gao J, Jung S. Embedded planar surface segmentation system for stereo images. Machine Vision and Applications, 2010, 21(2): 189–199

    Article  Google Scholar 

  33. Zhou S Z, Fu H B, Liu L G, Daniel C O, Han X G. Parametric reshaping of human bodies in images. ACM Transactions on Graphics, 2010, 29(4): 126: 1–10

    Article  Google Scholar 

  34. Han D F, Sonka M, Bayouth J, Wu X D. Optimal multiple-seams search for image resizing with smoothness and shape prior. The Visual Computer, 2010, 26(6–8): 749–759

    Article  Google Scholar 

  35. Li M. A fast algorithm for color image enhancement with total variation regularization. Science China Information Sciences, 2010, 53(9): 1913–1916

    Article  MathSciNet  Google Scholar 

  36. Laurence L S, Darbon J, Smith E H B. Enhancement of historical printed document images by combining total variation regularization and Non-local Means filtering. Image and Vision Computing, 2011, 29(5): 351–363

    Article  Google Scholar 

  37. Wu C L, Zhang J Y, Duan Y P, Tai X C. Augmented lagrangian method for total variation based image restoration and segmentation over triangulated surfaces. Journal of Scientific Computing, 2012, 50(1): 145–166

    Article  MathSciNet  MATH  Google Scholar 

  38. Cong L, Tong R F, Dong J X. Selective image abstraction. The Visual Computer, 2011, 27(3): 187–198

    Article  Google Scholar 

  39. Fu S J, Zhang C M. Adaptive bidirectional diffusion for image restoration. Science China Information Sciences, 2010, 53(12): 2452–2460

    Article  MathSciNet  MATH  Google Scholar 

  40. Ding M, Tong R F. Content-aware copying and pasting in images. The Visual Computer, 2010, 26(6–8): 721–729

    Article  Google Scholar 

  41. Zhang Y, Tong R F. Environment-sensitive cloning in images. The Visual Computer, 2011, 27(6–8): 739–748

    Article  Google Scholar 

  42. Du H, Jin X G. Object cloning using constrained mean value interpolation. The Visual Computer, 2012, Online First.

  43. Summa B, Scorzelli G, Jiang M, Bremer P T, Pascucci V. Interactive editing of massive imagery made simple: turning atlanta into atlantis. ACM Transactions on Graphics, 2011, 30(2): 7: 1–13

    Article  Google Scholar 

  44. Yang Lei, Sander P V, Lawrence J, Hoppe H. Antialiasing recovery. ACM Transactions on Graphics, 2011, 30(3): 22: 1–9

    Article  Google Scholar 

  45. Fu S J, Zhang C M, Tai X C. Image denoising and deblurring: nonconvex regularization, inverse diffusion and shock filter. Science China Information Sciences, 2011, 54(6): 1184–1198

    Article  MathSciNet  Google Scholar 

  46. Annadhason A. Fractal geometry in image processing. International Journal of Research in Management and Technology, 2012, 2(1): 110–114

    Google Scholar 

  47. Fisher Y. Fractal Image Compression: Theory and Application. Berlin, Germany: Springer-Verlag, 1995.

    Book  Google Scholar 

  48. Gu F C, Chang H C, Chen F H, Kuo C C. Partial discharge pattern recognition of power cable joints using extension method with fractal feature enhancement. Expert Systems with Applications, 2012, 39(3): 2804–2812

    Article  Google Scholar 

  49. Blackledge M, Dubovitskiy D A. Texture classification using fractal geometry for the diagnosis of skin cancers. In: Proceedings of the 7th Theory and Practice of Computer Graphics Conference. 2009, 41–48

  50. Li J J, Zhang C M, Fan H, Yuan D. Image inpainting algorithm based on fractal theory. Acta Electronica sinica, 2010, 38(10): 2430–2435

    Google Scholar 

  51. Xiao J X, Fang T, Tan P, Zhao P, Ofek E, Quan L. Image-based facade modeling. ACM Transactions on Graphics, 2008, 27(5): 161: 1–10

    Article  Google Scholar 

  52. Chen J W. The video mesh: a data structure for image-based three-dimensional video editing. In: Proceedings of IEEE International Conference on Computational Photography (ICCP11). 2011, 1–8

  53. Lipski C, Linz C, Berger K, Sellent A, Magnor M. Virtual video camera: image-based viewpoint navigation through space and time. Computer Graphics Forum, 2010, 29(8): 2555–2568

    Article  Google Scholar 

  54. Zhao R Z, Liu X Y, Li C C, Robert J S, Sun M G. Wavelet denoising via sparse representation. Science China Information Sciences, 2009, 52(8): 1371–1377

    Article  MATH  Google Scholar 

  55. Preety D S, Alok J. Segmentation based combined wavelet-curvelet approach for image denoising. International Journal of Information Engineering. 2012, 2(1): 32–37

    Google Scholar 

  56. Yang L, Guo B L, NiW. Multimodality medical image fusion based on multiscale geometric analysis of contourlet transform. Neurocomputing, 2008, 72(1–3): 203–211

    Article  Google Scholar 

  57. Chougdali K. Contourlet feature based kernel relevance weighted discriminant analysis for face recognition. In: Proceedings of International Conference on Multimedia Computing and Systems (ICMCS09). 2009, 268–272

  58. Chena G, Haya G J, Castillaa G, Benoit S O, Powersa R. A multiscale geographic object-based image analysis to estimate lidar-measured forest canopy height using Quickbird imagery. International Journal of Geographical Information Science, 2011, 25(6): 877–893

    Article  Google Scholar 

  59. Bakshi S, Mehrotra H, Majhi B. Real-time iris segmentation based on image morphology. In: Proceedings of the 2011 International Conference on Communication, Computing and Security. 2011, 335–338

  60. Annadurai S, Sundaresan M. Wavelet based color image compression using vector quantization and morphology. In: Proceedings of the International Conference on Advances in Computing, Communication and Control. 2009, 391–396

  61. Habash N, Roth R M. Using deep morphology to improve automatic error detection in Arabic handwriting recognition. In: Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics: Human Language Technologies. 2011, 875–884

  62. Yeniterzi R. Exploiting morphology in Turkish named entity recognition system. In: Proceedings of the ACL 2011 Student Session. 2011, 105–110

  63. Shi Y H. Realistic mesh compression based on geometry image. In: Proceedings of Picture Coding Symposium (PCS). 2012, 133–136

  64. Vetro A, Tourapis A M, Muller K, Chen T. 3D-TV content storage and transmission. IEEE Transactions on Broadcasting, 2011, 57(2): 384–394

    Article  Google Scholar 

  65. Chew B S. Spectral geometry image: image based 3D models for digital broadcasting applications. IEEE Transactions on Broadcasting, 2011, 57(3): 636–645

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jinjiang Li.

Additional information

Jinjiang Li received his PhD degree from Shandong University in 2010. He is a postdoctor at Tsinghua University. His research interests include computer graphics, image processing, and geometry-based modeling and rendering.

Hanyi Ge is a professor in Science and Technology on Complex Systems Simulation Laboratory, Beijing. Her research areas include complex systems simulation, image and video processing, and virtual reality.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, J., Ge, H. New progress in geometric computing for image and video processing. Front. Comput. Sci. 6, 769–775 (2012). https://doi.org/10.1007/s11704-012-2910-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11704-012-2910-4

Keywords

Navigation