We propose to solve the problem of image inpainting using the F-transform technique particularly of the zero and first degrees. We focus on the so-called patch inpainting. The proposed technique creates a feature vector of an image that characterizes the weighted average levels of the corresponding intensity function and its partial derivatives over certain areas. The results of the proposed algorithm are demonstrated on various patch sizes, and the issue of reconstruction quality is discussed.
AshikhminM., Synthesizing natural textures, in Proceedings of the 2001 symposium on Interactive 3D graphics, ACM, 2001, pp. 217-226.
2.
De BonetJ.S., Multiresolution sampling procedure for analysis and synthesis of texture images, in Proceedings of the 24th annual conference on Computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing Co., 1997, pp. 361-368.
3.
EfrosA.A. and FreemanW.T., Image quilting for texture synthesis and transfer, in Proceedings of the 28th annual conference on Computer graphics and interactive techniques, ACM, 2001, pp. 341-346.
4.
EfrosA.A. and LeungT.K., Texture synthesis by nonparametric sampling, in Computer Vision, The Proceedings of the Seventh IEEE International Conference on21999, pp. 1033-1038, IEEE.
5.
BallesterC., CasellesV., VerderaJ., BertalmioM. and SapiroG., A variational model for filling-in gray level and color images, in Computer Vision, 2001. ICCV 2001. Proceedings. Eighth IEEE International Conference on, vol. 1. IEEE, 2001, pp. 10-16.
6.
BertalmioM., BertozziA.L. and SapiroG., Navier-stokes, fluid dynamics, and image and video inpainting, in Computer Vision and Pattern Recognition, 2001, CVPR 2001, Proceedings of the 2001 IEEE Computer Society Conference on, vol. 1. IEEE, 2001, pp. 1-355.
7.
BertalmioM., SapiroG., CasellesV. and BallesterC., Image inpainting, in Proceedings of the 27th annual conference on Computer graphics and interactive techniques, ACM Press/Addison-Wesley Publishing Co., 2000, pp. 417-424.
8.
ChanT.F. and ShenJ., Nontexture inpainting by curvaturedriven diffusions, Journal of Visual Communication and Image Representation12(4) (2001), 436-449.
9.
PerfilievaI., DaňkováM. and BedeB., Towards a higher degree f-transform, Fuzzy Sets and Systems180(1) (2011), 3-19.
10.
GarberD.D., Computational models for texture analysis and texture synthesis, 1981.
11.
HeegerD.J. and BergenJ.R., Pyramid-based texture analysis/ synthesis, in Proceedings of the 22nd annual conference on Computer graphics and interactive techniques. ACM, 1995, pp. 229-238.
12.
CriminisiA., PérezP. and ToyamaK., Region filling and object removal by exemplar-based image inpainting, Image Processing, IEEE Transactions on13(9) (2004), 1200-1212.
13.
PerfilievaI., Fuzzy transforms: Theory and applications, Fuzzy sets and systems157(8) (2006), 993-1023.
14.
StefaniniL., F-transform with parametric generalized fuzzy partitions, Fuzzy Sets and Systems180(1) (2011), 98-120.
15.
VlašánekP. and PerfilievaI., F-transform and discrete convolution, in European Society for Fuzzy Logic and Technology, Atlantis Press, 2015.
16.
DaňkováM. and ŘtěpničkaM., Fuzzy transform as an additive normal form, Fuzzy Sets and Systems157(8) (2006), 1024-1035.
17.
PavelV. and IrinaP., Interpolation techniques versus ftransform in application to image reconstruction in Fuzzy Systems (FUZZ-IEEE), 2014 IEEE International Conference on. IEEE, 2014, pp. 533-539.
18.
Di MartinoF., LoiaV., PerfilievaI. and SessaS., An image coding/decoding method based on direct and inverse fuzzy transforms, International Journal of Approximate Reasoning48(1) (2008), 110-131.
19.
PerfilievaI. and VlašánekP., Image reconstruction by means of f-transform, Knowledge-Based Systems70 (2014), 55-63.
20.
VajglM., PerfilievaI. and HodákováP., Advanced ftransform-based image fusion, Advances in Fuzzy Systems2012 (2012), 4.
21.
PerfilievaI., HodákováP. and HurtíkP., Differentiation by the f-transform and application to edge detection, Fuzzy Sets and Systems, 2014.
22.
SerraJ., Image analysis and mathematical morphology. Academic Press, Inc., 1983.
23.
BuyssensP., DaisyM., TschumperleD. and L´ezorayO., Exemplar-based inpainting: Technical review and new heuristics for better geometric reconstructions, Image Processing, IEEE Transactions on24(6) (2015), 1809-1824.
