Graph Laplacian for Spectral Clustering and Seeded Image Segmentation
Resumo
Interactive segmentation methods have gained much attention lately, specially due to their good performance in segmenting complex images and easy utilization. However, most interactive segmentation algorithms rely on sophisticated mathematical formulations whose effectiveness highly depends on the kind of image to be processed. In fact, sharp adherence to the contours of image segments, uniqueness of solution, high computational burden, and extensive user interaction are some of the weaknesses of most existing methods. In this thesis we proposed two novel interactive image segmentation techniques that sort out the issues raised above. The proposed methods rely on Laplace operators, spectral graph theory, and optimization schemes towards enabling highly accurate segmentation tools which demand a reduced amount of user interaction while still being mathematically simple and computationally efficient. The good performance of our segmentation algorithms is attested by a comprehensive set of comparisons against representative state-of-the-art methods. As additional contribution, we have also proposed two new algorithms for inpainting and photo colorization, both of which rely on the accuracy of our segmentation apparatus
Referências
Casaca, W., Almeida, M. P., and Boaventura, M. (2013a). Denoising textured images via regularized anisotropic diffusion. In An Introduc. Guide to Image and Video Proc., pages 48–71. Brisbane, Australia.
Casaca, W., Almeida, M. P., Boaventura, M., and Nonato, L. G. (2014a). Combining anisotropic diffuison, transport equation and texture synthesis for inpainting textured images. Pattern Rec. Letters, 36:36–45.
Casaca, W. and Boaventura, M. (2010). A decomposition and noise removal method combining diffusion equation and wave atoms for textured images. Mathematical Problems in Engineering, 2010:1–21.
Casaca, W., Boaventura, M., and de Almeida, M. P. (2011a). Classifying texture and free-textured content from images using nonlinear anisotropic diffusion. In 5th Conf. Mathematical Analysis, pages 210–214.
Casaca, W., Colnago, M., and Nonato, L. G. (2015a). Interactive image colorization using laplacian coordinates. In 16th International Conf. on Computer Analysis of Images and Patterns (CAIP) (accepted).
Casaca, W., Gomez-Nieto, E., de O.L. Ferreira, C., Tavares, G., Pagliosa, P., Paulovich, F., Nonato, L. G., and Paiva, A. (2012). Colorization by multidimensional projection. In 25th SIBGRAPI, pages 32–38.
Casaca, W., Gomez-Nieto, E., Hartmann, I., Taubin, G., and Nonato, L. G. (2015b). Dealing with multiple requirements in geometric arrangements. IEEE Trans. Vis. and Computer Graphics (TVCG) (accepted).
Casaca, W., Motta, D., Taubin, G., and Nonato, L. G. (2015c). A user-friendly interactive image inpainting framework using laplacian coordinates. In IEEE Int. Conference on Image Processing (ICIP) (accepted).
Casaca, W., Nonato, L. G., and Taubin, G. (2014b). Laplacian coordinates for seeded image segmentation. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 384–391.
Casaca, W., Paiva, A., Gomez-Nieto, E., Joia, P., and Nonato, L. G. (2013b). Spectral image segmentation using image decomposition and inner product-based metric. J. of Math. Imag. and Vis., 45(3):227–238.
Casaca, W., Paiva, A., and Nonato, L. G. (2011b). Spectral segmentation using cartoon-texture decomposition and inner product-based metric. In 24th SIBGRAPI, pages 266–273.
Chung, F. (1997). Spectral Graph Theory. CBMS, Ameciran Mathematical Society.
Couprie, C., Grady, L., Najman, L., and Talbot, H. (2011). Power watershed: A unifying graph-based optimization framework. IEEE Trans. on PAMI, 33(7):1384–1399.
Cour, T., Bénézit, F., and Shi, J. (2005). Spectral segmentation with multiscale graph decomposition. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pages 1124–1131.
Cousty, J., Bertrand, G., Najman, L., and Couprie, M. (2009). Watershed cuts: Minimum spanning forests and the drop of water principle. IEEE Trans. on PAMI, 31(8):1362–1374.
Gomez-Nieto, E., Casaca, W., Nonato, L. G., and Taubin, G. (2013). Mixed integer optimization for layout arrangement. In 26th Conference on Graphics, Patterns and Images (SIBGRAPI), pages 115–122.
Gomez-Nieto, E., Roman, F., Pagliosa, P., Casaca,W., Helou, E., Oliveira, M. C., and Nonato, L. G. (2014). Similarity preserving snippet-based visualization of web search results. IEEE TVCG, 20:457–470.
Grady, L. (2006). Random walks for image segmentation. IEEE Trans. on PAMI, 28(11):1768–1783.
Joia, P., Gomez-Nieto, E., Neto, J. B., Casaca, W., , Paiva, A., and Nonato, L. G. (2012). Class-specific metrics for multidimensional data projection applied to cbir. Visual Computer, 28(10):1027–1037.
Peng, B. and Zhang, D. (2013). A survey of graph approaches to image seg. Pattern Rec., 46(3):1020–1038.
Shi, J. and Malik, J. (2000). Normalized cuts and image segmentation. IEEE Trans. on PAMI, 22:888–905.
