Abstract
Most digital processing nowadays is in digital format. Many transformations, such as contrast enhancement, restoration, color correction, etc. can be achieved through very simple and versatile algorithms However, a major branch of image processing algorithms makes extensive use of spatial transformations such as rotation, translation, zoom, anamorphosis, homography, distortion, derivation, etc. that are only defined in the analog domain. A digital image processing algorithm that mimics a spatial transformation is usually designed by using the so-called kernel based approach. This involves two kernels to ensure the continuous to discrete interplay: a sampling kernel and a reconstruction kernel, whose choice is highly arbitrary. The maxitive kernel based approach can be seen as an extension of the conventional kernel based approach and it reduces the impact of this arbitrary choice. It consists in replacing at least one of the kernels by a normalized fuzzy subset of the image plane. This replacement in the digital image spatial transformation framework leads to computing the convex set of all the images that would be obtained by using a (continuous convex) set of conventional kernels. Use of this set generates a kind of robustness that can reduce the risk of false interpretation. Medical imaging, for example, would be an application that could benefit from such an approach.
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Notes
- 1.
Computed Tomography scan is a computational method for reconstructing cross-sectional images from sets of X-ray measurements taken from different angles.
- 2.
Positron-Emission Tomography is a nuclear medicine functional imaging technique used to observe metabolic processes in the body.
References
Akrout, H., Crouzet, J-F., Strauss, O.: Multidimensional possibility/probability domination for extending maxitive kernel based signal processing. Fuzzy Sets Syst. (to appear)
Bloch, I.: Fuzzy sets for image processing and understanding. Fuzzy Sets Syst. 281, 280–291 (2015). Special Issue Celebrating the 50th Anniversary of Fuzzy Sets
Danielsson, P.-E., Hammerin, M.: High-accuracy rotation of images. CVGIP: Graph. Models Image Process. 54(4), 340–344 (1992)
Denneberg, D.: Non-Additive Measure and Integral. Kluwer Academic Publishers (1994)
Dubois, D.: Possibility theory and statistical reasoning. Comput. Stat. Data Anal. 51(1):47–69 (2006). The Fuzzy Approach to Statistical Analysis
Graba, F., Comby, F., Strauss, O.: Non-additive imprecise image super-resolution in a semi-blind context. IEEE Trans. Image Process. 26(3), 1379–1392 (2017)
Graba, F., Strauss, O.: An interval-valued inversion of the non-additive interval-valued f-transform: Use for upsampling a signal. Fuzzy Sets Syst. 288, 26–45 (2016)
Grabisch, M., Marichal, J.-L., Mesiar, R., Pap, E.: Aggregation Functions. Cambridge University Press (2009)
Komatsu, K., Sezaki, K.: Lossless rotation transformations with periodic structure. In: IEEE International Conference on Image Processing 2005, vol. 2, pp. II–273 (2005)
Kucharczak, F., Loquin, K., Buvat, I., Strauss, O., Mariano-Goulart, D.: Interval-based reconstruction for uncertainty quantification in pet. Phys. Med. Biol. 63(3), 035014 (2018)
Kucharczak, F., Mory, C., Strauss, O., Comby, F., Mariano-Goulart, D.: Regularized selection: a new paradigm for inverse based regularized image reconstruction techniques. In: Proceedings of IEEE International Conference on Image Processing, Beijin, China (2017)
Lehmann, T.M., Gonner, C., Spitzer, K.: Survey: interpolation methods in medical image processing. IEEE Trans. Med. Imaging 18(11), 1049–1075 (1999)
Loquin, K., Strauss, O.: On the granularity of summative kernels. Fuzzy Sets Syst. 159(15), 1952–1972 (2008)
Loquin, K., Strauss,O.: Linear filtering and mathematical morphology on an image: a bridge. In: Proceedings of IEEE International Conference on Image Processing, pp. 3965–3968. Le Caire, Egypt (2009)
Nie, Y., Barner, K.E.: The fuzzy transformation and its applications in image processing. IEEE Trans. Image Process. 15(4), 910–927 (2006)
Omhover, J., Detyniecki, M., Rifqi, M., Bouchon-Meunier, B.: Ranking invariance between fuzzy similarity measures applied to image retrieval. In: 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542), vol. 3, pp. 1367–1372 (2004)
Park, S.C., Park, M.K., Kang, M.G.: Super-resolution image reconstruction: a technical overview. Signal Process. Mag. IEEE 20(3), 21–36 (2003)
Perfilieva, I., Novák, V., Dvořák, A.: Fuzzy transform in the analysis of data. Int. J. Approx. Reason. 48(18), 36–46 (2008)
Rico, A., Strauss, O.: Imprecise expectations for imprecise linear filtering. Int. J. Approx. Reason. 51(8), 933–947 (2010)
Rico, A., Strauss, O.: Imprecise expectations for imprecise linear filtering. Int. J. Approx. Reason. 51(8), 933–947 (2010)
Rico, A., Strauss, O., Mariano-Goulart, D.: Choquet integrals as projection operators for quantified tomographic reconstruction. Fuzzy Sets Syst. 160(2), 198–211 (2009)
Ruspini, E.: New experimental results in fuzzy. Inf. Sci. 6, 273–284 (1973)
Schmeidler, D.: Integral representation without additivity. Process. Am. Math. Soc. 2 (1986)
Shen, J., Castan, S.: Towards the unification of band-limited derivative operators for edge detection. Signal Process. 31(2), 103–119 (1993)
Strauss, O.: Non-additive interval-valued f-transform. Fuzzy Sets Syst., 1–24 (2015)
Unser, M.: Splines: a perfect fit for signal and image processing. IEEE Signal Process. Mag. 16, 22–38 (1999)
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Strauss, O., Loquin, K., Kucharczak, F. (2021). On Maxitive Image Processing. In: Lesot, MJ., Marsala, C. (eds) Fuzzy Approaches for Soft Computing and Approximate Reasoning: Theories and Applications. Studies in Fuzziness and Soft Computing, vol 394. Springer, Cham. https://doi.org/10.1007/978-3-030-54341-9_18
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