By Pierre Soille
From studies of the 1st variation: "This is a scholarly journey de strength in the course of the international of morphological photo research […]. i like to recommend this e-book unreservedly because the top one i've got encountered in this specific subject […]" BMVA News
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9. Point-wise maximum V and point-wise minimum /\ between two signals or I-D images fand g. Another basic set operator is complementation. 3) j"(x) = t max - j(x). r, The c:omplementation of a binary image, a 1-D signal, and a grey tone image is illustrated in Fig. 10. The complementation operator is denotecl by C: C(f) = I r· In theoretical treatises dealing with real rat her than discrete intervals for grey levels, the point-wise maximum is called the supremum and the point-wise minimum the infimum.
12. A set B with an origin o is symmetrie if and only if B = B. In general, we define a set X to be symmetrie if X = Xb, for so me b E R 2 or Z2 for digital sets. , whether the first is included in the seeond or viee versa. In this seetion, we show how to ex te nd this not ion to grey tone images and to image transformations. Some advaneed definitions related to lattiee theory are also presented. 1 On images and image transformations An image f is less than or equal to an image 9 with the same definition domain if the value of f is less than or equal to the value of 9 at all pixels x in the eommon domain of definition .
Dougherty, P. Gader & J. Serra, eds, 'Image algebra and morphological image processing IV', Vol. SPIE-2030, pp. 43-53. Sternberg, S. (1986), 'Grayscale morphology', Computer Graphics and Image Processing 35, 333-355. Verwer, B. (1991), Distance transforms: metrics, algorithms and applications, PhD thesis, Technische Universiteit Delft. Vincent, L. (1991), Exact Euclidean distance function by chain propagations, in 'Proc. IEEE Computer Vision and Pattern Recognition', pp. 520-525. , Coyle, E. & Gallagher, N.