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Unformatted text preview: EECE\CS 253 Image Processing Richard Alan Peters II Department of Electrical Engineering and Computer Science Fall Semester 2007 Lecture Notes Lecture Notes on Mathematical Morphology: Grayscale Images This work is licensed under the Creative Commons AttributionNoncommercial 2.5 License. To view a copy of this license, visit http://creativecommons.org/licenses/bync/2.5/ or send a letter to Creative Commons, 543 Howard Street, 5th Floor, San Francisco, California, 94105, USA. December 6, 2011 2 December 6, 2011 2 19992007 by Richard Alan Peters Grayscale Morphology Grayscale morphology is a multidimensional generalization of the binary operations. Binary morphology is defined in terms of setinclusion of pixel sets. So is the grayscale case, but the pixel sets are of higher dimension. In particular, standard R × C, 1 band intensity images and the associated structuring elements are defined as 3D solids wherein the 3 rd axis is intensity and setinclusion is volumetric. set inclusion (explained on p. 11 ) set inclusion (explained on p. 11 ) (a) binary, (b) & (c) grayscale (a) binary, (b) & (c) grayscale (a) (b) (c) December 6, 2011 3 December 6, 2011 3 19992007 by Richard Alan Peters Recall: Types of Images ● A real image maps an ndimensional Euclidean vector space into the real numbers. Pixel coordinates and pixel values are real. ● A discrete image maps an ndimensional grid of points into the real numbers. Coordinates are ntuples of integers, pixel values are real. ● A digital image maps an ndimensional grid into a finite set of integers. Pixel coordinates and pixel values are integers. An image is a mapping, I, from a set, S P , of pixel coordinates to a set, G , of values such that for every coordinate vector, p , there is a value I( p ) drawn from G . An image is a mapping, I, from a set, S P , of pixel coordinates to a set, G , of values such that for every coordinate vector, p , there is a value I( p ) drawn from G . December 6, 2011 4 December 6, 2011 4 19992007 by Richard Alan Peters Extended Real Numbers Define the extended real numbers, * , as the real numbers plus two symbols, ∞ and ∞ such that for all numbers x ∈ . That is if x is any real number, then ∞ is always greater than x and ∞ is always less than x . Moreover, Let represent the real numbers. , , , = ∞ ∞∞ = ∞ ∞ = ∞ + x x for all numbers x ∈ . , ∞ < < ∞ x December 6, 2011 5 December 6, 2011 5 19992007 by Richard Alan Peters p , in an ndimensional vector space n . Associated with each p is a value from * . The set of pixel locations together with their associated values form the image – a set in n+1 : In mathematical morphology a real image, I, is defined as a function that occupies a volume in a Euclidean vector space....
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 Summer '07
 AlanPeters
 Electrical Engineering, Image processing, Mathematical morphology, Dilation, Structuring element, Richard Alan Peters

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