Download (2,k)-Factor-Critical Graphs and Toughness by Cai M.-C., Favaron O., Li H. PDF

By Cai M.-C., Favaron O., Li H.

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HINT: Use a ruler. The images in Fig. 3 illustrate the triangle inequality of the norm. They represent, clockwise from top left, A1 , A2 , A3 , and A1 + A2 + A3 , respectively. At any image point the pixel is a vector consisting of three color components. The norms of these images are A1 = 517, A2 = 527, A3 = 468, and A1 + A2 + A3 = 874, respectively. As expected from a norm, we obtain A 1 + A 2 + A 3 ≤ A 1 + A2 + A3 . 21) which equals 1 if both A1 and A2 are vectors that share the same direction.

The list of discrete image types can be made longer, but we stop here to proceed with an example illustrating what one can do with vector spaces. 1 A suitable name for these coordinates would be stixels, making allusion to the spatio– temporal nature of the data. 2 Discrete Image Types, Examples 39 Fig. 1. An image sequence and the average image (bottom) obtained by applying the matrix vector space rules of addition and multiplication by a scalar according to Eq. 1. The 2D discrete color images (of the same size) are vector spaces if we treat them as matrices having elements consisting of arrays representing the three color components, R, G, B .

Among the cones, our M-type need the least amount of photons for activation, meaning that more intense blues and reds, compared to green-yellows, are needed in order to be noticed by humans. The coarseness of a viewed pattern matters to the photoreceptors too. A retinal image with a very coarse pattern has small variations of light intensities in a given area of the retina than does a fine pattern that varies more. A repeating pattern is also called texture. Coarse textures contain more low spatial-variations than fine textures.

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