By Maria Petrou, Costas Petrou
Following the good fortune of the 1st variation, this completely up-to-date moment variation of snapshot Processing: the basics will make sure that it is still definitely the right textual content for somebody looking an advent to the fundamental recommendations of snapshot processing. New fabric comprises photograph processing and color, sine and cosine transforms, self sufficient part research (ICA), part congruency and the monogenic sign and several new subject matters. those updates are mixed with insurance of vintage themes in photograph processing, reminiscent of orthogonal transforms and photograph enhancement, making this a very entire textual content at the topic.
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Extra info for Image Processing, 2nd Edition: The Fundamentals
The reason for this is the way the quantisation was performed: the look up table created to convert the real recorded values to digital values took into consideration the full range of possible values a sensor may record (ie from 0 to 10). To utilise the full range of grey values for each image, we should have considered the minimum and the maximum value of its pixels, and map that range to the 8 distinct grey levels. 576]. 902] get grey value 7 We must create one such look up table for way are: ⎛ ⎞ ⎛ 3 3 6 0 R = ⎝0 6 7⎠ G = ⎝1 7 1 1 3 each band.
HrN 2 ⎜ .. ⎝ . ⎠ . . hcN N .. .. ... ... ... hc1N ⎞ ⎛ hc11 hcN 1 ⎜ hc12 hcN 2 ⎟ ⎟ ⎜ .. ⎟ . . hrN N ⎜ .. ⎝ . ⎠ . . hcN N .. .. hc1N ... ... ⎞⎞ hcN 1 hcN 2 ⎟ ⎟⎟ ⎟ .. ⎟⎟ . ⎠⎟ ⎟ hcN N ⎞⎟ ⎟ hcN 1 ⎟ ⎟ ⎟ hcN 2 ⎟ ⎟⎟ .. ⎟⎟ . ⎠⎟ ⎟ hcN N ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎞⎟ hcN 1 ⎟ ⎟ ⎟ hcN 2 ⎟ ⎟⎟ .. ⎟⎟ . 89) Here the arguments of functions hc (x, α) and hr (y, β) have been written as indices to save space. 91) 1. 92) How can a separable transform be written in matrix form? 93) y=1 Notice that factor N y=1 f (x, y)hr (y, β) actually represents the product f hr of two N × N matrices, which must be another matrix s ≡ f hr of the same size.
35) The right-hand side of this expression can be thought of as the dot product of vector hTαβ ≡ [h(1, α, 1, β), h(2, α, 1, β), . . , h(N, α, 1, β), h(1, α, 2, β), h(2, α, 2, β), . . , h(N, α, 2, β), . . , h(2, α, N, β), . . 36) 1. Introduction fT 19 ≡ [f (1, 1), f (2, 1), . . , f (N, 1), f (1, 2), f (2, 2), . . , f (N, 2), . . , f (1, N ), f (2, N ), . . 37) This last vector is actually the image f (x, y) written as a vector by stacking its columns one under the other. If we imagine writing g(α, β) in the same way, then vectors hTαβ will arrange themselves as the rows of a matrix H, where for β = 1, α will run from 1 to N to give the ﬁrst N rows of the matrix, then for β = 2, β will run again from 1 to N to give the second N rows of the matrix, and so on.