Introduction to Color - Brown University

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CS123 | INTRODUCTION TO COMPUTER GRAPHICS Non-linearity of Visual System (2/4) To achieve equal steps in brightness, space logarithmically rather than linearly, so that I j+1 = I j = r I j I j−1 Use the following relations: I 0 = I 0 , I 1 = r ⋅ I 0 , I 2 = r ⋅ I 1 = r 2 I 0 , I 3 = r ⋅ I 2 = r 3 I 0 , … , I 255 = r 255 ⋅ I 0 = 1 Therefore: r = 1 I 0 1 255 , Ij = r j ⋅ I 0 = 1 I 0 j 255 ⋅ I0 = I 0 255−j 255 for 0 ≤ j ≤ 255 Andries van Dam <strong>Color</strong> 16/57
CS123 | INTRODUCTION TO COMPUTER GRAPHICS Non-linearity of Visual System (3/4) In general for n+1 intensities: r = 1 I 0 n , 1 Ij = I 0 n−j n , for 0 ≤ j ≤ n Thus for: n = 3 (4 intensities) and I 0 =1/8, r=2, intensity values of 1/8, 1/4, 1/2, and 1 Andries van Dam <strong>Color</strong> 17/57
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