Then solve $ A$ \ $ b $ to obtain the pixel values of the output image, which is almost the same as the input image (with error of about $9e^$). Then we can insert a new row $k$ into $A$ and $b$, where $A(k, i) = 1, A(k, j) = -1, B(k) = s(x 1, y) - s(x, y)$ and rest of $A(k)$ will all be $0$. Suppose $i$ correspond to the index of $v(x 1, y)$ and $j$ correspond to the index of $v(y, x)$ in vector $b$. Since we want to minimize the value of it, we can write it as $v(x 1, y) - v(x, y) = s(x 1, y) - s(x, y)$. Sometimes you want a particular picture to be output as a grayscale image, yet the original image is in color. Take $(v(x 1, y) - v(x, y) - (s(x 1, y)-s(x, y)))^2$ as an example. Color2Gray for InDesign allows you to convert placed color photos to grayscale without modifying the original color image. We can now construct linear least square $Av = b$, where v is the pixel values of the output image, A is the coefficient matrix of equations and b is the vector of constants in the equations. Setting up the following constraints on the ouput image: Perception Preserving Decolorization Perception Preserving Decolorization L of CIELab Matlab Bala04 Color2Gray Rasche05 Smith08 Lu12.This is just an example for how to set up constraints and construct output images by solving linear least square problems. There are commands in MATLAB to set the limits of the color bar, you can find those reading the documentation. In the process of converting colored image into grayscale image, we may lose important gradient information. APID ToolAssistant is free, and Color2Gray is almost free (we charge a small amount of money for it US19). The resulting image is a proper conversion, and renders on the black (K) plate only. Implement color2gray with how-to, Q
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