Posted: 10/04/21

Due: 10/13/21, 11:55PM

1Introduction

• Define a painting

• Elements of a painting

• Painting techniques

• Mathematical/coding representations of painting creation

• Synthetic paintings

2Methods

2.1Importing images

Importing images into Julia is possible through the Images module. For example, Fig. displays .

∴ 

using Images, FileIO, ImageIO

∴ 

pre="/home/student/courses/MATH089/paintings/";

∴ 

imA=load(pre*"Frida_Kahlo_96.png"); typeof(imA)

∴ 

imB=load(pre*"Georges_Seurat_3.png");

∴ 

A = Float64.(Gray.(imA)); B = Float64.(Gray.(imB));

∴ 

imshow(A,cmap="gray");

∴ 

2.2Spatial correlation of picture elements (pixels)

The singular value decomposition (SVD) furnishes spatial correlation between pixels

with significance:

• $𝚺=\mathrm{diag}({\sigma }_1,\dots ,{\sigma }_n)$

  ${\displaystyle 𝚺=\left[\begin{array}{llll}{\sigma }_1& & & \\ & {\sigma }_2& & \\ & & \ddots & \\ & & & {\sigma }_n\end{array}\right]}$

• $𝑼,𝑽$ contain the correlation patterns

∴ 

U,S,V=svd(A);

∴ 

[size(A) size(U) size(S) size(V)]

∴ 

m,n=size(A)

∴ 

figure(2); imshow(S[1]*U[1:m,1]*V[1:n,1]'+S[2]*U[1:m,2]*V[1:n,2]',cmap="gray");

∴ 

3Results

4Discussion