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• Isotropic Expansion

• Isotropic Contraction

• Anisotropic Expansion

• Anisotropic Contraction

• ISOTROPIC EXPANSION
• 
  (a)
  
  (b)
• (a) Synthetic circle with radius equal to 50 pixels and center at the pixel (125,125).
• (b) Isotropic expanded images for different values of the parameter thr.
  Values of the parameters used for the transformation: l=0.01, it=1000, n_dir=32.
  The picture in black is the original image; the one in red corresponds to thr=200, whereas the one in blue corresponds to thr=250.
  
• 
  Animation for varying thr ranging between 180 and 254 and given values of l(=0.01) and it(=1000). As thr increases, so the image expands.
  

 
 


• 
  (a)
  
  (b)
• (a) Isotropic expanded images for different values of the parameter l.
  Values of the parameters used for the transformation: it=1000, n_dir=32, thr=240.
  The black is the original image; red corresponds to l=0.1, whereas blue corresponds to l=0.01.
• (b) Animation for varying l ranging between 1 and 0.01 and given values of it(=1000) and of thr(=240).
  As l decreases, so the circle expands.
  

• ISOTROPIC CONTRACTION
• 
  (a)
  
  (b)
• (a) Synthetic circle with radius equal to 50 pixels and center at the pixel (125,125).
• (b) Isotropic contracted images for different values of the parameter thr.
  Values of the parameters used for the transformation: l=0.01, it=1000, n_dir=32.
  The picture in black is the original image; the one in red corresponds to thr=50, whereas the one in blue corresponds to thr=10. As thr approaches zero, so the image contracts.
  
  
• 
  Animation for varying thr ranging between 2 and 160 and given values of l(=0.01) and it(=1000). As thr decreases, so the image contracts.
  

• ANISOTROPIC EXPANSION
• 
  (a)
  
  (b)
• (a) Synthetic circle with radius equal to 50 pixels and center at the pixel (125,125).
• (b) Anisotropic expanded images along the vertical direction and for different values of the parameter thr.
  Let e₁ denote the vertical direction and e₂ the perpendicular one, the values of the parameters used for the transformation are: l₁=0.001, l₂=100, it=1000, n_dir=32.
  The picture in black is the original image; the one in red corresponds to thr=200, whereas the one in blue corresponds to thr=250.
  
• 
  (a)
  
  (b)
• (a) Anisotropic expanded images along the horizontal direction e₁. The values of the parameters used for the transformation are: l₁=0.001, l₂=100, it=1000, n_dir=32.
  The picture in black is the original image; the one in red corresponds to thr=200, whereas the one in blue corresponds to thr=250.
• (b) Anisotropic expanded images along the direction e₁=(√2/2,√2/2). The values of the parameters used for the transformation are: l₁=0.001, l₂=100, it=1000, n_dir=32.
  The picture in black is the original image; the one in red corresponds to thr=200, whereas the one in blue corresponds to thr=250.
  
• 
  Animation for varying thr ranging between 10 and 254. As thr increases, so the image expands.
  

• ANISOTROPIC CONTRACTION
• 
  (a)
  
  (b)
• (a) Synthetic circle with radius equal to 50 pixels and center at the pixel (125,125).
• (b) Anisotropic contracted images along the direction e₁=(1,0) and for different values of the parameter thr.
  The values of the parameters used for the transformation are: l₁=0.01, l₂=10000, it=100, n_dir=32.
  The picture in black is the original image; the one in red corresponds to thr=50, whereas the one in blue corresponds to thr=5.
  
• 
  (a)
  
  (b)
• (a) Anisotropic contracted images along the direction e₁=(0,1). The values of the parameters used for the transformation are: l₁=0.01, l₂=10000, it=100, n_dir=32.
  The picture in black is the original image; the one in red corresponds to thr=50, whereas the one in blue corresponds to thr=5.
• (b) Anisotropic contracted images along the direction e₁=(√2/2,√2/2). The values of the parameters used for the transformation are: l₁=0.01, l₂=10000, it=100, n_dir=32.
  The picture in black is the original image; the one in red corresponds to thr=50, whereas the one in blue corresponds to thr=5.
  

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