Tree of Shapes of Multivariate Images: Leads and Traps

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Method Description

(Pre)order based methods

Colors are reduced to scalar value that defines an ordering to compute the Tree of Shapes. We have tested different pre-order on several color space, as well as several restitution rules.

  • Restitution Rules:
    • Nearest color (NC): A removed shape is assigned to the closest color in the parent shape.
    • Mean (Pmean): Every shape is assigned with the mean color of its pixels.
    • Mean Parent (MP): A removed shape is assigned with the mean color of the parent shape pixels.
  • Total orders considered: (NC, Pmean, MP are equivalent in this case).
    • Lexicographical (Lex): Lexicographical order with the R,G,B triplet.
  • Total pre-orders considered:
    • Lightness in La*b*
    • Lightness in HLS
    • Brightness
    • Chrominance in La*b*

Distance based method

Graph-based method

Evaluation Procedure Description

The clean dataset used for our benchmark is available here, as well as the noisy version of the previous dataset (here). The clean dataset used for our benchmark is available here, as well as the noisy version of the previous dataset (here).

Results Summary

Best Grain<br\> Size Min PSNR Max PSNR Avg. PSNR
Shape-Graph
Preorder CLa*b* (NC) 2 36.21 39.60 37.43
Preorder LLa*b* (NC) 5 36.32 38.43 37.43
Preorder LHLS (NC) 7 36.34 39.36 37.57
Preorder Brightness (NC) 8.5 36.39 39.60 37.67
Order Lex 100 36.42 47.78 38.10
Distance-Based 15 37.02 41.14 38.76
Preorder CLa*b* (MP) 300 36.31 41.37 38.92
Preorder CLa*b* (Pmean) 200 36.20 41.45 39.03
Preorder LLa*b* (MP) 300 36.77 41.38 39.34
Preorder LHLS (MP) 300 36.65 41.49 39.59
Preorder LLa*b* (Pmean) 200 37.00 42.22 39.72
Preorder Brightness (MP) 300 36.60 42.69 39.94
Preorder LHLS (Pmean) 200 37.03 41.84 39.96
Preorder Brightness (Pmean) 200 36.41 43.19 40.40
Shape-Graph (marginal) 50 37.59 50.21 41.66
Original image with gaussian noise corruption. PSNR = 36.46
Distance-based.
λ = 9, PSNR = 37.88
Shape-graph (marginal).<br\> λ = 30, PSNR = 39.98
Preorder Brightness I (NC). <br\> λ = 100, PNSR = 37.24
Preorder Brightness I (MP), <br\> λ = 100, PSNR = 37.98
Preorder Brightness I (Pmean),
λ = 100, PSNR = 38.23

Detailed Results

By methods

By images

Bibtex (lrde.bib)

@InProceedings{	  carlinet.14.icip,
  author	= {Edwin Carlinet and Thierry G\'eraud},
  title		= {Tree of Shapes of Multivariate Images: Leads and Traps},
  booktitle	= {Submitted to the 21st International Conference on Image
		  Processing (ICIP)},
  year		= 2014,
  address	= {Paris, France},
  pages		= {1--5},
  project	= {Image},
  abstract	= {},
  note		= {Submitted}
}