Publications/carlinet.14.icip.inc

Getting a morphological Tree of Shapes for mulativariate images: paths, traps, and pitfalls

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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle L_{HLS} = 0.30 R + 0.59 G + 0.11 B }
  • Brightness Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle I = (R+G+B) / 3 }
  • Chrominance in La*b* Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C = \sqrt{a^2 + b^2} }

Results Summary

	Best Grain<br\> Size	Min PSNR	Max PSNR	Avg. PSNR
Shape-Graph Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \dot{\mathcal{G}}}
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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \ddot{\mathcal{G}}} (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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \ddot{\mathcal{G}}} (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 images

madeleine