Revision as of 13:32, 18 February 2014

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 $L_{HLS}=0.30R+0.59G+0.11B$
- Brightness $I=(R+G+B)/3$
- Chrominance in La*b* $C={\sqrt {a^{2}+b^{2}}}$

Evaluation Procedure Description

Results Summary

	Best Grain Size	Min PSNR	Max PSNR	Avg. PSNR
Shape-Graph ${\dot {\mathcal {G}}}$
Preorder C_Lab (NC)	2	36.21	39.60	37.43
Preorder L_Lab (NC)	5	36.32	38.43	37.43
Preorder L_HLS (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 C_Lab (MP)	300	36.31	41.37	38.92
Preorder C_Lab (P_mean)	200	36.20	41.45	39.03
Preorder L_Lab (MP)	300	36.77	41.38	39.34
Preorder L_HLS (MP)	300	36.65	41.49	39.59
Preorder L_Lab (P_mean)	200	37.00	42.22	39.72
Preorder Brightness (MP)	300	36.60	42.69	39.94
Preorder L_HLS (P_mean)	200	37.03	41.84	39.96
Preorder Brightness (P_mean)	200	36.41	43.19	40.40
Shape-Graph ${\ddot {\mathcal {G}}}$ (marginal)	50	37.59	50.21	41.66

Detailed Results

By images

By methods

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@@ Line 27: / Line 27: @@
 !							!! Best Grain Size	!! Min PSNR	!! Max PSNR	!! Avg. PSNR
 |-
-| Shape-Graph \GI					||	||		||		||
+| Shape-Graph <math>\dot{\mathcal{G}}</math>					||	||		||		||
 |-
-| Preorder $C_\textrm{La*b*}$ (NC)			|| 2	|| 36.21	|| 39.60	|| 37.43
+| Preorder C<sub>La*b*</sub> (NC)			|| 2	|| 36.21	|| 39.60	|| 37.43
 |-
-|Preorder $L_\textrm{La*b*}$ (NC)			|| 5	|| 36.32	|| 38.43	|| 37.43
+|Preorder L<sub>La*b*</sub> (NC)			|| 5	|| 36.32	|| 38.43	|| 37.43
 |-
-|Preorder $L_\textrm{HLS}$ (NC)				|| 7	|| 36.34	|| 39.36	|| 37.57
+|Preorder L<sub>HLS</sub> (NC)				|| 7	|| 36.34	|| 39.36	|| 37.57
 |-
 |Preorder Brightness (NC)				|| 8.5	|| 36.39	|| 39.60	|| 37.67
@@ Line 41: / Line 41: @@
 |Distance-Based						|| 15	|| 37.02	|| 41.14	|| 38.76
 |-
-|Preorder $C_\textrm{La*b*}$ (MP)			|| 300	|| 36.31	|| 41.37	|| 38.92
+|Preorder C<sub>La*b*</sub> (MP)			|| 300	|| 36.31	|| 41.37	|| 38.92
 |-
-|Preorder $C_\textrm{La*b*}$ ($P_\textrm{mean}$)	|| 200	|| 36.20	|| 41.45	|| 39.03
+|Preorder C<sub>La*b*</sub> (P<sub>mean</sub>)	|| 200	|| 36.20	|| 41.45	|| 39.03
 |-
-|Preorder $L_\textrm{La*b*}$ (MP)			|| 300	|| 36.77	|| 41.38	|| 39.34
+|Preorder L<sub>La*b*</sub> (MP)			|| 300	|| 36.77	|| 41.38	|| 39.34
 |-
-|Preorder $L_\textrm{HLS}$ (MP)				|| 300	|| 36.65	|| 41.49	|| 39.59
+|Preorder L<sub>HLS</sub> (MP)				|| 300	|| 36.65	|| 41.49	|| 39.59
 |-
-|Preorder $L_\textrm{La*b*}$ ($P_\textrm{mean}$)	|| 200	|| 37.00	|| 42.22	|| 39.72
+|Preorder L<sub>La*b*</sub> (P<sub>mean</sub>)	|| 200	|| 37.00	|| 42.22	|| 39.72
 |-
 |Preorder Brightness (MP)				|| 300	|| 36.60	|| 42.69	|| 39.94
 |-
-|Preorder $L_\textrm{HLS}$ ($P_\textrm{mean}$)		|| 200	|| 37.03	|| 41.84	|| 39.96
+|Preorder L<sub>HLS</sub> (P<sub>mean</sub>)		|| 200	|| 37.03	|| 41.84	|| 39.96
 |-
-|Preorder Brightness ($P_\textrm{mean}$)		|| 200	|| 36.41	|| 43.19	|| 40.40
+|Preorder Brightness (P<sub>mean</sub>)		|| 200	|| 36.41	|| 43.19	|| 40.40
 |-
-|Shape-Graph $\GII$ (marginal)				|| 50	|| 37.59	|| 50.21	|| 41.66
+|Shape-Graph <math>\ddot{\mathcal{G}}</math> (marginal)				|| 50	|| 37.59	|| 50.21	|| 41.66
 |}

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