# Difference between revisions of "Publications/carlinet.14.icip"

## Abstract

The Tree of Shapes is a morphological tree that provides an high-level hierarchical representation of the image suitable for many image processing tasks. This structure has the desirable properties to be self-dual and contrast-invariant and describes the organization of the objects through level lines inclusion. Yet it is defined on gray-level while many images have multivariate data (color images, multispectral imagesldots) where information are split across channels. In this paper, we propose some leads to extend the tree of shapes on colors with classical approaches based on total orders, more recent approaches based on graphs and also a new distance-based method. Eventually, we compare these approaches through denoising to highlight their strengths and weaknesses and show the strong potential of the new methods compared to classical ones.

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

## 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 ${\displaystyle {\dot {\mathcal {G}}}}$
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 ${\displaystyle {\ddot {\mathcal {G}}}}$ (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 ${\displaystyle {\ddot {\mathcal {G}}}}$ (marginal). λ = 30, PSNR = 39.98
 Preorder Brightness I (NC). λ = 100, PNSR = 37.24 Preorder Brightness I (MP), λ = 100, PSNR = 37.98 Preorder Brightness I (Pmean), λ = 100, PSNR = 38.23

## Bibtex (lrde.bib)

@InProceedings{	  carlinet.14.icip,
author	= {Edwin Carlinet and Thierry G\'eraud},
title		= {Getting a morphological Tree of Shapes for Multivariate
Images: Paths, Traps and Pitfalls},
booktitle	= {Proceedings of the 21st International Conference on Image
Processing (ICIP)},
year		= 2014,
pages		= {615--619},
abstract	= {The Tree of Shapes is a morphological tree that provides
an high-level hierarchical representation of the image
suitable for many image processing tasks. This structure
has the desirable properties to be self-dual and
contrast-invariant and describes the organization of the
objects through level lines inclusion. Yet it is defined on
gray-level while many images have multivariate data (color
images, multispectral images\ldots) where information are
split across channels. In this paper, we propose some leads
to extend the tree of shapes on colors with classical
approaches based on total orders, more recent approaches
based on graphs and also a new distance-based method.
Eventually, we compare these approaches through denoising
to highlight their strengths and weaknesses and show the
strong potential of the new methods compared to classical
ones.},
doi		= {10.1109/ICIP.2014.7025123}
}