• Aucun résultat trouvé

Corrigendum: a mixed Boolean and deposit model for the modeling of metal pigments in paint layers

N/A
N/A
Protected

Academic year: 2021

Partager "Corrigendum: a mixed Boolean and deposit model for the modeling of metal pigments in paint layers"

Copied!
2
0
0

Texte intégral

(1)

HAL Id: hal-01232489

https://hal-mines-paristech.archives-ouvertes.fr/hal-01232489

Submitted on 27 Nov 2015

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Corrigendum: a mixed Boolean and deposit model for the modeling of metal pigments in paint layers

Enguerrand Couka, François Willot, Dominique Jeulin

To cite this version:

Enguerrand Couka, François Willot, Dominique Jeulin. Corrigendum: a mixed Boolean and deposit

model for the modeling of metal pigments in paint layers. Image Analysis and Stereology, International

Society for Stereology, 2015, 34 (3), pp.145. �10.5566/ias.1417�. �hal-01232489�

(2)

Submitted to Image Anal Stereol, 1 pages Corrigendum

CORRIGENDUM: A MIXED BOOLEAN AND DEPOSIT MODEL FOR THE MODELING OF METAL PIGMENTS IN PAINT LAYERS

E NGUERRAND C OUKA , F RANC ¸ OIS W ILLOT AND D OMINIQUE J EULIN

Center for Mathematical Morphology, MINES ParisTech, PSL Research University, 35 rue Saint-Honor´e, 77300 Fontainebleau, France

e-mail: [email protected], [email protected], [email protected]

(Submitted)

The expressions for the distribution function and the cumulative distribution of chord lengths given in (Couka et al., 2015) (Eqs. 3 and 4) are incorrect. The latter must be replaced by:

P

1

(ℓ) = P { L < ℓ } = 1

√ 1

( D

)

2

, (1)

P

2

(ℓ) = 1 D

 √(

D

)

2

1 cos

−1

(

D

)  , (2)

respectively. The above expressions are numericaly very similar to that given in (Couka et al., 2015) and to the measurements carried out on the SEM images (see updated Fig. 1 (a) and (b), which replace Figs. 7 and 18, resp).

(a) (b)

Fig. 1. (a): Cumulative distribution of the lengths of the particles along their main direction, on a 2D section: measurements (red), theoretical distribution for cylinders with constant (green) or uniform diameter (blue). (b): Cumulative distribution function of the length of particles along the main directions as observed on SEM images (blue) and stack model (red). Theoretical formula seen in Eq. (2) shown in green.

REFERENCES

Couka E, Willot F, Jeulin D (2015). A mixed boolean and deposit model for the modeling of metal pigments in paint layers. Image Anal Stereol 34(2):125-134.

1

Références

Documents relatifs

Especially in this area the modeling interface is considered in most cases perfectly bonded with a local behavior based on empirical fatigue laws or fracture mechanics such as

We can design spaces that encourage physical activity or increase productivity and job satisfaction.1 8 For those who find that being forced into social interaction is a

prove a large deviation principle for the discretised Young measures and the associated concentration prop- erty, which yields the maximum of entropy states presented in section 4

Another way to use STRING is to download and extend its relational database schema; this can, for example, be useful for projects dedicated to additional types of information

En ce qui concerne notre corpus, il est évident que Yasmina est le personnage le plus présent que les autres personnages, ainsi elle est présente toujours dans les lieux

The model values of the input nodes are given in parentheses in Table 2 and mock is represented by the logical steady state of the model without activation of any input node.. In

The system allows users to draw anything using the paint tool and augment it onto an object in real time while providing a new experience and enjoyment during the pro- cess.. The

In this paper we consider a class of MIMO bilinear systems (with constant delays in both the state and the input) as an input-output model for flow separation control