Observatorio de I+D+i UPM

Memorias de investigación
Research Publications in journals:
On the composition of digitally continuous multivalued functions
Year:2015
Research Areas
  • Mathematics
Information
Abstract
In Escribano et al. (Discrete Geometry for Computer Imagery. Lecture Notes in Computer Science, vol. 4992. Springer, Berlin, pp. 81?92, 2008), Escribano et al. (Discrete Geometry for Computer Imagery. Lecture Notes in Computer Science, vol. 5810. Springer, Berlin, pp. 275? 287, 2009) and Escribano et al. (J Math Imaging Vis 42:76? 91, 2012), a notion of continuity in digital spaces, which extends the usual notion of digital continuity, was introduced. In Escribano et al. (Discrete Geometry for Computer Imagery. Lecture Notes in Computer Science, vol. 4992. Springer, Berlin, pp. 81?92, 2008), it was claimed that the composition of two digitally continuous multivalued functions is a digitally continuous multivalued function. However, this result is only correct in the following situation: If X ? Zm, Y ? Zn, Z ? Zp, and F : X ? Y and G : Y ? Z are, respectively, a (k, k? )-continuous multivalued function and a (k? , k? )-continuous multivalued function, with k = 3m ? 1, then GF : X ? Z is a (k, k? )- continuous multivalued function. In this paper, we give a proof of this result. On the other hand, in Escribano et al. (Discrete Geometry for Computer Imagery. Lecture Notes in Computer Science, vol. 5810. Springer, Berlin, pp. 275?287, 2009) and Escribano et al. (J Math Imaging Vis 42:76-91, 2012), the continuity of the composition of continuous multivalued functions is used in some proofs. Therefore, those proofs are only valid for k = 8. We give in this paper new proofs for the case k = 4 not requiring this property, with the exception of a result on the sequential deletion of 4-simple points which we state here as Conjecture 1.
International
Si
JCR
Si
Title
Journal of Mathematical Imaging And Vision
ISBN
0924-9907
Impact factor JCR
2,33
Impact info
Datos JCR del año 2013
Volume
Journal number
From page
1
To page
14
Month
SIN MES
Ranking
Participants
  • Autor: Antonio Giraldo Carbajo (UPM)
  • Autor: M. Asuncion Sastre Rosa (UPM)
Research Group, Departaments and Institutes related
  • Creador: Departamento: Matemática Aplicada a Las Tecnologías de la Información y Las Comunicaciones
S2i 2020 Observatorio de investigación @ UPM con la colaboración del Consejo Social UPM
Cofinanciación del MINECO en el marco del Programa INNCIDE 2011 (OTR-2011-0236)
Cofinanciación del MINECO en el marco del Programa INNPACTO (IPT-020000-2010-22)