María Asunción Sastre

Digitally continuous multivalued functions

We introduce in this paper a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach uses multivalued maps. We show how the multivalued approach provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we characterize the deletion of simple points, one of the most important processing operations in digital topology, as a particular kind of retraction.

Moments of infinite convolutions of symmetric Bernoulli distributions

We study the infinite convolution of symmetric Bernoulli distributions associated to a parameter r. We obtain an explicit formula for the moments as a function of Bernoulli numbers and conditioned partitions. Applying this formula we obtain the moments as a quotient of polynomials in the parameter r. The leading coefficient of the numerator is related to the asymptotic behavior of the moments and, unexpectedly, this coefficients are the absolute values of Euler numbers.

Computing the Hessenberg matrix associated with a self-similar measure

We introduce in this paper a method to calculate the Hessenberg matrix of a sum of measures from the Hessenberg matrices of the component measures. Our method extends the spectral techniques used by G. Mantica to calculate the Jacobi matrix associated with a sum of measures from the Jacobi matrices of each of the measures. We apply this method to approximate the Hessenberg matrix associated with a self-similar measure and compare it with the result obtained by a former method for self-similar measures which uses a fixed point theorem for moment matrices. Results are given for a series of classical examples of self-similar measures. Finally, we also apply the method introduced in this paper to some examples of sums of (not self-similar) measures obtaining the exact value of the sections of the Hessenberg matrix.

Characterization of the deletion of (26,6)-simple points as multivalued (N,26)-retractions

Abstract In previous papers we have introduced a notion of multivalued continuity in digital spaces which extends the usual notion of digital continuity and allows us to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we have characterized the deletion of simple points in 2-D, one of the most important processing operations in digital topology, as a particular kind of retraction. In this work we extend this result to three-dimensional digital sets, characterizing the deletion of ( 26 , 6 ) -simple points in 3-D as ( N , 26 ) -retractions.

Ronse deletability conditions and ( N , k ) -retractions

Highlights? We consider retractions defined by digitally continuous multivalued maps. ? A special kind of retractions, called ( N , k ) -retractions, is considered. ? Deletion of simple points and many thinning algorithms are ( N , k ) -retractions. ? We characterize thinning algorithms that can be modeled as ( N , k ) -retractions. ? Characterization in terms of Ronse-like conditions for topology preservation. In some recent papers we have introduced a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach, which uses multivalued maps, provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we have characterized the deletion of simple points and some well known parallel thinning algorithm as a particular type of retractions, called ( N , k ) -retractions.In this paper we give a full characterization of the thinning algorithms that can be modeled as ( N , k ) -retractions. This class agrees, with minor modifications, with the class of thinning algorithms satisfying Ronse sufficient conditions for preservation of topology.

Thinning Algorithms as Multivalued {\mathcal{N}}-Retractions

In a recent paper we have introduced a notion of continuity in digital spaces which extends the usual notion of digital continuity. Our approach, which uses multivalued maps, provides a better framework to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we characterized the deletion of simple points, one of the most important processing operations in digital topology, as a particular kind of retraction.

Deletion of (26,6)-simple points as multivalued retractions

In a recent paper we have introduced a notion of multivalued continuity in digital spaces which extends the usual notion of digital continuity and allows to define topological notions, like retractions, in a far more realistic way than by using just single-valued digitally continuous functions. In particular, we have characterized the deletion of simple points in 2-D, one of the most important processing operations in digital topology, as a particular kind of retraction. In this work we extend some of these results to 3-dimensional digital sets.

Digital topology java applet

We present here a java applet, accessible through the World Wide Web, which allows to apply to a binary digital image a series of topological algorithms for image processing.

Multidisciplinary projects for first year engineering courses

In this work we will expose some proposals directed to the development of horizontal skills in the first year courses of Mathematics for Computer Science, with the purpose of stimulating the curiosity and the interest of the students by means of collaborative work. Our experience is based on the planning of multidisciplinary activities following projects based learning (PBL) pedagogies, included in the joint educational planning of the mathematics courses in first year of Computer Science.