Leoni Dalla

BIVARIATE FRACTAL INTERPOLATION FUNCTIONS ON GRIDS

In this paper, a method of construction of fractal interpolation functions (FIF) on random grids in ℝ2 is examined.

Construction of recurrent bivariate fractal interpolation surfaces and computation of their box-counting dimension

Recurrent bivariate fractal interpolation surfaces (RBFISs) generalise the notion of affine fractal interpolation surfaces (FISs) in that the iterated system of transformations used to construct such a surface is non-affine. The resulting limit surface is therefore no longer self-affine nor self-similar. Exact values for the box-counting dimension of the RBFISs are obtained. Finally, a methodology to approximate any natural surface using RBFISs is outlined.

HIDDEN VARIABLE VECTOR VALUED FRACTAL INTERPOLATION FUNCTIONS

We present a method of construction of vector valued bivariate fractal interpolation functions on random grids in ℝ2. Examples and applications are also included.

A note on the Fermat-Torricelli point of a d-simplex

Abstract. The isogonal property of the Fermat-Torricelli point for the vertex set of a d-simplex is examined. For d=2 and 3, it is known that the property holds true if the point is in the interior of the simplex, but for

The Blocking Numbers of Convex Bodies

d \geq 4

IMAGE COMPRESSION USING RECURRENT BIVARIATE FRACTAL INTERPOLATION SURFACES

an example is given, proving that the Fermat-Torricelli point is not necessarily isogonal.

STRICT CONVEXITY OF SETS IN ANALYTIC TERMS

Abstract. Besides determining the exact blocking numbers of cubes and balls, a conditional lower bound for the blocking numbers of convex bodies is achieved. In addition, several open problems are proposed.

On a class of some special sets on thek-skeleton of a convex compact set

A new method for constructing recurrent bivariate fractal interpolation surfaces through points sampled on rectangular lattices is proposed. This offers the advantage of a more flexible fractal modeling compared to previous fractal techniques that used affine transformations. The compression ratio for the above mentioned fractal scheme as applied to real images is higher than other fractal methods or JPEG, though not as high as JPEG2000. Theory, implementation and analytical study are also presented.

Fractal Interpolation Surfaces derived from Fractal Interpolation Functions

We compare the geometric concept of strict convexity of open subsets of R n with the analytic concept of 2-strict convexity, which is based on the defining functions of the set, and we do this by introducing the class of 2 N -strictly convex sets. We also describe an exhaustion process of convex sets by a sequence of 2-strictly convex sets.

Regular Article: On the Parameter Identification Problem in the Plane and the Polar Fractal Interpolation Functions

In this paper, generalizing the notion of a path we define ak-area to be the setD={g(t):t ∈J} on thek-skeleton of a convex compact setK in a Hilbert space, whereg is a continuous injection map from thek-dimensional convex compact setJ to thek-skeleton ofK. We also define anEk-area onK, whereEk is ak-dimensional subspace, to be ak-area with the propertyπ(g(t))=t,t ∈π(K), whereπ is the orthogonal projection onEk. This definition generalizes the notion of an increasing path on the 1-skeleton ofK. The existence of such sets is studied whenK is a subset of a Euclidean space or of a Hilbert space. Finally some conjectures are quoted for the number of such sets in some special cases.