Point-transformation schemes transform multidimensional points to one-dimensional values so that conventional access methods can be used to index multidimensional points, enabling convenient integration of multidimensional query facilities into complex transactional database management systems. However, in high-dimensional data spaces, the computational complexity of the required query transfor...

In this paper we investigate the problem of varying the size of dots in digital halftoning processes. We show that the dot size is the main factor determining the trade-oo between tonal and spatial resolution in the reproduction of gray scale images. We discuss the control of pixel aggregation in the context of dithering algorithms. In particular, we extend the dither with space lling curves me...

We design signatures for curves defined on genus zero surfaces. The signature classifies curves according to the conformal geometry of the given curves and their embedded surface. Based on Teichmüller theory, our signature describes not only the curve shape but also the intrinsic relationship between the curve and its embedded surface. Furthermore, the signature metric is stable, it is close to...

This paper presents a method for analogizing high-dimensional spacetime curves, and shows how it can be used to transform a motion sequence into new content and styles according to two accompanied reference sequences. By providing examples, our system can estimate the parameters of a statistical model which incorporates spatial and temporal factors for motion curves. A user can then easily modi...

Let S = C[x1, . . . , xn+1] be the set of polynomials in n+1 variables over C (usually corresponding to the homogeneous coordinate ring of P). Let ≻ be the reverse lexicographical order on the monomials of S. Given a homogeneous ideal I in S, gin(I), the generic initial ideal of I, is the Borel-fixed monomial ideal associated to I. (For details see [B], [BM], [BS] or [Gr].) The generic initial ...