Abstract. The area distance to a convex plane curve is an important concept in computer vision. In this paper we describe a strong link between area distances and improper affine spheres. This link makes possible a better understanding of both theories. The concepts of the theory of affine spheres lead to a new definition of an area distance on the outer part of a convex plane arc. Also, based ...

We present an exact algorithm for the computation of the moments of a region bounded by a curve represented in a scaling function or wavelet basis. Using Green’s theorem, we show that the computation of the area moments is equivalent to applying a suitable multidimensional filter on the coefficients of the curve and thereafter computing a scalar product. We compare this algorithm with existing ...

ROC curves and cost curves are two popular ways of visualising classifier performance, finding appropriate thresholds according to the operating condition, and deriving useful aggregated measures such as the area under the ROC curve (AUC) or the area under the optimal cost curve. In this note we present some new findings and connections between ROC space and cost space, by using the expected lo...

Determining Depth-Area-Duration (DAD) curves in drainage basins is one of the applied researches in hydrology. DAD curves exhibit the depth and the area covered by the rainfall with a particular duration. DAD analysis is widely used in characterization of precipitation extremes for specification of so-called design storms. In this study the DAD curves for the Kurdistan province were prepared an...

An article published in the journal Nature in January 2004-in which an international team of biologists predicted that climate change would, by 2050, doom 15-37% of the earth's species to extinction-attracted unprecedented, worldwide media attention. The predictions conflict with the conventional wisdom that habitat change and modification are the most important causes of current and future ext...

An Euler diagram C = {c1, c2, . . . , cn} is a collection of n simple closed curves (i.e., Jordan curves) that partition the plane into connected subsets, called regions, each of which is enclosed by a unique combination of curves. Typically, Euler diagrams are used to visualize the distribution of discrete characteristics across a sample population; in this case, each curve represents a charac...