In the plane R, we consider the sequence of points xi = (i, 0) (for i = 1, 2, . . .) and we denote by D(r) the disc of radius r, centered at the origin. In the space Xn of n-tuples of distinct points of D(n + 1/2), we consider the equivalence relation that identifies two n-tuples if one is obtained from the other by a permutation of the indices. We denote by X̃n the quotient space and by πn : Xn...

Chromatic Adaptation is the ability of the human visual system to approximately preserve the appearance of an object color, no matter which light “color” illuminates a particular scene. We perceive a white piece of paper as white, regardless whether viewed under a bluish daylight or yellowish tungsten light source. Similar effects can be observed with other color hues. Figure 1 illustrates this...

For this, we obtained a fractal dimension of the proximal convoluted tubuli in the dog kidney by mean box-counting method. The fractal value we obtained is a flat dimension, and it is different than the line fractal dimension of the dog kidney arterial pattern, which was previously calculated by us (Gil et al., 2006). Thus, from optical microscopy images, we are able to obtain a single quantita...

Detailed box counting analysis was conducted of (1) fractures observed in exposures of the Devonian Shale in the central Appalachians Valley and Ridge Province of West Virginia, (2) several fracture patterns presented in the literature, and (3) active faults mapped throughout the main island (Honshu) of Japan. Box curves reveal, with few exceptions, that most naturally occurring fracture patter...

We present a novel technique for analyzing the geometry of streamlines representing large scale flow fields produced in scientific simulations. We introduce the box counting ratio, a metric related to the Kolmogorov capacity or box counting dimension, for quantifying geometric complexity of streamlines (or streamline segments). We utilize this metric to drive a visual analytic framework for ext...

In this session we want to review the basic concepts introduced in class for convolution in continuous-time. It has been proved that in order to determine the characteristics of a linear, time-invariant (LTI) system we need to know the impulse response of the system. When we apply an input x(t) to a system that has h(t) as its impulse response, we obtain an output y(t) (see Figure 1). One of th...

Using box-counting and spatial regression, this paper analyzes the morphological characteristics of coastal settlement patterns and their spatial determinants, with a case of the Wen-Tai region on the Chinese eastern coast. Coastal settlement patterns, which reflect the interactions between people and the surrounding environment, can indicate the anthropogenic pressure sustained in the coastal ...

We refer to the point p′ satisfying (1) as an -approximate solution. Clearly, approximation to a prescribed absolute error is also possible. We refer to a point p′ satisfying (2) as witness. This condition holds if and only if p 6∈ conv(S). This is because in this case we can prove the Voronoi cell of p′ with respect to the two point set {p, p′} contains conv(S) (see Figure 1). Equivalently, th...

1. Data collection High resolution aerial photography was taken in Aberfoyle in September 2002. We selected 12 plots representing mature Sitka spruce stands between 30 and 40 years in age that were surveyed at the beginning of 2003. The aim of this field data collection was the validation of the results of the image processing analysis in the tree counting and LiDAR analysis projects. The propo...