Convex roof extensions are widely used to create entanglement measures in quantum information theory. The aim of the article is to present some tools which could be helpful for their treatment. Sections 2 and 3 introduce into the subject. It follows descriptions of the Wootters’ method, of the “subtraction procedure”, and examples on how to use symmetries.

The aim of this study is the estimation of solar irradiance on building roofs in complex Alpine landscapes. Very high resolution geometric models of the building roofs are generated by means of advanced automated image matching methods. Models are combined with raster and vector data sources to estimate the incoming solar radiation hitting the roofs. The methodology takes into account for atmos...

The automatic reconstruction of roofs and buildings has been an important research topic during the last years. This paper elaborates on the automatic and semi-automatic reconstruction of roofs from aerial laser scan data. Two approaches are considered in detail. First, a program has been developed, which segments laser scan data into planar patches, labels them according to their adjacency, an...

We present a technique to extract complex suburban roofs from sets of aerial images. Because we combine 2-D edge information, photometric and chromatic attributes and 3-D information, we can deal with complex houses. Neither do we assume the roofs to be at or recti-linear nor do we require parameterized building models. From only one image, 2-D edges and their corresponding attributes and relat...

3D city model reconstruction is one of the main application of airborne laser scanning system. Roof detection is a primary step which needs to find each roof from irregular point clouds with noise points involved. Another problem existed in roof detection is that the detected sequence of roofs will affect the size and shape of detected roofs even though a lot fancy algorithm are applied. In thi...

Increasing urban albedo can reduce summertime temperatures, resulting in better air quality and savings from reduced air-conditioning costs. In addition, increasing urban albedo can result in less absorption of incoming solar radiation by the surface-troposphere system, countering to some extent the global scale effects of increasing greenhouse gas concentrations. Pavements and roofs typically ...

In this paper we describe a procedure for generating building models from large scale vector maps and laser altimeter data. First the vector map is analyzed to group the outlines of buildings and to obtain a hierarchical description of buildings or building complexes. The base area is used to mask the elevation data of single buildings and to derive a coarse 3D-description by prismatic models. ...

Green roofs are constructed ecosystems that provide ecosystem services in urban environments. Shallow substrate green roofs subject the vegetation layer to desiccation and other environmental extremes, so researchers have evaluated a variety of stress-tolerant vegetation types for green roof applications. Lichens can be found in most terrestrial habitats.  They are able to survive extremely har...

Curve estimation from observed noisy data has broad applications. In certain applications, the underlying regression curve may have singularities, including jumps and roofs/valleys (i.e., jumps in the first order derivative of the regression curve), at some unknown positions, representing structural changes of the related process. Detection of such singularities is important for understanding t...

The development of LIDAR (Light Detection and Ranging) system makes the acquisition of 3D surface information more convenient and immediate than other geomatics technologies. However, the 3D coordinates of the surface features, such as the corners, edges and planes of buildings, cannot be obtained directly from the LIDAR data because of its blind characteristics. How to detect the feature locat...