Many tasks in modern urban planning require 3-dimensional (3D) spatial information, preferably in the form of 3D city models. Constructing such models requires automatic methods for reliable 3D building reconstruction. House roofs encountered in residential areas in European cities exhibit a wide variety in their shapes. This limits the use of predefined roof models for their reconstruction. The strategy put forward in this paper is, first, to construct a polyhedral model of the roof structure, which captures the topology of the roof, but which might not be very accurate in a metric sense; and then, in a second step, to improve the metric accuracy by fitting this model to the data. This decoupling of topology extraction from metric reconstruction allows a more efficient roof modelling involving less criteria. And, restricting the processing, at all stages, to one or just a few roof structures, by using a colour-based segmentation of the images, allows to use constraints that are not very tight. The approach has been tested on a state-of-the-art dataset of aerial images of residential areas in Brussels.

We consider the efficiency of Cournot and Bertrand equilibria in a duopoly with substitutable goods where firms invest in process R&D that generates input spillovers. Under Cournot competition firms always invest more in R&D than under Bertrand competition. More importantly, Cournot competition yields lower prices than Bertrand competition when the R&D production process is efficient, when spillovers are substantial, and when goods are not too differentiated. The range of cases for which total surplus under Cournot competition exceeds that under Bertrand competition is even larger as competition over quantities always yields the largest producers' surplus.

In this paper some reflections are developed on the relation between the organization of markets and innovative activities. The IO (Industrial Organization) predictions often depend crucially on the structural and behavioral characteristics of markets (or industries). To some extent this is also the case for the relation between innovation and competition. But a synthesis of existing work provides nevertheless some robust tendencies, including the predictions that in many cases the aggregate R&D activity is positively or inverted-U related with competition intensity. Clearly this tendency may be useful for positive analysis and policy.

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The focus of this paper is on the incentives of firms to invest in research and development (R&D) when sequential moves are taken into account. Leading firms move before followers in investment and in output choices in a four stage game setting. Leaders may compete or cooperate in R&D with other leaders, given that followers compete. Followers may compete or cooperate in R&D with other followers given that leaders compete. There may be spillovers between leaders and between followers and also between these two groups of players. Due to the complexity of the model, results are obtained by numerical simulations. The impact of symmetric spillovers is similar but not identical to the tendencies in two stage models with simultaneous R&D moves. A relatively wide set of circumstances is identified where followers tend to invest more than leaders. Critical spillover values are identified that drive the effects of cooperation in R&D as is the case in simpler settings. Situations are detailed, where consumer surplus and static welfare are best served by cooperation of followers rather than cooperation of leaders.Cost-reducing R&D, Sequential game, Cooperation, Asymmetric spillovers, Asymmetric spillovers, JEL Classification , D72, D43, L13,