Jan Vandekerckhove

Automatic Modeling and 3D Reconstruction of Urban House Roofs from High Resolution Aerial Imagery

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.

Automatic modelling and 3D reconstruction of urban buildings from aerial imagery

A method is presented that automatically generates 3D models of generic house roofs from aerial images of residential areas in urban sites. Crucial to the method is the possibility of delineating regions in the images that correspond well to actual roof structures. Restricting the processing to relatively small regions allows at all stages of the algorithm to use constraints that are not very tight, and, at the same time, to keep the combinatorics under control. All modelling is done by reasoning in 3D. By adopting a strategy of hypothesis generation and verification the authors are not only are capable of exploiting all available image data at every step in the algorithm, but also to treat all views equally. Decoupling topology retrieval from metric accuracy makes it possible to generate and test combinations which otherwise would have been ruled out by more tight constraints. The method is implemented and tests on the correctness and completeness of the extracted roof models have been performed.

On the reconstruction of urban house roofs from aerial images

A method is presented to automatically generate 3D models of house roofs from aerial images of residential areas in urban sites. Following the methodology of (Bignone et al. 1996) a house roof is modelled as a set of planar polygonal patches, each of which encloses a compact area with consistent photometric and chromatic properties, and that mutually adjoin along common boundaries. The approach presented here differs from that in (Bignone et al. 1996) in the sense that it starts by delineating in the images homogeneous regions which correspond to roof structures by navigating through a constraint triangulation network, and that line segment matching, 3D reconstruction, coplanar grouping and polygonal patch formation are initialized from corresponding regions in different views. Each polygon hypothesis is tested for consistency with the 2D and 3D data, and, if necessary, it is changed accordingly.

Market Performance Implications of the Transfer Price Rule

The “transfer price rule” (TPR) defines a vertical price squeeze as an input price, output price combination set by a vertically-integrated firm monopoly producer of an essential input that would not allow the firms downstream unit to earn at least a normal rate of return on investment in the “as-if” case that it had to purchase the input at the price charged independent firms. In its 2009 linkLine decision, the U.S. Supreme Court rejected the TPR for the purpose of enforcing the anti-monopolization prohibition of Section 2 of the Sherman Act. In contrast, a vertical price squeeze, defined by a TPR-like standard, is an abuse of a dominant position under Article 102 of the Treaty on the Functioning of the European Union. In this article, we model the impact of the TPR on market performance. We find that the TPR increases consumer surplus and net social welfare if all firms remain active in the downstream market. It sometimes induces the upstream firm to refuse to supply the downstream firm, and in such cases, consumer surplus and net social welfare are reduced. The impact of the TPR on market performance thus depends on whether or not an upstream firm can refuse to supply downstream firms on terms that would offer it at least a normal rate of return on investment.

Asymmetric Spillovers and Sequential Strategic Investments

The focus of this paper is on the consequences of asymmetric spillovers on the strategic investments in an oligopoly with leaders and followers. Both in the investment and output game, leaders move before the followers. Spillovers may occur between leaders and between followers and from leaders to followers. The consequences are detailed for:- the comparison of leader and follower efforts;- the comparison of investments with or without cooperation of leaders, followers or leaders and followers;- other specific real world situations. It will be argued that there are critical levels of spillovers that drive the relevant tendencies. They tend to depend in a complex way on the other parameters of the oligopoly. Still some clear tendencies emerge that can help to understand asymmetric leader-follower rivalry.

The strategic interplay between bundling and merging in complementary markets

In this paper, two pairs of complementors have to decide whether to merge and eventually bundle their products. Depending on the degree of competitive pressure in the market, either both pairs decide to merge (with or without bundling), or only one pair merges and bundles, while rivals remain independent. The latter case can very harmful for consumers as it brings surge in prices. We also consider the case in which one pair moves first. Interestingly, we find a parametric region where first movers merge but refrain from bundling, to not induce rivals to merge as well.

Product market competition and investments in cooperative R&D

Abstract Building on the framework developed by Qiu (1997) we investigate the influence of product market competition on incentives to invest in cooperative R&D. For that we disentangle the three components that make up the combined-profits externality. The strategic component is always negative and the size component is always positive. The spillover component is negative (positive) with Bertrand (Cournot) competition. Cournot competition thus yields more cooperative R&D, which could drive the Cournot-Nash price below the Bertrand-Nash price. Our decomposition also explains why, under Cournot competition, cooperative R&D exceeds non-cooperative R&D only if spillovers are “high enough.”

Semi-automatic modelling of urban buildings from high resolution aerial imagery

A method is presented to (semi-)automatically generate 3D models of urban buildings from aerial images. The process starts by selecting (with a mouse click) one or more roofs in the image(s). The program then automatically delineates the roof structures in the images and extracts straight line segments which are matched across different views and reconstructed in 3D. These 3D line segments are then grouped into coplanar sets and combined into polygonal shapes. Each polygon hypothesis is verified with respect to the 3D reconstruction and the original image data; and, if necessary, corrected accordingly. Subsequently, the polygons are combined into a polyhedral roof model. The emphasis here is on extracting the correct topology of the roof structure. Metric accuracy is obtained by back-projecting the model into the images and minimizing the total reprojection error. Finally, the building model is completed by adding vertical walls to the reconstructed roof. The approach is tested on a state-of-the-art dataset of aerial images of residential areas in Brussels.

3D reconstruction of generic house roofs from aerial images of urban areas

A method is presented to automatically generate 3D models of house roofs from aerial images of residential areas in urban sites. First, homogeneous regions with consistent photometric and chromatic triangulation network. Stereo matching of straight line segments is performed between corresponding regions only. Line segments that are matched across at lest three views are reconstructed by a bundle adjustment procedure. The reconstructed line segments are hypothesis is subjected to a consistency verification with respect to the 3D reconstruction and the original image data, and, if necessary, corrected accordingly. Observe that the combinatorics is kept under control by processing one region at the time. In a next stage, the polygons are glued together into a roof model. The emphasis here is on extracting the correct topology of the roof structure. Metric accuracy of the reconstruction is obtained in an additional step by backprojecting the recovered model of the roof structure onto the images and minimizing the total reprojection error. The viability of this approach has been tested on a state-of-the-art dataset or aerial images of residential areas in Brussels.

Innovation by Leaders Without Winner-Take-All

In innovative races with winner takes all, leading firms invest less than each follower, given exogenous entry (Reinganum, 1985). But with endogenous entry this result is reversed (Etro, 2004). It is argued here that sharing of rewards between the players may alter these predictions.