Geometric reconstruction from point-normal data

Geometric reconstruction from point-normal data Eleanor G. Rieffel FXPAL rieffel@fxpal.com Don Kimber FXPAL kimber@fxpal.com Jim Vaughan FXPAL jimv@fxpal.com Abstract Creating virtual models of real spaces and objects is cumber- some and time consuming. This paper focuses on the prob- lem of geometric reconstruction from sparse data obtained from certain image-based modeling approaches. A number of elegant and simple-to-state problems arise concerning when the geometry can be reconstructed. We describe results and counterexamples, and list open problems. 1 Introduction. While three-dimensional virtual models have long been used in industry for design, the increased speed and graphics capabilities of today’s computers, higher band- width, and the popularity of virtual environments mean that virtual models are becoming ever easier to view, manipulate, and distribuite. This improved ease of use has spawned an increasing desire for better methods to create models, including models of real objects and spaces. At FXPAL, we are particularly interested in the use of virtual models in a factory setting [11] and in surveil- lance [15, 26]. Common applications include training, immersive telepresence, military exercises, and design and testing of emergency response plans. Other appli- cations range from virtual tourism [28, 27] and psychi- atric treatment for post-traumatic stress disorder [14], phobias [21], and autism [30]. Real estate offices are beginning to use three-dimensional models to support the creation of virtual tours [4]. Not only are marketing departments beginning to make models of their prod- ucts available to potential purchasers, but applications are springing up around these models. For example, MyDeco [5] enables users to create models of a three- dimensional space, place models of real furniture and other home accessories that are available for purchase in the virtual space, and then buy any of these products directly from the site. Virtual worlds such as Second Life [7] are filled with more or less realistic models of real places and objects. Google Earth [3] now includes three-dimensional models of various buildings. Unfortunately, creating virtual models of real ob- jects and spaces remains cumbersome and time con- Figure 1: Model of an IKEA Bookcase cabinet gener- ated by the Pantheia system. suming. Current state of the art modeling is done by artists using interactive modeling tools, often supported by measurement and photographs of the real space. An ambitious long term research goal is to automatically construct such models from collected images; fully au- tomatic approaches are not yet possible. FXPAL’s Pan- theia system [17, 25] enables users to create models by marking up the real world with pre-printed uniquely identifiable markers. Predefined meanings associated with the markers guide the system in creating mod- els. The position and outward pointing normal at each marker can be estimated from user-captured images or video of the marked-up space. Point-normal data, con- sisting of the position and outward pointing normal, can be obtained using other technologies such as range scan- ners. This paper focuses on the problem of reconstructing the geometry from the marker information. Our initial attempts at reconstruction used ad hoc reconstruction algorithms and markup placement strategies. When we tried to model a new space, we often needed to place additional markers, add meanings to the markup language, or revise the reconstruction algorithm to make it more powerful. This paper is the result of our work to place the geometric reconstruction aspect of our system on a firmer formal footing. arXiv:1003.3499v1 [cs.CG] 18 Mar 2010 2 Related Work. This section discusses two types of related work. First, we discuss related work in the area of image-based modeling. Then we survey previous work in polyhedral reconstruction from simple geometric data. Researchers such as [23, 24, 13] work on non- marker-based methods for constructing models from im- ages. Their work advances progress on the hard prob- lem of deducing geometric structure from image fea- tures. Instead, we make the problem simpler by plac- ing markers that are easily detected and have meanings that greatly simplify the geometric deduction. Further- more, a marker-based approach enables users to specify which parts of the scene are important. In this way, Pantheia handles clutter removal and certain occlusion issues easily, since it renders what the markers indicate rather than what is seen. From a large number of photographs of a place or object, visual features, such as SIFT features [19], can be extracted and rendered as point cloud models [28, 29]. More generally, the area of ‘point based graphics’ provides methods for representing surfaces by point data, without requiring other graphics primitives such as meshes [16]. These methods have been used as primitives for modeling tools [9]. Amenta et al. [10] describe the point based not

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