In this paper, we address the following research problem: How can we generate a meaningful split grammar that explains a given facade layout? To evaluate if a grammar is meaningful, we propose a cost function based on the description length and minimize this cost using an approximate dynamic programming framework. Our evaluation indicates that our framework extracts meaningful split grammars that are competitive with those of expert users, while some users and all competing automatic solutions are less successful.
There are several papers that propose initial solutions on deriving a shape grammar from facade images. The pioneering work by Bekins, Aliaga, and Rosen @cite_3 @cite_20 proposes a grammar that splits a facade into floors and then encodes a one-dimensional sequence of elements. The advantage of this approach is that it reduces the problem to a sequence of one-dimensional problems, but the disadvantage is that it only applies to facades with this structure and is not applicable to general two-dimensional layouts. This approach is therefore more similar to finding the parameters of a pre-determined shape grammar. Several other authors also follow this general approach @cite_24 @cite_2 . An important contribution is the inverse procedural modeling of vector art @cite_29 , because it is the first formal treatment of the inverse procedural modeling problem in computer graphics.
@cite_29 @cite_3 @cite_24 @cite_2 @cite_20
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We present an important step towards the solution of the problem of inverse procedural modeling by generating parametric context-free L-systems that represent an input 2D model. The L-systemrules efficiently code the regular structures and the parameters represent the properties of the structure transformations. The algorithm takes as input a 2D vector image that is composed of atomic elements, such as curves and poly-lines. Similar elements are recognized and assigned terminal symbols ofan L-systemalphabet. Theterminal symbols’ position and orientation are pair-wise compared and the transformations are stored as points in multiple 4D transformation spaces. By careful analysis of the clusters in the transformation spaces, we detect sequences of elements and code them as L-system rules. The coded elements are then removed from the clusters, the clusters are updated, and then the analysis attempts to code groups of elements in (hierarchies) the same way. The analysis ends with a single group of elements that is coded as an L-system axiom. We recognize and code branching sequences of linearly translated, scaled, and rotated elements and their hierarchies. The L-system not only represents the input image, but it can also be used for various editing operations. By changing the L-system parameters, the image can be randomized, symmetrized, and groups of elements and regular structures can be edited. By changing the terminal and non-terminal symbols, elements or groups of elements can be replaced. We present build-by-number, a technique for quickly designing architectural structures that can be rendered photorealistically at interactive rates. We combine image-based capturing and rendering with procedural modeling techniques to allow the creation of novel structures in the style of real-world structures. Starting with a simple model recovered from a sparse image set, the model is divided into feature regions, such as doorways, windows, and brick. These feature regions essentially comprise a mapping from model space to image space, and can be recombined to texture a novel model. Procedural rules for the growth and reorganization of the model are automatically derived to allow for very fast editing and design. Further, the redundancies marked by the feature labeling can be used to perform automatic occlusion replacement and color equalization in the finished scene, which is rendered using view-dependent texture mapping on standard graphics hardware. Results using four captured scenes show that a great variety of novel structures can be created very quickly once a captured scene is available, and rendered with a degree of realism comparable to the original scene. Abstract Frequently, terrestrial LiDAR and image data are used to extract high resolution building geometry like windows, doors and protrusions for three-dimensional (3D) facade reconstruction. However, such a purely data driven bottom-up modelling of facade structures is only feasible if the available observations meet considerable requirements on data quality. Errors in measurement, varying point densities, reduced accuracies, as well as incomplete coverage affect the achievable correctness and reliability of the reconstruction result. While dependence on data quality is a general disadvantage with data driven bottom-up approaches, model based top-down reconstructions are much more robust. Algorithms introduce knowledge about the appearance and arrangement of objects. Thus, they cope with data uncertainty and allow for a procedural modelling of building structures in a predefined architectural style, which is inherent in grammar or model descriptions. We aim at a quality sensitive facade reconstruction which is on the one hand robust against erroneous and incomplete data, but on the other hand not subject to prespecified rules or models. For this purpose, we combine bottom-up and top-down strategies by integrating automatically inferred rules into a data driven reconstruction process. Facade models reconstructed during a bottom-up method serve as a knowledge base for further processing. Dominant or repetitive features and regularities as well as their hierarchical relationship are detected from the modelled facade elements and automatically translated into rules. These rules together with the 3D representations of the modelled facade elements constitute a formal grammar. It holds all the information which is necessary to reconstruct facades in the style of the given building. The paper demonstrates that the proposed algorithm is very flexible towards different data quality and incomplete sensor data. The inferred grammar is used for the verification of the facade model produced during the data driven reconstruction process and the generation of synthetic facades for which only partial or no sensor data is available. Moreover, knowledge propagation is not restricted to facades of one single building. Based on a small set of formal grammars derived from just a few observed buildings, facade reconstruction is also possible for whole districts featuring uniform architectural styles. Interactive visualization of architecture provides a way to quickly visualize existing or novel buildings and structures. Such applications require both fast rendering and an effortless input regimen for creating and changing architecture using high-level editing operations that automatically fill in the necessary details. Procedural modeling and synthesis is a powerful paradigm that yields high data amplification and can be coupled with fast-rendering techniques to quickly generate plausible details of a scene without much or any user interaction. Previously, forward generating procedural methods have been proposed where a procedure is explicitly created to generate particular content. In this paper, we present our work in inverse procedural modeling of buildings and describe how to use an extracted repertoire of building grammars to facilitate the visualization and quick modification of architectural structures and buildings. We demonstrate an interactive application where the user draws simple building blocks and, using our system, can automatically complete the building "in the style of other buildings using view-dependent texture mapping or nonphotorealistic rendering techniques. Our system supports an arbitrary number of building grammars created from user subdivided building models and captured photographs. Using only edit, copy, and paste metaphors, the entire building styles can be altered and transferred from one building to another in a few operations, enhancing the ability to modify an existing architectural structure or to visualize a novel building in the style of the others.