Discovering Regularity in Point Clouds of Urban Scenes

Despite the apparent chaos of the urban environment, cities are actually replete with regularity. From the grid of streets laid out over the earth, to the lattice of windows thrown up into the sky, periodic regularity abounds in the urban scene. Just as salient, though less uniform, are the self-similar branching patterns of trees and vegetation that line streets and fill parks. We propose novel methods for discovering these regularities in 3D range scans acquired by a time-of-flight laser sensor. The applications of this regularity information are broad, and we present two original algorithms. The first exploits the efficiency of the Fourier transform for the real-time detection of periodicity in building facades. Periodic regularity is discovered online by doing a plane sweep across the scene and analyzing the frequency space of each column in the sweep. The simplicity and online nature of this algorithm allow it to be embedded in scanner hardware, making periodicity detection a built-in feature of future 3D cameras. We demonstrate the usefulness of periodicity in view registration, compression, segmentation, and facade reconstruction. The second algorithm leverages the hierarchical decomposition and locality in space of the wavelet transform to find stochastic parameters for procedural models that succinctly describe vegetation. These procedural models facilitate the generation of virtual worlds for architecture, gaming, and augmented reality. The self-similarity of vegetation can be inferred using multi-resolution analysis to discover the underlying branching patterns. We present a unified framework of these tools, enabling the modeling, transmission, and compression of high-resolution, accurate, and immersive 3D images

Automatic Procedural Modeling of Tree Structures in Point Clouds Using Wavelets

Abstract—We present a method for discovering the structure of trees in 3D point clouds by linking wavelets with shape grammars. Given a range scan of a tree we find a grammar that can reproduce that tree, and others like it, with sub-voxel accuracy. The grammar inferred is stochastic, allowing us to generate many permutations of related trees. The method of multiresolution analysis, employed by the discrete wavelet transform, gives great insight into tree structure. Trees are self-similar and exhibit similar branching patterns at different resolutions. The wavelets make these patterns explicit by decomposing the tree into different levels of detail. The multi-resolution structure of the wavelet transform also allows us to infer an L-System grammar. The productions in the grammar are derived from the progressive levels of refinement in the wavelet transform. Each production maps a vector in the low resolution image to a set of vectors in the higher resolution image. Our method utilizes the Fast Wavelet Transform opening the door to real-time inference of procedural models. The grammar inferred is concise and generative, allowing for compression and graphics applications of our algorithm. We demonstrate novel applications of the grammar for shape completion, scan enhancement and geometry propagation. Keywords-inverse procedural modeling, tree modeling, wavelets, l-systems I