We study error propagation through implicit geometric problems by linearizing and estimating the linearization error. The method is particularly useful for quadratic constraints, which turns out to be no big restriction for many geometric problems in applications.

Automatically discovering high-level facade structures in unorganized 3D point clouds of urban scenes is crucial for applications like digitalization of real cities. However, this problem is challenging due to poor-quality input data, contaminated with severe missing areas, noise and outliers. This work introduces the concept of adaptive partitioning to automatically derive a flexible and hierarchical representation of 3D urban facades. Our key observation is that urban facades are largely governed by concatenated and/or interlaced grids. Hence, unlike previous automatic facade analysis works which are typically restricted to globally rectilinear grids, we propose to automatically partition the facade in an adaptive manner, in which the splitting direction, the number and location of splitting planes are all adaptively determined. Such an adaptive partition operation is performed recursively to generate a hierarchical representation of the facade. We show that the concept of adaptive partitioning is also applicable to flexible and robust analysis of image facades. We evaluate our method on a dozen of LiDAR scans of various complexity and styles, and the image facades from the eTRIMS database and the Ecole Centrale Paris database. A series of applications that benefit from our approach are also demonstrated.

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Object proposals are currently used for increasing the computational efficiency of object detection. We propose a novel adaptive pipeline for interleaving object proposals with object classification and use it as a formulation for asset detection. We first preprocess the images using a novel and efficient rectification technique. We then employ a particle filter approach to keep track of three priors, which guide proposed samples and get updated using classifier output. Tests performed on over 1000 urban images demonstrate that our rectification method is faster than existing methods without loss in quality, and that our interleaved proposal method outperforms current state-of-the-art. We further demonstrate that other methods can be improved by incorporating our interleaved proposals.

We present an algorithm for recognition and reconstruction of scanned 3D indoor scenes. 3D indoor reconstruction is particularly challenging due to object interferences, occlusions and overlapping which yield incomplete yet very complex scene arrangements. Since it is hard to assemble scanned segments into complete models, traditional methods for object recognition and reconstruction would be inefficient. We present a search-classify approach which interleaves segmentation and classification in an iterative manner. Using a robust classifier we traverse the scene and gradually propagate classification information. We reinforce classification by a template fitting step which yields a scene reconstruction. We deform-to-fit templates to classified objects to resolve classification ambiguities. The resulting reconstruction is an approximation which captures the general scene arrangement. Our results demonstrate successful classification and reconstruction of cluttered indoor scenes, captured in just few minutes.