Julian Straub

A Mixture of Manhattan Frames: Beyond the Manhattan World

Objects and structures within man-made environments typically exhibit a high degree of organization in the form of orthogonal and parallel planes. Traditional approaches to scene representation exploit this phenomenon via the somewhat restrictive assumption that every plane is perpendicular to one of the axes of a single coordinate system. Known as the Manhattan-World model, this assumption is widely used in computer vision and robotics. The complexity of many real-world scenes, however, necessitates a more flexible model. We propose a novel probabilistic model that describes the world as a mixture of Manhattan frames: each frame defines a different orthogonal coordinate system. This results in a more expressive model that still exploits the orthogonality constraints. We propose an adaptive Markov-Chain Monte-Carlo sampling algorithm with Metropolis-Hastings split/merge moves that utilizes the geometry of the unit sphere. We demonstrate the versatility of our Mixture-of-Manhattan-Frames model by describing complex scenes using depth images of indoor scenes as well as aerial-LiDAR measurements of an urban center. Additionally, we show that the model lends itself to focal-length calibration of depth cameras and to plane segmentation.

Small-variance nonparametric clustering on the hypersphere

Structural regularities in man-made environments reflect in the distribution of their surface normals. Describing these surface normal distributions is important in many computer vision applications, such as scene understanding, plane segmentation, and regularization of 3D reconstructions. Based on the small-variance limit of Bayesian nonparametric von-Mises-Fisher (vMF) mixture distributions, we propose two new flexible and efficient k-means-like clustering algorithms for directional data such as surface normals. The first, DP-vMF-means, is a batch clustering algorithm derived from the Dirichlet process (DP) vMF mixture. Recognizing the sequential nature of data collection in many applications, we extend this algorithm to DDP-vMF-means, which infers temporally evolving cluster structure from streaming data. Both algorithms naturally respect the geometry of directional data, which lies on the unit sphere. We demonstrate their performance on synthetic directional data and real 3D surface normals from RGB-D sensors. While our experiments focus on 3D data, both algorithms generalize to high dimensional directional data such as protein backbone configurations and semantic word vectors.

Semantically-Aware Aerial Reconstruction from Multi-modal Data

We consider a methodology for integrating multiple sensors along with semantic information to enhance scene representations. We propose a probabilistic generative model for inferring semantically-informed aerial reconstructions from multi-modal data within a consistent mathematical framework. The approach, called Semantically-Aware Aerial Reconstruction (SAAR), not only exploits inferred scene geometry, appearance, and semantic observations to obtain a meaningful categorization of the data, but also extends previously proposed methods by imposing structure on the prior over geometry, appearance, and semantic labels. This leads to more accurate reconstructions and the ability to fill in missing contextual labels via joint sensor and semantic information. We introduce a new multi-modal synthetic dataset in order to provide quantitative performance analysis. Additionally, we apply the model to real-world data and exploit OpenStreetMap as a source of semantic observations. We show quantitative improvements in reconstruction accuracy of large-scale urban scenes from the combination of LiDAR, aerial photography, and semantic data. Furthermore, we demonstrate the models ability to fill in for missing sensed data, leading to more interpretable reconstructions.

Real-time manhattan world rotation estimation in 3D

Drift of the rotation estimate is a well known problem in visual odometry systems as it is the main source of positioning inaccuracy. We propose three novel algorithms to estimate the full 3D rotation to the surrounding Manhattan World (MW) in as short as 20 ms using surface-normals derived from the depth channel of a RGB-D camera. Importantly, this rotation estimate acts as a structure compass which can be used to estimate the bias of an odometry system, such as an inertial measurement unit (IMU), and thus remove its angular drift. We evaluate the run-time as well as the accuracy of the proposed algorithms on groundtruth data. They achieve zerodrift rotation estimation with RMSEs below 3.4° by themselves and below 2.8° when integrated with an IMU in a standard extended Kalman filter (EKF). Additional qualitative results show the accuracy in a large scale indoor environment as well as the ability to handle fast motion. Selected segmentations of scenes from the NYU depth dataset demonstrate the robustness of the inference algorithms to clutter and hint at the usefulness of the segmentation for further processing.

Bayesian nonparametric modeling of driver behavior

Modern vehicles are equipped with increasingly complex sensors. These sensors generate large volumes of data that provide opportunities for modeling and analysis. Here, we are interested in exploiting this data to learn aspects of behaviors and the road network associated with individual drivers. Our dataset is collected on a standard vehicle used to commute to work and for personal trips. A Hidden Markov Model (HMM) trained on the GPS position and orientation data is utilized to compress the large amount of position information into a small amount of road segment states. Each state has a set of observations, i.e. car signals, associated with it that are quantized and modeled as draws from a Hierarchical Dirichlet Process (HDP). The inference for the topic distributions is carried out using an online variational inference algorithm. The topic distributions over joint quantized car signals characterize the driving situation in the respective road state. In a novel manner, we demonstrate how the sparsity of the personal road network of a driver in conjunction with a hierarchical topic model allows data driven predictions about destinations as well as likely road conditions.

The Manhattan Frame Model—Manhattan World Inference in the Space of Surface Normals

Objects and structures within man-made environments typically exhibit a high degree of organization in the form of orthogonal and parallel planes. Traditional approaches utilize these regularities via the restrictive, and rather local, Manhattan World (MW) assumption which posits that every plane is perpendicular to one of the axes of a single coordinate system. The aforementioned regularities are especially evident in the surface normal distribution of a scene where they manifest as orthogonally-coupled clusters. This motivates the introduction of the Manhattan-Frame (MF) model which captures the notion of an MW in the surface normals space, the unit sphere, and two probabilistic MF models over this space. First, for a single MF we propose novel real-time MAP inference algorithms, evaluate their performance and their use in drift-free rotation estimation. Second, to capture the complexity of real-world scenes at a global scale, we extend the MF model to a probabilistic mixture of Manhattan Frames (MMF). For MMF inference we propose a simple MAP inference algorithm and an adaptive Markov-Chain Monte-Carlo sampling algorithm with Metropolis-Hastings split/merge moves that let us infer the unknown number of mixture components. We demonstrate the versatility of the MMF model and inference algorithm across several scales of man-made environments.

Efficient Global Point Cloud Alignment Using Bayesian Nonparametric Mixtures

Point cloud alignment is a common problem in computer vision and robotics, with applications ranging from 3D object recognition to reconstruction. We propose a novel approach to the alignment problem that utilizes Bayesian nonparametrics to describe the point cloud and surface normal densities, and branch and bound (BB) optimization to recover the relative transformation. BB uses a novel, refinable, near-uniform tessellation of rotation space using 4D tetrahedra, leading to more efficient optimization compared to the common axis-angle tessellation. We provide objective function bounds for pruning given the proposed tessellation, and prove that BB converges to the optimum of the cost function along with providing its computational complexity. Finally, we empirically demonstrate the efficiency of the proposed approach as well as its robustness to real-world conditions such as missing data and partial overlap.