This paper presents a novel probabilistic foundation for volumetric 3-d reconstruction. We formulate the problem as inference in a Markov random field, which accurately captures the dependencies between the occupancy and appearance of each voxel, given all input images. Our main contribution is an approximate highly parallelized discrete-continuous inference algorithm to compute the marginal distributions of each voxel's occupancy and appearance. In contrast to the MAP solution, marginals encode the underlying uncertainty and ambiguity in the reconstruction. Moreover, the proposed algorithm allows for a Bayes optimal prediction with respect to a natural reconstruction loss. We compare our method to two state-of-the-art volumetric reconstruction algorithms on three challenging aerial datasets with LIDAR ground truth. Our experiments demonstrate that the proposed algorithm compares favorably in terms of reconstruction accuracy and the ability to expose reconstruction uncertainty.

Inferring 3D objects and the layout of indoor scenes from a single RGB-D image captured with a Kinect camera is a challenging task. Towards this goal, we propose a high-order graphical model and jointly reason about the layout, objects and superpixels in the image. In contrast to existing holistic approaches, our model leverages detailed 3D geometry using inverse graphics and explicitly enforces occlusion and visibility constraints for respecting scene properties and projective geometry. We cast the task as MAP inference in a factor graph and solve it efficiently using message passing. We evaluate our method with respect to several baselines on the challenging NYUv2 indoor dataset using 21 object categories. Our experiments demonstrate that the proposed method is able to infer scenes with a large degree of clutter and occlusions.

Three-dimensional reconstruction of dynamic scenes is an important prerequisite for applications like mobile robotics or autonomous driving. While much progress has been made in recent years, imaging conditions in natural outdoor environments are still very challenging for current reconstruction and recognition methods. In this paper, we propose a novel unified approach which reasons jointly about 3D scene flow as well as the pose, shape and motion of vehicles in the scene. Towards this goal, we incorporate a deformable CAD model into a slanted-plane conditional random field for scene flow estimation and enforce shape consistency between the rendered 3D models and the parameters of all superpixels in the image. The association of superpixels to objects is established by an index variable which implicitly enables model selection. We evaluate our approach on the challenging KITTI scene flow dataset in terms of object and scene flow estimation. Our results provide a prove of concept and demonstrate the usefulness of our method.

In this paper we propose a system for the problem of facade segmentation. Building facades are highly structured images and consequently most methods that have been proposed for this problem, aim to make use of this strong prior information. We are describing a system that is almost domain independent and consists of standard segmentation methods. A sequence of boosted decision trees is stacked using auto-context features and learned using the stacked generalization technique. We find that this, albeit standard, technique performs better, or equals, all previous published empirical results on all available facade benchmark datasets. The proposed method is simple to implement, easy to extend, and very efficient at test time inference.

Stereo techniques have witnessed tremendous progress over the last decades, yet some aspects of the problem still remain challenging today. Striking examples are reflecting and textureless surfaces which cannot easily be recovered using traditional local regularizers. In this paper, we therefore propose to regularize over larger distances using object-category specific disparity proposals (displets) which we sample using inverse graphics techniques based on a sparse disparity estimate and a semantic segmentation of the image. The proposed displets encode the fact that objects of certain categories are not arbitrarily shaped but typically exhibit regular structures. We integrate them as non-local regularizer for the challenging object class 'car' into a superpixel based CRF framework and demonstrate its benefits on the KITTI stereo evaluation.

As the collection of large datasets becomes increasingly automated, the occurrence of outliers will increase – “big data” implies “big outliers”. While principal component analysis (PCA) is often used to reduce the size of data, and scalable solutions exist, it is well-known that outliers can arbitrarily corrupt the results. Unfortunately, state-of-the-art approaches for robust PCA do not scale beyond small-to-medium sized datasets. To address this, we introduce the Grassmann Average (GA), which expresses dimensionality reduction as an average of the subspaces spanned by the data. Because averages can be efficiently computed, we immediately gain scalability. GA is inherently more robust than PCA, but we show that they coincide for Gaussian data. We exploit that averages can be made robust to formulate the Robust Grassmann Average (RGA) as a form of robust PCA. Robustness can be with respect to vectors (subspaces) or elements of vectors; we focus on the latter and use a trimmed average. The resulting Trimmed Grassmann Average (TGA) is particularly appropriate for computer vision because it is robust to pixel outliers. The algorithm has low computational complexity and minimal memory requirements, making it scalable to “big noisy data.” We demonstrate TGA for background modeling, video restoration, and shadow removal. We show scalability by performing robust PCA on the entire Star Wars IV movie.

Despite the success of recent object class recognition systems, the long-standing problem of partial occlusion re- mains a major challenge, and a principled solution is yet to be found. In this paper we leave the beaten path of meth- ods that treat occlusion as just another source of noise – instead, we include the occluder itself into the modelling, by mining distinctive, reoccurring occlusion patterns from annotated training data. These patterns are then used as training data for dedicated detectors of varying sophistica- tion. In particular, we evaluate and compare models that range from standard object class detectors to hierarchical, part-based representations of occluder/occludee pairs. In an extensive evaluation we derive insights that can aid fur- ther developments in tackling the occlusion challenge.

Multi-metric learning techniques learn local metric tensors in different parts of a feature space. With such an approach, even simple classifiers can be competitive with the state-of-the-art because the distance measure locally adapts to the structure of the data. The learned distance measure is, however, non-metric, which has prevented multi-metric learning from generalizing to tasks such as dimensionality reduction and regression in a principled way. We prove that, with appropriate changes, multi-metric learning corresponds to learning the structure of a Riemannian manifold. We then show that this structure gives us a principled way to perform dimensionality reduction and regression according to the learned metrics. Algorithmically, we provide the first practical algorithm for computing geodesics according to the learned metrics, as well as algorithms for computing exponential and logarithmic maps on the Riemannian manifold. Together, these tools let many Euclidean algorithms take advantage of multi-metric learning. We illustrate the approach on regression and dimensionality reduction tasks that involve predicting measurements of the human body from shape data.

Many computer vision, signal processing and statistical problems can be posed as problems of learning low dimensional linear or multi-linear models. These models have been widely used for the representation of shape, appearance, motion, etc., in computer vision applications. Methods for learning linear models can be seen as a special case of subspace fitting. One draw-back of previous learning methods is that they are based on least squares estimation techniques and hence fail to account for “outliers” which are common in realistic training sets. We review previous approaches for making linear learning methods robust to outliers and present a new method that uses an intra-sample outlier process to account for pixel outliers. We develop the theory of Robust Subspace Learning (RSL) for linear models within a continuous optimization framework based on robust M-estimation. The framework applies to a variety of linear learning problems in computer vision including eigen-analysis and structure from motion. Several synthetic and natural examples are used to develop and illustrate the theory and applications of robust subspace learning in computer vision.