3D geometry is a very informative cue when interacting with and navigating an environment. This writing proposes a new approach to 3D reconstruction and scene understanding, which implicitly learns 3D geometry from depth maps pairing a deep convolutional neural network architecture with an auto-encoder. A data set of synthetic depth views and voxelized 3D representations is built based on ModelNet, a large-scale collection of CAD models, to train networks. The proposed method offers a significant advantage over current, explicit reconstruction methods in that it learns key geometric features offline and makes use of those to predict the most probable reconstruction of an unseen object. The relatively small network, consisting of roughly 4 million weights, achieves a 92.9 reconstruction accuracy at a 30x30x30 resolution through the use of a pre-trained decompression layer. This is roughly 1 4 the weights of the current leading network. The fast execution time of the model makes it suitable for real-time applications.
Early works in the area of 3D reconstruction proposed sparse methods involving a minimum of two views, which attempt to explicitly calculate the depth of a set of points in a set of images. The 8-point algorithm @cite_1 by Longuet-Higgins in 1981 followed by Hartley's normalized adaptation in 1997 make use of the epipolar constraint between a minimum of 8 points to determine corresponding depths. The two-view case was generalized by Weng, Liu and Huang @cite_0 as well as Spetsakis and Aloimonos @cite_3 to support an arbitrary number of views with the introduction of the trifocal tensor , which captures the trilinear relationship of points between more than two views. Most recently in 2015, trained a convolutional deep belief network on depth maps and volumetric representations of objects to learn generic shape representations concurrently with object classifications @cite_2 . As part of this work, the ModelNet data set was created, which is used throughout this project.
@cite_0 @cite_1 @cite_3 @cite_2
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We consider the task of 3-d depth estimation from a single still image. We take a supervised learning approach to this problem, in which we begin by collecting a training set of monocular images (of unstructured indoor and outdoor environments which include forests, sidewalks, trees, buildings, etc.) and their corresponding ground-truth depthmaps. Then, we apply supervised learning to predict the value of the depthmap as a function of the image. Depth estimation is a challenging problem, since local features alone are insufficient to estimate depth at a point, and one needs to consider the global context of the image. Our model uses a hierarchical, multiscale Markov Random Field (MRF) that incorporates multiscale local- and global-image features, and models the depths and the relation between depths at different points in the image. We show that, even on unstructured scenes, our algorithm is frequently able to recover fairly accurate depthmaps. We further propose a model that incorporates both monocular cues and stereo (triangulation) cues, to obtain significantly more accurate depth estimates than is possible using either monocular or stereo cues alone. Each chapter of the book addresses a problem, provides a survey of major issues, ideas, and research projects, and presents reprints of key papers. In total, the book presents sixty research papers, most written since 1980. Inferring scene geometry and camera motion from a stream of images is possible in principle, but is an ill-conditioned problem when the objects are distant with respect to their size. We have developed a factorization method that can overcome this difficulty by recovering shape and motion under orthography without computing depth as an intermediate step. An image stream can be represented by the 2FxP measurement matrix of the image coordinates of P points tracked through F frames. We show that under orthographic projection this matrix is of rank 3. Based on this observation, the factorization method uses the singular-value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively. Two of the three translation components are computed in a preprocessing stage. The method can also handle and obtain a full solution from a partially filled-in measurement matrix that may result from occlusions or tracking failures. The method gives accurate results, and does not introduce smoothing in either shape or motion. We demonstrate this with a series of experiments on laboratory and outdoor image streams, with and without occlusions. 3D shape is a crucial but heavily underutilized cue in today's computer vision systems, mostly due to the lack of a good generic shape representation. With the recent availability of inexpensive 2.5D depth sensors (e.g. Microsoft Kinect), it is becoming increasingly important to have a powerful 3D shape representation in the loop. Apart from category recognition, recovering full 3D shapes from view-based 2.5D depth maps is also a critical part of visual understanding. To this end, we propose to represent a geometric 3D shape as a probability distribution of binary variables on a 3D voxel grid, using a Convolutional Deep Belief Network. Our model, 3D ShapeNets, learns the distribution of complex 3D shapes across different object categories and arbitrary poses from raw CAD data, and discovers hierarchical compositional part representations automatically. It naturally supports joint object recognition and shape completion from 2.5D depth maps, and it enables active object recognition through view planning. To train our 3D deep learning model, we construct ModelNet -- a large-scale 3D CAD model dataset. Extensive experiments show that our 3D deep representation enables significant performance improvement over the-state-of-the-arts in a variety of tasks.