A Model-Selection Framework for Multibody Structure-and-Motion of Image Sequences

Given an image sequence of a scene consisting of multiple rigidly moving objects, multi-body structure-and-motion (MSaM) is the task to segment the image feature tracks into the different rigid objects and compute the multiple-view geometry of each object. We present a framework for multibody structure-and-motion based on model selection. In a recover-and-select procedure, a redundant set of hypothetical scene motions is generated. Each subset of this pool of motion candidates is regarded as a possible explanation of the image feature tracks, and the most likely explanation is selected with model selection. The framework is generic and can be used with any parametric camera model, or with a combination of different models. It can deal with sets of correspondences, which change over time, and it is robust to realistic amounts of outliers. The framework is demonstrated for different camera and scene model

Model Selection for Geometric Fitting: Geometric Ale and Geometric MDL

Contrasting "geometric fitting", for which the noise level is taken as the asymptotic variable, with "statistical inference", for which the number of observations is taken as the asymptotic variable, we give a new definition of the "geometric AIC" and the "geometric MDL" as the counterparts of Akaike's AIC and Rissanen's MDL. We discuss various theoretical and practical problems that emerge from our analysis. Finally, we show, doing experiments using synthetic and real images, that the geometric MDL does not necessarily outperform the geometric AIC and that the two criteria have very different characteristics

Uncertainty modeling and model selection for geometric inference

We first investigate the meaning of &#34;statistical methods&#34; for geometric inference based on image feature points. Tracing back the origin of feature uncertainty to image processing operations, we discuss the implications of asymptotic analysis in reference to &#34;geometric fitting&#34; and &#34;geometric model selection&#34; and point out that a correspondence exists between the standard statistical analysis and the geometric inference problem. Then, we derive the &#34;geometric AIC&#34; and the &#34;geometric MDL&#34; as counterparts of Akaike's AIC and Rissanen's MDL. We show by experiments that the two criteria have contrasting characteristics in detecting degeneracy. </p

Learning Dense 3D Models from Monocular Video

Reconstructing dense, detailed, 3D shape of dynamic scenes from monocular sequences is a challenging problem in computer vision. While robust and even real-time solutions exist to this problem if the observed scene is static, for non-rigid dense shape capture current systems are typically restricted to the use of complex multi-camera rigs, taking advantage of the additional depth channel available in RGB-D cameras, or dealing with specific shapes such as faces or planar surfaces. In this thesis, we present two pieces of work for reconstructing dense generic shapes from monocular sequences. In the first work, we propose an unsupervised approach to the challenging problem of simultaneously segmenting the scene into its constituent objects and reconstructing a 3D model of the scene. The strength of our approach comes from the ability to deal with real-world dynamic scenes and to handle seamlessly different types of motion: rigid, articulated and non-rigid. We formulate the problem as a hierarchical graph-cuts based segmentation where we decompose the whole scene into background and foreground objects and model the complex motion of non-rigid or articulated objects as a set of overlapping rigid parts. To validate the capability of our approach to deal with real-world scenes, we provide 3D reconstructions of some challenging videos from the YouTube Objects and KITTI dataset, etc. In the second work, we propose a direct approach for capturing the dense, detailed 3D geometry of generic, complex non-rigid meshes using a single camera. Our method makes use of a single RGB video as input; it can capture the deformations of generic shapes; and the depth estimation is dense, per-pixel and direct. We first reconstruct a dense 3D template of the shape of the object, using a short rigid sequence, and subsequently perform online reconstruction of the non-rigid mesh as it evolves over time. In our experimental evaluation, we show a range of qualitative results on novel datasets and quantitative comparison results with stereo reconstruction

Local Deformation Modelling for Non-Rigid Structure from Motion

PhDReconstructing the 3D geometry of scenes based on monocular image sequences is a long-standing problem in computer vision. Structure from motion (SfM) aims at a data-driven approach without requiring a priori models of the scene. When the scene is rigid, SfM is a well understood problem with solutions widely used in industry. However, if the scene is non-rigid, monocular reconstruction without additional information is an ill-posed problem and no satisfactory solution has yet been found. Current non-rigid SfM (NRSfM) methods typically aim at modelling deformable motion globally. Additionally, most of these methods focus on cases where deformable motion is seen as small variations from a mean shape. In turn, these methods fail at reconstructing highly deformable objects such as a flag waving in the wind. Additionally, reconstructions typically consist of low detail, sparse point-cloud representation of objects. In this thesis we aim at reconstructing highly deformable surfaces by modelling them locally. In line with a recent trend in NRSfM, we propose a piecewise approach which reconstructs local overlapping regions independently. These reconstructions are merged into a global object by imposing 3D consistency of the overlapping regions. We propose our own local model – the Quadratic Deformation model – and show how patch division and reconstruction can be formulated in a principled approach by alternating at minimizing a single geometric cost – the image re-projection error of the reconstruction. Moreover, we extend our approach to dense NRSfM, where reconstructions are preformed at the pixel level, improving the detail of state of the art reconstructions. Finally we show how our principled approach can be used to perform simultaneous segmentation and reconstruction of articulated motion, recovering meaningful segments which provide a coarse 3D skeleton of the object.Fundacao para a Ciencia e a Tecnologia (FCT) under Doctoral Grant SFRH/BD/70312/2010; European Research Council under ERC Starting Grant agreement 204871-HUMANI

Automatic Camera Model Selection for Multibody Motion Segmentation

We study the problem of segmenting independently moving objects in a video sequence. Several algorithms exist for classifying the trajectories of the feature points into independent motions, but the performance depends on the validity of the underlying camera imaging model. In this paper, we present a scheme for automatically selecting the best model using the geometric AIC before the segmentation stage, Using real video sequences, we confirm that the segmentation accuracy indeed improves if the segmentation is based on the selected model. We also show that the trajectory data can be compressed into low-dimensional vectors using the selected model. This is very effective in reducing the computation time for a long video sequence

Uncertainty Modeling and Geometric Inference

We investigate the meaning of "statistical methods" for geometric inference based on image feature points. Tracing back the origin of feature uncertainty to image processing operations, we discuss the implications of asymptotic analysis in reference to "geometric fitting" and "geometric model selection", We point out that a correspondence exists between the standard statistical analysis and the geometric inference problem. We also compare the capability of the "geometric AIC" and the "geometric MDL' in detecting degeneracy. Next, we review recent progress in geometric fitting techniques for linear constraints, describing the "FNS method", the "HEIV method", the "renormalization method", and other related techniques. Finally, we discuss the "Neyman-Scott problem" and "semiparametric models" in relation to geometric inference. We conclude that applications of statistical methods requires careful considerations about the nature of the problem in question