Template-free monocular reconstruction of deformable surfaces

It has recently been shown that deformable 3D surfaces could be recovered from single video streams. However, existing techniques either require a reference view in which the shape of the surface is known a priori, which often may not be available, or require tracking points over long sequences, which is hard to do. In this paper, we overcome these limitations. To this end, we establish correspondences between pairs of frames in which the shape is different and unknown. We then estimate homographies between corresponding local planar patches in both images. These yield approximate 3D reconstructions of points within each patch up to a scale factor. Since we consider overlapping patches, we can enforce them to be consistent over the whole surface. Finally, a local deformation model is used to fit a triangulated mesh to the 3D point cloud, which makes the reconstruction robust to both noise and outliers in the image data

Surface Deformation Models for Non-Rigid 3--D Shape Recovery

3--D detection and shape recovery of a non-rigid surface from video sequences require deformation models to effectively take advantage of potentially noisy image data. Here we introduce an approach to creating such models for deformable 3--D surfaces. We exploit the fact that the shape of an inextensible triangulated mesh can be parameterized in terms of a small subset of the angles between its facets. We use this set of angles to create a representative set of potential shapes, which we feed to a simple dimensionality reduction technique to produce low-dimensional 3--D deformation models. We show that these models can be used to accurately model a wide range of deforming 3--D surfaces from video sequences acquired under realistic conditions

Linear Local Models for Monocular Reconstruction of Deformable Surfaces

Recovering the 3D shape of a nonrigid surface from a single viewpoint is known to be both ambiguous and challenging. Resolving the ambiguities typically requires prior knowledge about the most likely deformations that the surface may undergo. It often takes the form of a global deformation model that can be learned from training data. While effective, this approach suffers from the fact that a new model must be learned for each new surface, which means acquiring new training data and may be impractical. In this paper, we replace the global models by linear local ones for surface patches, which can be assembled to represent arbitrary surface shapes as long as they are made of the same material. Not only do they eliminate the need to retrain the model for different surface shapes, they also let us formulate 3D shape reconstruction from correspondences as either an algebraic problem that can be solved in closed-form or a convex optimization problem whose solution can be found using standard numerical packages. We present quantitative results on synthetic data, as well as qualitative ones on real images

Data Preparation in Machine Learning for Condition-based Maintenance

ABSTRACT: Using Machine Learning (ML) prediction to achieve a successful, cost-effective, Condition-Based Maintenance (CBM) strategy has become very attractive in the context of Industry 4.0. In other fields, it is well known that in order to benefit from the prediction capability of ML algorithms, the data preparation phase must be well conducted. Thus, the objective of this paper is to investigate the effect of data preparation on the ML prediction accuracy of Gas Turbines (GTs) performance decay. First a data cleaning technique for robust Linear Regression imputation is proposed based on the Mixed Integer Linear Programming. Then, experiments are conducted to compare the effect of commonly used data cleaning, normalization and reduction techniques on the ML prediction accuracy. Results revealed that the best prediction accuracy of GTs decay, found with the k-Nearest Neighbors ML algorithm, considerately deteriorate when changing the data preparation steps and/or techniques. This study has shown that, for effective CBM application in industry, there is a need to develop a systematic methodology for design and selection of adequate data preparation steps and techniques with the proposed ML algorithms

Recovering articulated non-rigid shapes, motions and kinematic chains from video

Recovering articulated shape and motion, especially human body motion, from video is a challenging problem with a wide range of applications in medical study, sport analysis and animation, etc. Previous work on articulated motion recovery generally requires prior knowledge of the kinematic chain and usually does not concern the recovery of the articulated shape. The non-rigidity of some articulated part, e.g. human body motion with non-rigid facial motion, is completely ignored. We propose a factorization-based approach to recover the shape, motion and kinematic chain of an articulated object with non-rigid parts altogether directly from video sequences under a unified framework. The proposed approach is based on our modeling of the articulated non-rigid motion as a set of intersecting motion subspaces. A motion subspace is the linear subspace of the trajectories of an object. It can model a rigid or non-rigid motion. The intersection of two motion subspaces of linked parts models the motion of an articulated joint or axis. Our approach consists of algorithms for motion segmentation, kinematic chain building, and shape recovery. It is robust to outliers and can be automated. We test our approach through synthetic and real experiments and demonstrate how to recover articulated structure with non-rigid parts via a single-view camera without prior knowledge of its kinematic chain

Resolving Ambiguities in Monocular 3D Reconstruction of Deformable Surfaces

In this thesis, we focus on the problem of recovering 3D shapes of deformable surfaces from a single camera. This problem is known to be ill-posed as for a given 2D input image there exist many 3D shapes that give visually identical projections. We present three methods which make headway towards resolving these ambiguities. We believe that our work represents a significant step towards making surface reconstruction methods of practical use. First, we propose a surface reconstruction method that overcomes the limitations of the state-of-the-art template-based and non-rigid structure from motion methods. We neither track points over many frames, nor require a sophisticated deformation model, or depend on a reference image. In our method, we establish correspondences between pairs of frames in which the shape is different and unknown. We then estimate homographies between corresponding local planar patches in both images. These yield approximate 3D reconstructions of points within each patch up to a scale factor. Since we consider overlapping patches, we can enforce them to be consistent over the whole surface. Finally, a local deformation model is used to fit a triangulated mesh to the 3D point cloud, which makes the reconstruction robust to both noise and outliers in the image data. Second, we propose a novel approach to recovering the 3D shape of a deformable surface from a monocular input by taking advantage of shading information in more generic contexts than conventional Shape-from-Shading (SfS) methods. This includes surfaces that may be fully or partially textured and lit by arbitrarily many light sources. To this end, given a lighting model, we learn the relationship between a shading pattern and the corresponding local surface shape. At run time, we first use this knowledge to recover the shape of surface patches and then enforce spatial consistency between the patches to produce a global 3D shape. Instead of treating texture as noise as in many SfS approaches, we exploit it as an additional source of information. We validate our approach quantitatively and qualitatively using both synthetic and real data. Third, we introduce a constrained latent variable model that inherently accounts for geometric constraints such as inextensibility defined on the mesh model. To this end, we learn a non-linear mapping from the latent space to the output space, which corresponds to vertex positions of a mesh model, such that the generated outputs comply with equality and inequality constraints expressed in terms of the problem variables. Since its output is encouraged to satisfy such constraints inherently, using our model removes the need for computationally expensive methods that enforce these constraints at run time. In addition, our approach is completely generic and could be used in many other different contexts as well, such as image classification to impose separation of the classes, and articulated tracking to constrain the space of possible poses

Learning and recovering 3D surface deformations

Recovering the 3D deformations of a non-rigid surface from a single viewpoint has applications in many domains such as sports, entertainment, and medical imaging. Unfortunately, without any knowledge of the possible deformations that the object of interest can undergo, it is severely under-constrained, and extremely different shapes can have very similar appearances when reprojected onto an image plane. In this thesis, we first exhibit the ambiguities of the reconstruction problem when relying on correspondences between a reference image for which we know the shape and an input image. We then propose several approaches to overcoming these ambiguities. The core idea is that some a priori knowledge about how a surface can deform must be introduced to solve them. We therefore present different ways to formulate that knowledge that range from very generic constraints to models specifically designed for a particular object or material. First, we propose generally applicable constraints formulated as motion models. Such models simply link the deformations of the surface from one image to the next in a video sequence. The obvious advantage is that they can be used independently of the physical properties of the object of interest. However, to be effective, they require the presence of texture over the whole surface, and, additionally, do not prevent error accumulation from frame to frame. To overcome these weaknesses, we propose to introduce statistical learning techniques that let us build a model from a large set of training examples, that is, in our case, known 3D deformations. The resulting model then essentially performs linear or non-linear interpolation between the training examples. Following this approach, we first propose a linear global representation that models the behavior of the whole surface. As is the case with all statistical learning techniques, the applicability of this representation is limited by the fact that acquiring training data is far from trivial. A large surface can undergo many subtle deformations, and thus a large amount of training data must be available to build an accurate model. We therefore propose an automatic way of generating such training examples in the case of inextensible surfaces. Furthermore, we show that the resulting linear global models can be incorporated into a closed-form solution to the shape recovery problem. This lets us not only track deformations from frame to frame, but also reconstruct surfaces from individual images. The major drawback of global representations is that they can only model the behavior of a specific surface, which forces us to re-train a new model for every new shape, even though it is made of a material observed before. To overcome this issue, and simultaneously reduce the amount of required training data, we propose local deformation models. Such models describe the behavior of small portions of a surface, and can be combined to form arbitrary global shapes. For this purpose, we study both linear and non-linear statistical learning methods, and show that, whereas the latter are better suited for traking deformations from frame to frame, the former can also be used for reconstruction from a single image