A Constrained Latent Variable Model

Latent variable models provide valuable compact representations for learning and inference in many computer vision tasks. However, most existing models cannot directly encode prior knowledge about the specific problem at hand. In this paper, we introduce a constrained latent variable model whose generated output inherently accounts for such knowledge. To this end, we propose an approach that explicitly imposes equality and inequality constraints on the model's output during learning, thus avoiding the computational burden of having to account for these constraints at inference. Our learning mechanism can exploit non-linear kernels, while only involving sequential closed-form updates of the model parameters. We demonstrate the effectiveness of our constrained latent variable model on the problem of non-rigid 3D reconstruction from monocular images, and show that it yields qualitative and quantitative improvements over several baselines.

Graph-based image representation learning

Renata Khasanova

Though deep learning (DL) algorithms are very powerful for image processing tasks, they generally require a lot of data to reach their full potential. Furthermore, there is no straightforward way to impose various properties, given by the prior knowledge about the target task, on the features extracted by a DL model. Therefore, in this thesis we propose several techniques that rely on the power of graph representations to embed prior knowledge inside the learning process. This allows to reduce the solution space and leads to faster optimization convergence and higher accuracy in the representation learning. In our first work, inspired by the ability of a human to correctly classify rotated, shifted or flipped objects, we propose an algorithm that permits to inherently encode invariance to isometric transformations of objects in an image. Our DL architecture is based on graph representations and consists of three novel layers, which we refer to as graph convolutional, dynamic pooling and statistical layers. Our experiments on the image classification tasks show that our network correctly recognizes isometrically transformed objects even though such types of transformation are not seen by the network at training time. Standard DL techniques are typically not able to succeed in solving such a problem without extensive data augmentation. Then, we propose to exploit the properties of graph-based approaches to efficiently process images with various types of projective geometry. In particular, we are interested in increasingly popular omnidirectional cameras, which have a 360 degree field of view. Despite their effectiveness, such cameras create images with specific geometric properties, which require special techniques for efficient processing. We propose an efficient way of adjusting the weights of the graph edges to adapt the filter responses to the geometric image properties introduced by omnidirectional cameras. Our experiments prove that using the proposed graph with properly adjusted edge weights permits to reach better performance as compared to using regular grid graph with equal weights. Finally, the approach described above relies on the isotropic filters, which work well within our transformation invariant architecture for image classification. However, for other problems (e.g. image compression) or even when used without dynamic pooling and statistical layers that are defined within the proposed architecture, these filters are unable to efficiently encode the information about the object. Thus, we introduce a different technique based on anisotropic filters that adapt their shape and size according to the omnidirectional image geometry. The main advantage of this approach compared to the previous one is the ability to encode the orientation of an image pattern, which is important for various tasks such as image compression. Our experiments show that our approach adapts to different image projective geometries and achieves state-of-the-art performance on image classification and compression tasks. Overall we propose several methods, which combine the power of DL and graph signal processing towards incorporating prior information about the target task inside the optimization procedure. We hope that the research efforts presented in this thesis will help the development of efficient DL algorithms that can use various types of prior knowledge to make them efficient even when the available training data is scarce.

EPFL2019

Resolving Ambiguities in Monocular 3D Reconstruction of Deformable Surfaces

Aydin Varol

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.

EPFL2012

Learning to Represent and Reconstruct 3D Deformable Objects

Jan Bednarík

Representing and reconstructing 3D deformable shapes are two tightly linked problems that have long been studied within the computer vision field. Deformable shapes are truly ubiquitous in the real world, whether be it specific object classes such as humans, garments and animals or more abstract ones such as generic materials deforming under an external force. Practical computer vision algorithms must be able to understand the shapes of objects in the observed scenes to unlock the wide spectrum of much sought after applications ranging from virtual try-on to automated surgeries.Automatic shape reconstruction is known to be an ill-posed problem, especially in the common scenario of a single image input. Therefore, the modern approaches rely on deep learning paradigm which has proven to be extremely effective even for the severely under-constrained computer vision problems. We, too, exploit the success of data-driven approaches, however, we also show that generic deep learning models can greatly benefit from being combined with explicit knowledge originating in computational geometry. We analyze the use of various 3D shape representations and we distinctly focus on one of them, the atlas-based representation, which turns out to be especially suitable for modeling deformable shapes and which we further improve and extend.The atlas-based representation models the surfaces as an ensemble of continuous functions and thus allows for arbitrary resolution and analytical surface analysis. We identify its major shortcomings, namely the patch collapse, patch overlap and strong mapping distortions, and we propose novel regularizers based on analytically computed properties of the reconstructed surfaces. Our approach counteracts the aforementioned drawbacks while yielding higher reconstruction accuracy.We dive into the problematics of atlas-based shape representation deeper and focus on another design flaw, the global inconsistency of the mappings. While it is not reflected in quantitative metrics, it is detrimental to the visual quality of the reconstructed surfaces. Specifically, we design loss functions encouraging intercommunication among the mappings which pushes the resulting surface towards a C1 smooth function and thus dramatically improves the visual quality.Furthermore, we adapt the atlas-based representation so that it could model a full sequence of a deforming object in a temporally-consistent way. The goal is to produce such reconstruction where each surface point always represents the same semantic point on the target GT surface. To achieve such behavior, we note that if each surface point deforms close-to-isometrically, its semantic location likely remains unchanged. Practically, we make use of the Riemannian metric, and force it to remain point-wise constant throughout the sequence. The experiments show that our method yields SotA results on correspondence estimation task.Finally, we look into a particular problem of monocular texture-less deformable shape reconstruction. We propose a multi-task learning approach which jointly produces a normal map, a depth map and a mesh corresponding to the observed surface. We show that producing multiple different 3D representations of the same objects results in higher reconstruction quality. We acquire a large real-world annotated dataset of texture-less deforming objects and we release it for public use.

EPFL2022