Anastasios Roussos

Dense Variational Reconstruction of Non-rigid Surfaces from Monocular Video

This paper offers the first variational approach to the problem of dense 3D reconstruction of non-rigid surfaces from a monocular video sequence. We formulate non-rigid structure from motion (nrsfm) as a global variational energy minimization problem to estimate dense low-rank smooth 3D shapes for every frame along with the camera motion matrices, given dense 2D correspondences. Unlike traditional factorization based approaches to nrsfm, which model the low-rank non-rigid shape using a fixed number of basis shapes and corresponding coefficients, we minimize the rank of the matrix of time-varying shapes directly via trace norm minimization. In conjunction with this low-rank constraint, we use an edge preserving total-variation regularization term to obtain spatially smooth shapes for every frame. Thanks to proximal splitting techniques the optimization problem can be decomposed into many point-wise sub-problems and simple linear systems which can be easily solved on GPU hardware. We show results on real sequences of different objects (face, torso, beating heart) where, despite challenges in tracking, illumination changes and occlusions, our method reconstructs highly deforming smooth surfaces densely and accurately directly from video, without the need for any prior models or shape templates.

A Variational Approach to Video Registration with Subspace Constraints

This paper addresses the problem of non-rigid video registration, or the computation of optical flow from a reference frame to each of the subsequent images in a sequence, when the camera views deformable objects. We exploit the high correlation between 2D trajectories of different points on the same non-rigid surface by assuming that the displacement of any point throughout the sequence can be expressed in a compact way as a linear combination of a low-rank motion basis. This subspace constraint effectively acts as a trajectory regularization term leading to temporally consistent optical flow. We formulate it as a robust soft constraint within a variational framework by penalizing flow fields that lie outside the low-rank manifold. The resulting energy functional can be decoupled into the optimization of the brightness constancy and spatial regularization terms, leading to an efficient optimization scheme. Additionally, we propose a novel optimization scheme for the case of vector valued images, based on the dualization of the data term. This allows us to extend our approach to deal with colour images which results in significant improvements on the registration results. Finally, we provide a new benchmark dataset, based on motion capture data of a flag waving in the wind, with dense ground truth optical flow for evaluation of multi-frame optical flow algorithms for non-rigid surfaces. Our experiments show that our proposed approach outperforms state of the art optical flow and dense non-rigid registration algorithms.

A 3D Morphable Model Learnt from 10,000 Faces

We present Large Scale Facial Model (LSFM) - a 3D Morphable Model (3DMM) automatically constructed from 9,663 distinct facial identities. To the best of our knowledge LSFM is the largest-scale Morphable Model ever constructed, containing statistical information from a huge variety of the human population. To build such a large model we introduce a novel fully automated and robust Morphable Model construction pipeline. The dataset that LSFM is trained on includes rich demographic information about each subject, allowing for the construction of not only a global 3DMM but also models tailored for specific age, gender or ethnicity groups. As an application example, we utilise the proposed model to perform age classification from 3D shape alone. Furthermore, we perform a systematic analysis of the constructed 3DMMs that showcases their quality and descriptive power. The presented extensive qualitative and quantitative evaluations reveal that the proposed 3DMM achieves state-of-the-art results, outperforming existing models by a large margin. Finally, for the benefit of the research community, we make publicly available the source code of the proposed automatic 3DMM construction pipeline. In addition, the constructed global 3DMM and a variety of bespoke models tailored by age, gender and ethnicity are available on application to researchers involved in medically oriented research.

Structure Tensor Total Variation

We introduce a novel generic energy functional that we employ to solve inverse imaging problems within a variational framework. The proposed regularization family, termed as structure tensor total variation (STV), penalizes the eigenvalues of the structure tensor and is suitable for both grayscale and vector-valued images. It generalizes several existing variational penalties, including the total variation seminorm and vectorial extensions of it. Meanwhile, thanks to the structure tensors ability to capture first-order information around a local neighborhood, the STV functionals can provide more robust measures of image variation. Further, we prove that the STV regularizers are convex while they also satisfy several invariance properties w.r.t. image transformations. These properties qualify them as ideal candidates for imaging applications. In addition, for the discrete version of the STV functionals we derive an equivalent definition that is based on the patch-based Jacobian operator, a novel linear operator which extends the Jacobian matrix. This alternative definition allow us to derive a dual problem formulation. The duality of the problem paves the way for employing robust tools from convex optimization and enables us to design an efficient and parallelizable optimization algorithm. Finally, we present extensive experiments on various inverse imaging problems, where we compare our regularizers with other competing regularization approaches. Our results are shown to be systematically superior, both quantitatively and visually.

Convex Generalizations of Total Variation Based on the Structure Tensor with Applications to Inverse Problems

We introduce a generic convex energy functional that is suitable for both grayscale and vector-valued images. Our functional is based on the eigenvalues of the structure tensor, therefore it penalizes image variation at every point by taking into account the information from its neighborhood. It generalizes several existing variational penalties, such as the Total Variation and vectorial extensions of it. By introducing the concept of patch-based Jacobian operator, we derive an equivalent formulation of the proposed regularizer that is based on the Schatten norm of this operator. Using this new formulation, we prove convexity and develop a dual definition for the proposed energy, which gives rise to an efficient and parallelizable minimization algorithm. Moreover, we establish a connection between the minimization of the proposed convex regularizer and a generic type of nonlinear anisotropic diffusion that is driven by a spatially regularized and adaptive diffusion tensor. Finally, we perform extensive experiments with image denoising and deblurring for grayscale and color images. The results show the effectiveness of the proposed approach as well as its improved performance compared to Total Variation and existing vectorial extensions of it.

Dense multibody motion estimation and reconstruction from a handheld camera

Existing approaches to camera tracking and reconstruction from a single handheld camera for Augmented Reality (AR) focus on the reconstruction of static scenes. However, most real world scenarios are dynamic and contain multiple independently moving rigid objects. This paper addresses the problem of simultaneous segmentation, motion estimation and dense 3D reconstruction of dynamic scenes. We propose a dense solution to all three elements of this problem: depth estimation, motion label assignment and rigid transformation estimation directly from the raw video by optimizing a single cost function using a hill-climbing approach. We do not require prior knowledge of the number of objects present in the scene - the number of independent motion models and their parameters are automatically estimated. The resulting inference method combines the best techniques in discrete and continuous optimization: a state of the art variational approach is used to estimate the dense depth maps while the motion segmentation is achieved using discrete graph-cut based optimization. For the rigid motion estimation of the independently moving objects we propose a novel tracking approach designed to cope with the small fields of view they induce and agile motion. Our experimental results on real sequences show how accurate segmentations and dense depth maps can be obtained in a completely automated way and used in marker-free AR applications.

Tensor-based image diffusions derived from generalizations of the Total Variation and Beltrami Functionals

We introduce a novel functional for vector-valued images that generalizes several variational methods, such as the Total Variation and Beltrami Functionals. This functional is based on the structure tensor that describes the geometry of image structures within the neighborhood of each point. We first generalize the Beltrami functional based on the image patches and using embeddings in high dimensional spaces. Proceeding to the most general form of the proposed functional, we prove that its minimization leads to a nonlinear anisotropic diffusion that is regularized, in the sense that its diffusion tensor contains convolutions with a kernel. Using this result we propose two novel diffusion methods, the Generalized Beltrami Flow and the Tensor Total Variation. These methods combine the advantages of the variational approaches with those of the tensor-based diffusion approaches.

Tongue tracking in Ultrasound images with Active Appearance Models

Tongue Ultrasound imaging is widely used for human speech production analysis and modeling. In this paper, we propose a novel method to automatically detect and track the tongue contour in Ultrasound (US) videos. Our method is built on a variant of Active Appearance Modeling. It incorporates shape prior information and can estimate the entire tongue contour robustly and accurately in a sequence of US frames. Experimental evaluation demonstrates the effectiveness of our approach and its improved performance compared to previously proposed tongue tracking techniques.

Large Scale 3D Morphable Models

We present large scale facial model (LSFM)—a 3D Morphable Model (3DMM) automatically constructed from 9663 distinct facial identities. To the best of our knowledge LSFM is the largest-scale Morphable Model ever constructed, containing statistical information from a huge variety of the human population. To build such a large model we introduce a novel fully automated and robust Morphable Model construction pipeline, informed by an evaluation of state-of-the-art dense correspondence techniques. The dataset that LSFM is trained on includes rich demographic information about each subject, allowing for the construction of not only a global 3DMM model but also models tailored for specific age, gender or ethnicity groups. We utilize the proposed model to perform age classification from 3D shape alone and to reconstruct noisy out-of-sample data in the low-dimensional model space. Furthermore, we perform a systematic analysis of the constructed 3DMM models that showcases their quality and descriptive power. The presented extensive qualitative and quantitative evaluations reveal that the proposed 3DMM achieves state-of-the-art results, outperforming existing models by a large margin. Finally, for the benefit of the research community, we make publicly available the source code of the proposed automatic 3DMM construction pipeline, as well as the constructed global 3DMM and a variety of bespoke models tailored by age, gender and ethnicity.

Reversible Interpolation of Vectorial Images by an Anisotropic Diffusion-Projection PDE

In this paper, a nonlinear model for the interpolation of vector-valued images is proposed. This model is based on an anisotropic diffusion PDE and performs an interpolation that is reversible. The interpolation solution is restricted to the subspace of functions that can recover the discrete input image, after an appropriate smoothing and sampling. The proposed nonlinear diffusion flow lies on this subspace while its strength and anisotropy adapt to the local variations and geometry of image structures. The derived method effectively reconstructs the real image structures and yields a satisfactory interpolation result. Compared to classic and other existing PDE-based interpolation methods, our proposed method seems to increase the accuracy of the result and to reduce the undesirable artifacts, such as blurring, ringing, block effects and edge distortion. We present extensive experimental results that demonstrate the potential of the method as applied to graylevel and color images.