SPA: Sparse Photorealistic Animation using a single RGB-D camera

Photorealistic animation is a desirable technique for computer games and movie production. We propose a new method to synthesize plausible videos of human actors with new motions using a single cheap RGB-D camera. A small database is captured in a usual office environment, which happens only once for synthesizing different motions. We propose a markerless performance capture method using sparse deformation to obtain the geometry and pose of the actor for each time instance in the database. Then, we synthesize an animation video of the actor performing the new motion that is defined by the user. An adaptive model-guided texture synthesis method based on weighted low-rank matrix completion is proposed to be less sensitive to noise and outliers, which enables us to easily create photorealistic animation videos with new motions that are different from the motions in the database. Experimental results on the public dataset and our captured dataset have verified the effectiveness of the proposed method

Variational Discretization of Higher Order Geometric Gradient Flows Based on Phase Field Models

In this thesis a phase field based nested variational time discretization for Willmore flow is presented. The basic idea of our model is to approximate the mean curvature by a time-discrete, approximate speed of the mean curvature motion. This speed is computed by a fully implicit time step of mean curvature motion, which forms the inner problem of our model. It is set up as a minimization problem taking into account the concept of natural time discretization. The outer problem is a variational problem balancing between the L2-distance of the surface at two consecutive time steps and the decay of the Willmore energy. This is a typical ansatz in case of natural time discretization as it is used in the inner problem. Within the Willmore energy the mean curvature is approximated as mentioned above. Consequently our model is a nested variational and leads to a PDE constraint optimization problem to compute a single time step. It allows time steps up to the size of the spatial grid width. A corresponding parametric version of this model based on finite elements on a triangulation of the evolving geometry was investigated by Olischläger and Rumpf. In this work we derive the corresponding phase field version and prove the existence of a solution. Since biharmonic heat flow is a linear model problem for our nested time discretization of Willmore flow we transfer our model to the linear case. Moreover we present error estimates for the fully discrete biharmonic heat flow and validate them numerically. In addition we compare our model with the semi-implicit phase field scheme for Willmore flow introduced by Du et al. which leads to the result that our nested variational method is significantly more robust. An application of our nested time discretized Willmore model consists in reconstructing a hypersurface corresponding to a given lower-dimensional apparent contour or Huffman labeling. The apparent contour separates the regions where the number of intersections between the hypersurface and the projection ray is constant and the labeling which specifies these intersection numbers is called Huffman labeling. For reconstructing the hypersurface we minimize a regularization energy consisting of the scaled area and Willmore energy subject to the constraint that the Huffman labeling of the minimizing surface equals the given Huffman labeling almost everywhere. To solve the corresponding phase field problem we use an algorithm alternating the minimizes of the regularization and mismatch energy. Moreover we use a multigrid ansatz. In most parts of this work our nested variational problem is solved by setting up the corresponding Lagrange equation and solving the resulting saddle point problem. An alternative is presented in the last part of this work. It deals with the problem of solving the linear model problem as well as our nested variational problem with an Augmented Lagrange method

Side information in robust principal component analysis: algorithms and applications

Dimensionality reduction and noise removal are fundamental machine learning tasks that are vital to artificial intelligence applications. Principal component analysis has long been utilised in computer vision to achieve the above mentioned goals. Recently, it has been enhanced in terms of robustness to outliers in robust principal component analysis. Both convex and non-convex programs have been developed to solve this new formulation, some with exact convergence guarantees. Its effectiveness can be witnessed in image and video applications ranging from image denoising and alignment to background separation and face recognition. However, robust principal component analysis is by no means perfect. This dissertation identifies its limitations, explores various promising options for improvement and validates the proposed algorithms on both synthetic and real-world datasets. Common algorithms approximate the NP-hard formulation of robust principal component analysis with convex envelopes. Though under certain assumptions exact recovery can be guaranteed, the relaxation margin is too big to be squandered. In this work, we propose to apply gradient descent on the Burer-Monteiro bilinear matrix factorisation to squeeze this margin given available subspaces. This non-convex approach improves upon conventional convex approaches both in terms of accuracy and speed. On the other hand, oftentimes there is accompanying side information when an observation is made. The ability to assimilate such auxiliary sources of data can ameliorate the recovery process. In this work, we investigate in-depth such possibilities for incorporating side information in restoring the true underlining low-rank component from gross sparse noise. Lastly, tensors, also known as multi-dimensional arrays, represent real-world data more naturally than matrices. It is thus advantageous to adapt robust principal component analysis to tensors. Since there is no exact equivalence between tensor rank and matrix rank, we employ the notions of Tucker rank and CP rank as our optimisation objectives. Overall, this dissertation carefully defines the problems when facing real-world computer vision challenges, extensively and impartially evaluates the state-of-the-art approaches, proposes novel solutions and provides sufficient validations on both simulated data and popular real-world datasets for various mainstream computer vision tasks.Open Acces

Computer aided puzzle assembly based on shape and texture information /

Puzzle assembly’s importance lies into application in many areas such as restoration and reconstruction of archeological findings, the repairing of broken objects, solving of the jigsaw type puzzles, molecular docking problem, etc. Puzzle pieces usually include not only geometrical shape information but also visual information of texture, color, continuity of lines, and so on. Moreover, textural information is mainly used to assembly pieces in some cases, such as classic jigsaw puzzles. This research presents a new approach in that pictorial assembly, in contrast to previous curve matching methods, uses texture information as well as geometric shape. The assembly in this study is performed using textural features and geometrical constraints. First, the texture of a band outside the border of pieces is predicted by inpainting and texture synthesis methods. The feature values are derived by these original and predicted images of pieces. A combination of the feature and confidence values is used to generate an affinity measure of corresponding pieces. Two new algorithms using Fourier based image registration techniques are developed to optimize the affinity. The algorithms for inpainting, affinity and Fourier based assembly are explained with experimental results on real and artificial data. The main contributions of this research are: The development of a performance measure that indicates the level of success of assembly of pieces based on textural features and geometrical shape. Solution of the assembly problem by using of the Fourier based methods

Geodesic Active Fields:A Geometric Framework for Image Registration

Image registration is the concept of mapping homologous points in a pair of images. In other words, one is looking for an underlying deformation field that matches one image to a target image. The spectrum of applications of image registration is extremely large: It ranges from bio-medical imaging and computer vision, to remote sensing or geographic information systems, and even involves consumer electronics. Mathematically, image registration is an inverse problem that is ill-posed, which means that the exact solution might not exist or not be unique. In order to render the problem tractable, it is usual to write the problem as an energy minimization, and to introduce additional regularity constraints on the unknown data. In the case of image registration, one often minimizes an image mismatch energy, and adds an additive penalty on the deformation field regularity as smoothness prior. Here, we focus on the registration of the human cerebral cortex. Precise cortical registration is required, for example, in statistical group studies in functional MR imaging, or in the analysis of brain connectivity. In particular, we work with spherical inflations of the extracted hemispherical surface and associated features, such as cortical mean curvature. Spatial mapping between cortical surfaces can then be achieved by registering the respective spherical feature maps. Despite the simplified spherical geometry, inter-subject registration remains a challenging task, mainly due to the complexity and inter-subject variability of the involved brain structures. In this thesis, we therefore present a registration scheme, which takes the peculiarities of the spherical feature maps into particular consideration. First, we realize that we need an appropriate hierarchical representation, so as to coarsely align based on the important structures with greater inter-subject stability, before taking smaller and more variable details into account. Based on arguments from brain morphogenesis, we propose an anisotropic scale-space of mean-curvature maps, built around the Beltrami framework. Second, inspired by concepts from vision-related elements of psycho-physical Gestalt theory, we hypothesize that anisotropic Beltrami regularization better suits the requirements of image registration regularization, compared to traditional Gaussian filtering. Different objects in an image should be allowed to move separately, and regularization should be limited to within the individual Gestalts. We render the regularization feature-preserving by limiting diffusion across edges in the deformation field, which is in clear contrast to the indifferent linear smoothing. We do so by embedding the deformation field as a manifold in higher-dimensional space, and minimize the associated Beltrami energy which represents the hyperarea of this embedded manifold as measure of deformation field regularity. Further, instead of simply adding this regularity penalty to the image mismatch in lieu of the standard penalty, we propose to incorporate the local image mismatch as weighting function into the Beltrami energy. The image registration problem is thus reformulated as a weighted minimal surface problem. This approach has several appealing aspects, including (1) invariance to re-parametrization and ability to work with images defined on non-flat, Riemannian domains (e.g., curved surfaces, scalespaces), and (2) intrinsic modulation of the local regularization strength as a function of the local image mismatch and/or noise level. On a side note, we show that the proposed scheme can easily keep up with recent trends in image registration towards using diffeomorphic and inverse consistent deformation models. The proposed registration scheme, called Geodesic Active Fields (GAF), is non-linear and non-convex. Therefore we propose an efficient optimization scheme, based on splitting. Data-mismatch and deformation field regularity are optimized over two different deformation fields, which are constrained to be equal. The constraint is addressed using an augmented Lagrangian scheme, and the resulting optimization problem is solved efficiently using alternate minimization of simpler sub-problems. In particular, we show that the proposed method can easily compete with state-of-the-art registration methods, such as Demons. Finally, we provide an implementation of the fast GAF method on the sphere, so as to register the triangulated cortical feature maps. We build an automatic parcellation algorithm for the human cerebral cortex, which combines the delineations available on a set of atlas brains in a Bayesian approach, so as to automatically delineate the corresponding regions on a subject brain given its feature map. In a leave-one-out cross-validation study on 39 brain surfaces with 35 manually delineated gyral regions, we show that the pairwise subject-atlas registration with the proposed spherical registration scheme significantly improves the individual alignment of cortical labels between subject and atlas brains, and, consequently, that the estimated automatic parcellations after label fusion are of better quality

Advances in generative modelling: from component analysis to generative adversarial networks

This Thesis revolves around datasets and algorithms, with a focus on generative modelling. In particular, we first turn our attention to a novel, multi-attribute, 2D facial dataset. We then present deterministic as well as probabilistic Component Analysis (CA) techniques which can be applied to multi-attribute 2D as well as 3D data. We finally present deep learning generative approaches specially designed to manipulate 3D facial data. Most 2D facial datasets that are available in the literature, are: a) automatically or semi-automatically collected and thus contain noisy labels, hindering the benchmarking and comparisons between algorithms. Moreover, they are not annotated for multiple attributes. In the first part of the Thesis, we present the first manually collected and annotated database, which contains labels for multiple attributes. As we demonstrate in a series of experiments, it can be used in a number of applications ranging from image translation to age-invariant face recognition. Moving on, we turn our attention to CA methodologies. CA approaches, although being able to only capture linear relationships between data, can still be proven to be efficient in data such as UV maps or 3D data registered in a common template, since they are well aligned. The introduction of more complex datasets in the literature, which contain labels for multiple attributes, naturally brought the need for novel algorithms that can simultaneously handle multiple attributes. In this Thesis, we cover novel CA approaches which are specifically designed to be utilised in datasets annotated with respect to multiple attributes and can be used in a variety of tasks, such as 2D image denoising and translation, as well as 3D data generation and identification. Nevertheless, while CA methods are indeed efficient when handling registered 3D facial data, linear 3D generative models lack details when it comes to reconstructing or generating finer facial characteristics. To alleviate this, in the final part of this Thesis we propose a novel generative framework harnessing the power of Generative Adversarial Networks.Open Acces

Low-rank Based Algorithms for Rectification, Repetition Detection and De-noising in Urban Images

In this thesis, we aim to solve the problem of automatic image rectification and repeated patterns detection on 2D urban images, using novel low-rank based techniques. Repeated patterns (such as windows, tiles, balconies and doors) are prominent and significant features in urban scenes. Detection of the periodic structures is useful in many applications such as photorealistic 3D reconstruction, 2D-to-3D alignment, facade parsing, city modeling, classification, navigation, visualization in 3D map environments, shape completion, cinematography and 3D games. However both of the image rectification and repeated patterns detection problems are challenging due to scene occlusions, varying illumination, pose variation and sensor noise. Therefore, detection of these repeated patterns becomes very important for city scene analysis. Given a 2D image of urban scene, we automatically rectify a facade image and extract facade textures first. Based on the rectified facade texture, we exploit novel algorithms that extract repeated patterns by using Kronecker product based modeling that is based on a solid theoretical foundation. We have tested our algorithms in a large set of images, which includes building facades from Paris, Hong Kong and New York

Large Scale Inverse Problems

This book is thesecond volume of a three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation &amp Analysis in Energy and the Environment" that took placein Linz, Austria, October 3-7, 2011. This volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications. The solution of inverse problems is fundamental to a wide variety of applications such as weather forecasting, medical tomography, and oil exploration. Regularisation techniques are needed to ensure solutions of sufficient quality to be useful, and soundly theoretically based. This book addresses the common techniques required for all the applications, and is thus truly interdisciplinary. This collection of survey articles focusses on the large inverse problems commonly arising in simulation and forecasting in the earth sciences

Motion capture data processing, retrieval and recognition.

Character animation plays an essential role in the area of featured film and computer games. Manually creating character animation by animators is both tedious and inefficient, where motion capture techniques (MoCap) have been developed and become the most popular method for creating realistic character animation products. Commercial MoCap systems are expensive and the capturing process itself usually requires an indoor studio environment. Procedural animation creation is often lacking extensive user control during the generation progress. Therefore, efficiently and effectively reusing MoCap data can brings significant benefits, which has motivated wider research in terms of machine learning based MoCap data processing. A typical work flow of MoCap data reusing can be divided into 3 stages: data capture, data management and data reusing. There are still many challenges at each stage. For instance, the data capture and management often suffer from data quality problems. The efficient and effective retrieval method is also demanding due to the large amount of data being used. In addition, classification and understanding of actions are the fundamental basis of data reusing. This thesis proposes to use machine learning on MoCap data for reusing purposes, where a frame work of motion capture data processing is designed. The modular design of this framework enables motion data refinement, retrieval and recognition. The first part of this thesis introduces various methods used in existing motion capture processing approaches in literature and a brief introduction of relevant machine learning methods used in this framework. In general, the frameworks related to refinement, retrieval, recognition are discussed. A motion refinement algorithm based on dictionary learning will then be presented, where kinematical structural and temporal information are exploited. The designed optimization method and data preprocessing technique can ensure a smooth property for the recovered result. After that, a motion refinement algorithm based on matrix completion is presented, where the low-rank property and spatio-temporal information is exploited. Such model does not require preparing data for training. The designed optimization method outperforms existing approaches in regard to both effectiveness and efficiency. A motion retrieval method based on multi-view feature selection is also proposed, where the intrinsic relations between visual words in each motion feature subspace are discovered as a means of improving the retrieval performance. A provisional trace-ratio objective function and an iterative optimization method are also included. A non-negative matrix factorization based motion data clustering method is proposed for recognition purposes, which aims to deal with large scale unsupervised/semi-supervised problems. In addition, deep learning models are used for motion data recognition, e.g. 2D gait recognition and 3D MoCap recognition. To sum up, the research on motion data refinement, retrieval and recognition are presented in this thesis with an aim to tackle the major challenges in motion reusing. The proposed motion refinement methods aim to provide high quality clean motion data for downstream applications. The designed multi-view feature selection algorithm aims to improve the motion retrieval performance. The proposed motion recognition methods are equally essential for motion understanding. A collection of publications by the author of this thesis are noted in publications section