It is well known that popular optimization techniques can lead to overfitting or even a lack of convergence altogether; thus, practitioners often utilize ad hoc regularization terms added to the energy functional. When carefully crafted, these regularizations can produce compelling results. However, regularization changes both the energy landscape and the solution to the optimization problem, which can result in underfitting. Surprisingly, many practitioners both add regularization and claim that their model lacks the expressivity to fit the data. Motivated by a geometric interpretation of the linearized search space, we propose an approach that ameliorates overfitting without the need for regularization terms that restrict the expressiveness of the underlying model. We illustrate the efficacy of our approach on minimization problems related to three-dimensional facial expression estimation where overfitting clouds semantic understanding and regularization may lead to underfitting that misses or misinterprets subtle expressions.
When solving for facial blendshape parameters @cite_18 , L2-norm regularization of the parameters is commonly used by practitioners to obtain more reasonable solutions due to its ease of use in commodity least squares solvers @cite_17 @cite_34 @cite_3 @cite_7 . Others instead choose to bound the blendshape weights between some minimum and maximum value (typically @math and @math or @math and @math ) @cite_24 @cite_29 @cite_37 . The usage of the L1-norm regularization is relatively rare, even though it results in sparser solutions @cite_4 @cite_21 @cite_19 . Other methods use Laplacian regularization @cite_24 @cite_15 or anatomically motivated regularization @cite_6 to constrain the deformation of the face.
@cite_18 @cite_37 @cite_4 @cite_7 @cite_29 @cite_21 @cite_3 @cite_6 @cite_24 @cite_19 @cite_15 @cite_34 @cite_17
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We present a multi-view stereo reconstruction technique that directly produces a complete high-fidelity head model with consistent facial mesh topology. While existing techniques decouple shape estimation and facial tracking, our framework jointly optimizes for stereo constraints and consistent mesh parameterization. Our method is therefore free from drift and fully parallelizable for dynamic facial performance capture. We produce highly detailed facial geometries with artist-quality UV parameterization, including secondary elements such as eyeballs, mouth pockets, nostrils, and the back of the head. Our approach consists of deforming a common template model to match multi-view input images of the subject, while satisfying cross-view, cross-subject, and cross-pose consistencies using a combination of 2D landmark detection, optical flow, and surface and volumetric Laplacian regularization. Since the flow is never computed between frames, our method is trivially parallelized by processing each frame independently. Accurate rigid head pose is extracted using a PCA-based dimension reduction and denoising scheme. We demonstrate high-fidelity performance capture results with challenging head motion and complex facial expressions around eye and mouth regions. While the quality of our results is on par with the current state-of-the-art, our approach can be fully parallelized, does not suffer from drift, and produces face models with production-quality mesh topologies. Recent breakthroughs have been made in the use of semi-definite programming and its application to real polynomial solving. For example, the real radical of a zero dimensional ideal, can be determined by such approaches. Some progress has been made on the determination of the real radical in positive dimension by Ma, Wang and Zhi[5, 4]. Such work involves the determination of maximal rank semidefinite matrices. Existing methods are computationally expensive and have poorer accuracy on larger examples. In previous work we showed that regularity in the form of the Slater constraint qualification (strict feasibility) fails for the moment matrix in the SDP feasibility problem[6]. We used facial reduction to obtain a smaller regularized problem for which strict feasibility holds. However we did not have a theoretical guarantee that our methods, based on facial reduction and Douglas-Rachford iteration ensured the satisfaction of the maximum rank condition. Our work is motivated by the problems above. We discuss how to compute the moment matrix and its kernel using facial reduction techniques where the maximum rank property can be guaranteed by solving the dual problem. The facial reduction algorithms on the primal form is presented. We give examples that exhibit for the first time additional facial reductions beyond the first which are effective in practice with much better accuracy than SeDuMi(CVX). Face alignment, which fits a face model to an image and extracts the semantic meanings of facial pixels, has been an important topic in CV community. However, most algorithms are designed for faces in small to medium poses (below 45), lacking the ability to align faces in large poses up to 90. The challenges are three-fold: Firstly, the commonly used landmark-based face model assumes that all the landmarks are visible and is therefore not suitable for profile views. Secondly, the face appearance varies more dramatically across large poses, ranging from frontal view to profile view. Thirdly, labelling landmarks in large poses is extremely challenging since the invisible landmarks have to be guessed. In this paper, we propose a solution to the three problems in an new alignment framework, called 3D Dense Face Alignment (3DDFA), in which a dense 3D face model is fitted to the image via convolutional neutral network (CNN). We also propose a method to synthesize large-scale training samples in profile views to solve the third problem of data labelling. Experiments on the challenging AFLW database show that our approach achieves significant improvements over state-of-the-art methods. We present a new anatomically-constrained local face model and fitting approach for tracking 3D faces from 2D motion data in very high quality. In contrast to traditional global face models, often built from a large set of blendshapes, we propose a local deformation model composed of many small subspaces spatially distributed over the face. Our local model offers far more flexibility and expressiveness than global blendshape models, even with a much smaller model size. This flexibility would typically come at the cost of reduced robustness, in particular during the under-constrained task of monocular reconstruction. However, a key contribution of this work is that we consider the face anatomy and introduce subspace skin thickness constraints into our model, which constrain the face to only valid expressions and helps counteract depth ambiguities in monocular tracking. Given our new model, we present a novel fitting optimization that allows 3D facial performance reconstruction from a single view at extremely high quality, far beyond previous fitting approaches. Our model is flexible, and can be applied also when only sparse motion data is available, for example with marker-based motion capture or even face posing from artistic sketches. Furthermore, by incorporating anatomical constraints we can automatically estimate the rigid motion of the skull, obtaining a rigid stabilization of the performance for free. We demonstrate our model and single-view fitting method on a number of examples, including, for the first time, extreme local skin deformation caused by external forces such as wind, captured from a single high-speed camera.