Distributed Solution of the Inverse Rig Problem in Blendshape Facial Animation

The problem of rig inversion is central in facial animation as it allows for a realistic and appealing performance of avatars. With the increasing complexity of modern blendshape models, execution times increase beyond practically feasible solutions. A possible approach towards a faster solution is clustering, which exploits the spacial nature of the face, leading to a distributed method. In this paper, we go a step further, involving cluster coupling to get more confident estimates of the overlapping components. Our algorithm applies the Alternating Direction Method of Multipliers, sharing the overlapping weights between the subproblems. The results obtained with this technique show a clear advantage over the naive clustered approach, as measured in different metrics of success and visual inspection. The method applies to an arbitrary clustering of the face. We also introduce a novel method for choosing the number of clusters in a data-free manner. The method tends to find a clustering such that the resulting clustering graph is sparse but without losing essential information. Finally, we give a new variant of a data-free clustering algorithm that produces good scores with respect to the mentioned strategy for choosing the optimal clustering

A Majorization-Minimization Based Method for Nonconvex Inverse Rig Problems in Facial Animation: Algorithm Derivation

Automated methods for facial animation are a necessary tool in the modern industry since the standard blendshape head models consist of hundreds of controllers and a manual approach is painfully slow. Different solutions have been proposed that produce output in real-time or generalize well for different face topologies. However, all these prior works consider a linear approximation of the blendshape function and hence do not provide a high-enough level of details for modern realistic human face reconstruction. We build a method for solving the inverse rig in blendshape animation using quadratic corrective terms, which increase accuracy. At the same time, due to the proposed construction of the objective function, it yields a sparser estimated weight vector compared to the state-of-the-art methods. The former feature means lower demand for subsequent manual corrections of the solution, while the latter indicates that the manual modifications are also easier to include. Our algorithm is iterative and employs a Majorization Minimization paradigm to cope with the increased complexity produced by adding the corrective terms. The surrogate function is easy to solve and allows for further parallelization on the component level within each iteration. This paper is complementary to an accompanying paper, Rackovi\'c et al. (2023), where we provide detailed experimental results and discussion, including highly-realistic animation data, and show a clear superiority of the results compared to the state-of-the-art methods

High-fidelity Interpretable Inverse Rig: An Accurate and Sparse Solution Optimizing the Quartic Blendshape Model

We propose a method to fit arbitrarily accurate blendshape rig models by solving the inverse rig problem in realistic human face animation. The method considers blendshape models with different levels of added corrections and solves the regularized least-squares problem using coordinate descent, i.e., iteratively estimating blendshape weights. Besides making the optimization easier to solve, this approach ensures that mutually exclusive controllers will not be activated simultaneously and improves the goodness of fit after each iteration. We show experimentally that the proposed method yields solutions with mesh error comparable to or lower than the state-of-the-art approaches while significantly reducing the cardinality of the weight vector (over 20 percent), hence giving a high-fidelity reconstruction of the reference expression that is easier to manipulate in the post-production manually. Python scripts for the algorithm will be publicly available upon acceptance of the paper

Accurate and Interpretable Solution of the Inverse Rig for Realistic Blendshape Models with Quadratic Corrective Terms

We propose a new model-based algorithm solving the inverse rig problem in facial animation retargeting, exhibiting higher accuracy of the fit and sparser, more interpretable weight vector compared to SOTA. The proposed method targets a specific subdomain of human face animation - highly-realistic blendshape models used in the production of movies and video games. In this paper, we formulate an optimization problem that takes into account all the requirements of targeted models. Our objective goes beyond a linear blendshape model and employs the quadratic corrective terms necessary for correctly fitting fine details of the mesh. We show that the solution to the proposed problem yields highly accurate mesh reconstruction even when general-purpose solvers, like SQP, are used. The results obtained using SQP are highly accurate in the mesh space but do not exhibit favorable qualities in terms of weight sparsity and smoothness, and for this reason, we further propose a novel algorithm relying on a MM technique. The algorithm is specifically suited for solving the proposed objective, yielding a high-accuracy mesh fit while respecting the constraints and producing a sparse and smooth set of weights easy to manipulate and interpret by artists. Our algorithm is benchmarked with SOTA approaches, and shows an overall superiority of the results, yielding a smooth animation reconstruction with a relative improvement up to 45 percent in root mean squared mesh error while keeping the cardinality comparable with benchmark methods. This paper gives a comprehensive set of evaluation metrics that cover different aspects of the solution, including mesh accuracy, sparsity of the weights, and smoothness of the animation curves, as well as the appearance of the produced animation, which human experts evaluated

Extreme Multilabel Classification for Specialist Doctor Recommendation with Implicit Feedback and Limited Patient Metadata

Recommendation Systems (RS) are often used to address the issue of medical doctor referrals. However, these systems require access to patient feedback and medical records, which may not always be available in real-world scenarios. Our research focuses on medical referrals and aims to predict recommendations in different specialties of physicians for both new patients and those with a consultation history. We use Extreme Multilabel Classification (XML), commonly employed in text-based classification tasks, to encode available features and explore different scenarios. While its potential for recommendation tasks has often been suggested, this has not been thoroughly explored in the literature. Motivated by the doctor referral case, we show how to recast a traditional recommender setting into a multilabel classification problem that current XML methods can solve. Further, we propose a unified model leveraging patient history across different specialties. Compared to state-of-the-art RS using the same features, our approach consistently improves standard recommendation metrics up to approximately $10\%$ for patients with a previous consultation history. For new patients, XML proves better at exploiting available features, outperforming the benchmark in favorable scenarios, with particular emphasis on recall metrics. Thus, our approach brings us one step closer to creating more effective and personalized doctor referral systems. Additionally, it highlights XML as a promising alternative to current hybrid or content-based RS, while identifying key aspects to take into account when using XML for recommendation tasks

A hybrid compartmental model with a case study of COVID-19 in Great Britain and Israel

Abstract Given the severe impact of COVID-19 on several societal levels, it is of crucial importance to model the impact of restriction measures on the pandemic evolution, so that governments are able to make informed decisions. Even though there have been countless attempts to propose diverse models since the rise of the outbreak, the increase in data availability and start of vaccination campaigns calls for updated models and studies. Furthermore, most of the works are focused on a very particular place or application and we strive to attain a more general model, resorting to data from different countries. In particular, we compare Great Britain and Israel, two highly different scenarios in terms of vaccination plans and social structure. We build a network-based model, complex enough to model different scenarios of government-mandated restrictions, but generic enough to be applied to any population. To ease the computational load we propose a decomposition strategy for our model