Regularization of Persistent Homology Gradient Computation

Persistent homology is a method for computing the topological features present in a given data. Recently, there has been much interest in the integration of persistent homology as a computational step in neural networks or deep learning. In order for a given computation to be integrated in such a way, the computation in question must be differentiable. Computing the gradients of persistent homology is an ill-posed inverse problem with infinitely many solutions. Consequently, it is important to perform regularization so that the solution obtained agrees with known priors. In this work we propose a novel method for regularizing persistent homology gradient computation through the addition of a grouping term. This has the effect of helping to ensure gradients are defined with respect to larger entities and not individual points.

Fast and Robust Iterative Closet Point

The Iterative Closest Point (ICP) algorithm and its variants are a fundamental technique for rigid registration between two point sets, with wide applications in different areas from robotics to 3D reconstruction. The main drawbacks for ICP are its slow convergence as well as its sensitivity to outliers, missing data, and partial overlaps. Recent work such as Sparse ICP achieves robustness via sparsity optimization at the cost of computational speed. In this paper, we propose a new method for robust registration with fast convergence. First, we show that the classical point-to-point ICP can be treated as a majorization-minimization (MM) algorithm, and propose an Anderson acceleration approach to improve its convergence. In addition, we introduce a robust error metric based on the Welsch's function, which is minimized efficiently using the MM algorithm with Anderson acceleration. On challenging datasets with noises and partial overlaps, we achieve similar or better accuracy than Sparse ICP while being at least an order of magnitude faster. Finally, we extend the robust formulation to point-to-plane ICP, and solve the resulting problem using a similar Anderson-accelerated MM strategy. Our robust ICP methods improve the registration accuracy on benchmark datasets while being competitive in computational time.

Quasi-Newton Solver for Robust Non-Rigid Registration

Imperfect data (noise, outliers and partial overlap) and high degrees of freedom make non-rigid registration a classical challenging problem in computer vision. Existing methods typically adopt the $\ell_{p}$ type robust estimator to regularize the fitting and smoothness, and the proximal operator is used to solve the resulting non-smooth problem. However, the slow convergence of these algorithms limits its wide applications. In this paper, we propose a formulation for robust non-rigid registration based on a globally smooth robust estimator for data fitting and regularization, which can handle outliers and partial overlaps. We apply the majorization-minimization algorithm to the problem, which reduces each iteration to solving a simple least-squares problem with L-BFGS. Extensive experiments demonstrate the effectiveness of our method for non-rigid alignment between two shapes with outliers and partial overlap, with quantitative evaluation showing that it outperforms state-of-the-art methods in terms of registration accuracy and computational speed. The source code is available at https://github.com/Juyong/Fast_RNRR.

Lightweight Photometric Stereo for Facial Details Recovery

Recently, 3D face reconstruction from a single image has achieved great success with the help of deep learning and shape prior knowledge, but they often fail to produce accurate geometry details. On the other hand, photometric stereo methods can recover reliable geometry details, but require dense inputs and need to solve a complex optimization problem. In this paper, we present a lightweight strategy that only requires sparse inputs or even a single image to recover high-fidelity face shapes with images captured under near-field lights. To this end, we construct a dataset containing 84 different subjects with 29 expressions under 3 different lights. Data augmentation is applied to enrich the data in terms of diversity in identity, lighting, expression, etc. With this constructed dataset, we propose a novel neural network specially designed for photometric stereo based 3D face reconstruction. Extensive experiments and comparisons demonstrate that our method can generate high-quality reconstruction results with one to three facial images captured under near-field lights. Our full framework is available at https://github.com/Juyong/FacePSNet.

Robust RGB-D Face Recognition Using Attribute-Aware Loss

Existing convolutional neural network (CNN) based face recognition algorithms typically learn a discriminative feature mapping, using a loss function that enforces separation of features from different classes and/or aggregation of features within the same class. However, they may suffer from bias in the training data such as uneven sampling density, because they optimize the adjacency relationship of the learned features without considering the proximity of the underlying faces. Moreover, since they only use facial images for training, the learned feature mapping may not correctly indicate the relationship of other attributes such as gender and ethnicity, which can be important for some face recognition applications. In this paper, we propose a new CNN-based face recognition approach that incorporates such attributes into the training process. Using an attribute-aware loss function that regularizes the feature mapping using attribute proximity, our approach learns more discriminative features that are correlated with the attributes. We train our face recognition model on a large-scale RGB-D data set with over 100K identities captured under real application conditions. By comparing our approach with other methods on a variety of experiments, we demonstrate that depth channel and attribute-aware loss greatly improve the accuracy and robustness of face recognition.

3D Face Reconstruction with Geometry Details from a Single Image

3D face reconstruction from a single image is a classical and challenging problem, with wide applications in many areas. Inspired by recent works in face animation from RGB-D or monocular video inputs, we develop a novel method for reconstructing 3D faces from unconstrained 2D images, using a coarse-to-fine optimization strategy. First, a smooth coarse 3D face is generated from an example-based bilinear face model, by aligning the projection of 3D face landmarks with 2D landmarks detected from the input image. Afterwards, using local corrective deformation fields, the coarse 3D face is refined using photometric consistency constraints, resulting in a medium face shape. Finally, a shape-from-shading method is applied on the medium face to recover fine geometric details. Our method outperforms state-of-the-art approaches in terms of accuracy and detail recovery, which is demonstrated in extensive experiments using real world models and publicly available datasets.

Fast K-Means Clustering with Anderson Acceleration

We propose a novel method to accelerate Lloyd's algorithm for K-Means clustering. Unlike previous acceleration approaches that reduce computational cost per iterations or improve initialization, our approach is focused on reducing the number of iterations required for convergence. This is achieved by treating the assignment step and the update step of Lloyd's algorithm as a fixed-point iteration, and applying Anderson acceleration, a well-established technique for accelerating fixed-point solvers. Classical Anderson acceleration utilizes m previous iterates to find an accelerated iterate, and its performance on K-Means clustering can be sensitive to choice of m and the distribution of samples. We propose a new strategy to dynamically adjust the value of m, which achieves robust and consistent speedups across different problem instances. Our method complements existing acceleration techniques, and can be combined with them to achieve state-of-the-art performance. We perform extensive experiments to evaluate the performance of the proposed method, where it outperforms other algorithms in 106 out of 120 test cases, and the mean decrease ratio of computational time is more than 33%.

Deep Face Feature for Face Alignment

In this paper, we present a deep learning based image feature extraction method designed specifically for face images. To train the feature extraction model, we construct a large scale photo-realistic face image dataset with ground-truth correspondence between multi-view face images, which are synthesized from real photographs via an inverse rendering procedure. The deep face feature (DFF) is trained using correspondence between face images rendered from different views. Using the trained DFF model, we can extract a feature vector for each pixel of a face image, which distinguishes different facial regions and is shown to be more effective than general-purpose feature descriptors for face-related tasks such as matching and alignment. Based on the DFF, we develop a robust face alignment method, which iteratively updates landmarks, pose and 3D shape. Extensive experiments demonstrate that our method can achieve state-of-the-art results for face alignment under highly unconstrained face images.