We propose the Canonical 3D Deformer Map, a new representation of the 3D shape of common object categories that can be learned from a collection of 2D images of independent objects. Our method builds in a novel way on concepts from parametric deformation models, non-parametric 3D reconstruction, and canonical embeddings, combining their individual advantages. In particular, it learns to associate each image pixel with a deformation model of the corresponding 3D object point which is canonical, i.e. intrinsic to the identity of the point and shared across objects of the category. The result is a method that, given only sparse 2D supervision at training time, can, at test time, reconstruct the 3D shape and texture of objects from single views, while establishing meaningful dense correspondences between object instances. It also achieves state-of-the-art results in dense 3D reconstruction on public in-the-wild datasets of faces, cars, and birds.

This is true -- CMR did not backprop on texture loss. However this CVPR'20 work from Henderson et al. shows that you can https://arxiv.org/abs/2004.04180. This paper may not have been known to the authors (CVPR happened around the NeurIPS deadline), so I'm fine if they correct and discuss this point in the main paper. To me, it seems that these are the main differences between CMR, CSM, and the proposed approach: (i) CMR is akin to a direct method - backpropagation through the texture results in a photometric-like loss (it's not quite a photometric loss since a perceptual loss is used instead, but it's close enough); (ii) CSM learns to establish correspondences from image pixels to a fixed shape template that does not adapt to the depicted shape (their articulated-CSM follow-up CVPR 2020 paper allows the template to deform, but the shape deforms based on a semi-manually defined skeleton, which does not have the capacity to capture surface details); (iii) the proposed approach learns to establish correspondences from image pixels to the parameterized surface of a (C3DPO) shape basis that then deforms to the depicted shape. In the classical debate of direct versus correspondence methods, I view the proposed method as belonging to the latter camp. My hypothesis is, similar to how correspondence methods played out in the late 90s and 2000s, the proposed approach may be less susceptible to local minima than direct methods during shape-fitting optimization. But I think there's room to investigate this issue more fully, which may be outside the scope of this paper. Although I think (iii) is still a hybrid of CMR and CSM (but still with known keypoints). With that said, I'm changing my mind on this, I find this combination a reasonable idea.

How much of the improvement is coming from the implicit shape representation over meshes? The proposed approach of combining local and global information via CSM's consistency loss could have been done with meshes (CSM was mesh based). What does the result look like with meshes? Or CMR could have also used this implicit shape representation. This key ablative study is missing.

Relation to Prior Work: The paper is missing references to and comparisons with important related works on adversarial examples for nearest neighbors and other non-parametric methods. For example, [1] provides a direct convergence rate for robustness of nearest neighbors to adversarial examples; it would be good to discuss how the bounds in this paper are different. Similarly, the convex program proposed by this paper feels similar to [5] as well as [2]; it would be good to discuss the relationship between these works.

We propose the Canonical 3D Deformer Map, a new representation of the 3D shape of common object categories that can be learned from a collection of 2D images of independent objects. Our method builds in a novel way on concepts from parametric deformation models, non-parametric 3D reconstruction, and canonical embeddings, combining their individual advantages. In particular, it learns to associate each image pixel with a deformation model of the corresponding 3D object point which is canonical, i.e. intrinsic to the identity of the point and shared across objects of the category. The result is a method that, given only sparse 2D supervision at training time, can, at test time, reconstruct the 3D shape and texture of objects from single views, while establishing meaningful dense correspondences between object instances. It also achieves state-of-the-art results in dense 3D reconstruction on public in-the-wild datasets of faces, cars, and birds.

Local intrinsic dimension (LID) estimation methods have received a lot of attention in recent years thanks to the progress in deep neural networks and generative modeling. In opposition to old non-parametric methods, new methods use generative models to approximate diffused dataset density and scale the methods to high-dimensional datasets like images. In this paper, we investigate the recent state-of-the-art parametric LID estimation methods from the perspective of the Wiener process. We explore how these methods behave when their assumptions are not met. We give an extended mathematical description of those methods and their error as a function of the probability density of the data.

Graph clustering algorithms with autoencoder structures have recently gained popularity due to their efficient performance and low training cost. However, for existing graph autoencoder clustering algorithms based on GCN or GAT, not only do they lack good generalization ability, but also the number of clusters clustered by such autoencoder models is difficult to determine automatically. To solve this problem, we propose a new framework called Graph Clustering with Masked Autoencoders (GCMA). It employs our designed fusion autoencoder based on the graph masking method for the fusion coding of graph. It introduces our improved density-based clustering algorithm as a second decoder while decoding with multi-target reconstruction. By decoding the mask embedding, our model can capture more generalized and comprehensive knowledge. The number of clusters and clustering results can be output end-to-end while improving the generalization ability. As a nonparametric class method, extensive experiments demonstrate the superiority of \textit{GCMA} over state-of-the-art baselines.

Supervised learning is a type of machine learning where an algorithm is trained on a labeled dataset. In supervised learning, the algorithm is provided with input-output pairs, and it learns to predict the output for new inputs. The goal of supervised learning is to train the algorithm to generalize to new inputs and outputs beyond the training data. Supervised learning is often used in applications where there is a well-defined output variable, such as predicting stock prices, diagnosing diseases, or recognizing objects in images. It is an effective technique for solving a wide range of problems, including regression and classification tasks.

Evaluating the efficiency of organizations and branches within an organization is a challenging issue for managers. Evaluation criteria allow organizations to rank their internal units, identify their position concerning their competitors, and implement strategies for improvement and development purposes. Among the methods that have been applied in the evaluation of bank branches, non-parametric methods have captured the attention of researchers in recent years. One of the most widely used non-parametric methods is the data envelopment analysis (DEA) which leads to promising results. However, the static DEA approaches do not consider the time in the model. Therefore, this paper uses a dynamic DEA (DDEA) method to evaluate the branches of a private Iranian bank over three years (2017-2019). The results are then compared with static DEA. After ranking the branches, they are clustered using the K-means method. Finally, a comprehensive sensitivity analysis approach is introduced to help the managers to decide about changing variables to shift a branch from one cluster to a more efficient one.

Within the rail industry, anything which helps keep trains moving, avoiding operational delays and improves customer experience, is worth pursuing. Many OEMs are now investing significant resources into one of the most valuable and potentially rewarding currencies in business: Big Data. In rail, and specifically when it comes to rolling stock maintenance, big data is synonymous with Condition Based Maintenance (CBM) and Predictive Maintenance (PM). Thanks to the rapidly expanding scale of manufacturing and asset maintenance industries, they are now adapting to the wider applications of advanced algorithms on consumer generated big data. Though CBM and PM are commonly adopted practices in rail industry, the scope of CBM is far wider than that of PM.