Self-attention mechanisms and non-local blocks have become crucial building blocks for state-of-the-art neural architectures thanks to their unparalleled ability in capturing long-range dependencies in the input. However their cost is quadratic with the number of spatial positions hence making their use impractical in many real case applications. In this work, we analyze these methods through a polynomial lens, and we show that self-attention can be seen as a special case of a 3 rd order polynomial. Within this polynomial framework, we are able to design polynomial operators capable of accessing the same data pattern of non-local and self-attention blocks while reducing the complexity from quadratic to linear. As a result, we propose two modules (Poly-NL and Poly-SA) that can be used as "drop-in" replacements for more-complex non-local and self-attention layers in state-of-the-art CNNs and ViT architectures. Our modules can achieve comparable, if not better, performance across a wide range of computer vision tasks while keeping a complexity equivalent to a standard linear layer.

Spatial self-attention layers, in the form of Non-Local blocks, introduce long-range dependencies in Convolutional Neural Networks by computing pairwise similarities among all possible positions. Such pairwise functions underpin the effectiveness of non-local layers, but also determine a complexity that scales quadratically with respect to the input size both in space and time. This is a severely limiting factor that practically hinders the applicability of non-local blocks to even moderately sized inputs. Previous works focused on reducing the complexity by modifying the underlying matrix operations, however in this work we aim to retain full expressiveness of non-local layers while keeping complexity linear. We overcome the efficiency limitation of non-local blocks by framing them as special cases of 3rd order polynomial functions. This fact enables us to formulate novel fast Non-Local blocks, capable of reducing the complexity from quadratic to linear with no loss in performance, by replacing any direct computation of pairwise similarities with element-wise multiplications. The proposed method, which we dub as "Poly-NL", is competitive with state-of-the-art performance across image recognition, instance segmentation, and face detection tasks, while having considerably less computational overhead.

Representation learning is a fundamental part of modern computer vision, where abstract representations of data are encoded as tensors optimized to solve problems like image segmentation and inpainting. Recently, self-attention in the form of Non-Local Block has emerged as a powerful technique to enrich features, by capturing complex interdependencies in feature tensors. However, standard self-attention approaches leverage only spatial relationships, drawing similarities between vectors and overlooking correlations between channels. In this paper, we introduce a new method, called Tensor Element Self-Attention (TESA) that generalizes such work to capture interdependencies along all dimensions of the tensor using matricization. An order R tensor produces R results, one for each dimension. The results are then fused to produce an enriched output which encapsulates similarity among tensor elements. Additionally, we analyze self-attention mathematically, providing new perspectives on how it adjusts the singular values of the input feature tensor. With these new insights, we present experimental results demonstrating how TESA can benefit diverse problems including classification and instance segmentation. By simply adding a TESA module to existing networks, we substantially improve competitive baselines and set new state-of-the-art results for image inpainting on Celeb and low light raw-to-rgb image translation on SID.

Discriminative classification models have been successfully applied for various computer vision tasks such as object and face detection and recognition. However, deformations can change objects coordinate space and perturb robust similarity measurement, which is the essence of all classification algorithms. The common approach to deal with deformations is either to seek for deformation invariant features or to develop models that describe objects deformations. However, the former approach requires a huge amount of data and a good amount of engineering to be properly trained, while the latter require considerable human effort in the form of carefully annotated data. In this paper, we propose a method that jointly learns with minimal human intervention a generative deformable model using only a simple shape model of the object and images automatically downloaded from the Internet, and also extracts features appropriate for classification. The proposed algorithm is applied on various classification problems such as “in-thewild” face recognition, gender classification and eye glasses detection on data retrieved by querying into a web image search engine. We demonstrate that not only it outperforms other automatic methods by large margins, but also performs comparably with supervised methods trained on thousands of manually annotated data.

This work introduces a novel Convolutional Network architecture (ConvNet) for the task of human pose estimation, that is the localization of body joints in a single static image. The proposed coarse to fine architecture addresses shortcomings of the baseline architecture that stem from the fact that large inaccuracies of its coarse ConvNet cannot becorrected by the refinement ConvNet that refines the estimation with in small windows of the coarse prediction. This is achieved by (a) changes in architectural parameters that both increase the accuracy of the coarse model and make the refinement model more capable of correcting the errors of the coarse model, (b) the introduction of a Markov Random Field (MRF)-based spatial model network between the coarse and the refinement model that introduces geometric constraints and (c) a training scheme that adapts the data augmentation and the learning rate according to the difficulty of the data examples. The proposed architecture is trained in an end-to-end fashion. Experimental results show that the proposed method improves the baseline model and provides state of the art results on the FashionPose[8] and MPII benchmarks [1].

This work introduces a novel Convolutional Network architecture (ConvNet) for the task of human pose estimation, that is the localization of body joints in a single static image. We propose a coarse to fine architecture that addresses shortcomings of the baseline architecture in [26] that stem from the fact that large inaccuracies of its coarse ConvNet cannot be corrected by the refinement ConvNet that refines the estimation within small windows of the coarse prediction. We overcome this by introducing a Markov Random Field (MRF)-based spatial model network between the coarse and the refinement model that introduces geometric constraints on the relative locations of the body joints. We propose an architecture in which a) the filters that implement the message passing in the MRF inference are factored in a way that constrains them by a low dimensional pose manifold the projection to which is estimated by a separate branch of the proposed ConvNet and b) the strengths of the pairwise joint constraints are modeled by weights that are jointly estimated by the other parameters of the network. The proposed network is trained in an end-to-end fashion. Experimental results show that the proposed method improves the baseline model and provides state of the art results on very challenging benchmarks.

This paper presents a novel approach for estimating 3D head pose in single-view video sequences acquired by an uncalibrated camera. Following the initialization by a face detector, a tracking technique localizes the faces in each frame in the video sequence. Head pose estimation is performed by using a structure from motion and self-calibration technique in a sequential way. The proposed method was applied to the IDIAP database that contains head pose ground truth data. The obtained results demonstrate that the method can estimate the head pose with satisfying accuracy.

This paper introduces, a virtual teeth drilling system named virtual dental patient designed to aid dentists in getting acquainted with the teeth anatomy, the handling of drilling instruments and the challenges associated with the drilling procedure. The basic aim of the system is to be used for the training of dental students. The application features a 3D model of the face and the oral cavity that can be adapted to the characteristics of a specific person and animated. Drilling using a haptic device is performed on realistic teeth models (constructed from real data), within the oral cavity. Results and intermediate steps of the drilling procedure can be saved for future use