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3D reconstruction of deformable (or non-rigid) scenes from a set of monocular 2D image observations is a long-standing and actively researched area of computer vision and graphics. It is an ill-posed inverse problem, since--without additional prior assumptions--it permits infinitely many solutions leading to accurate projection to the input 2D images. Non-rigid reconstruction is a foundational building block for downstream applications like robotics, AR/VR, or visual content creation. The key advantage of using monocular cameras is their omnipresence and availability to the end users as well as their ease of use compared to more sophisticated camera set-ups such as stereo or multi-view systems. This survey focuses on state-of-the-art methods for dense non-rigid 3D reconstruction of various deformable objects and composite scenes from monocular videos or sets of monocular views. It reviews the fundamentals of 3D reconstruction and deformation modeling from 2D image observations. We then start from general methods--that handle arbitrary scenes and make only a few prior assumptions--and proceed towards techniques making stronger assumptions about the observed objects and types of deformations (e.g. human faces, bodies, hands, and animals). A significant part of this STAR is also devoted to classification and a high-level comparison of the methods, as well as an overview of the datasets for training and evaluation of the discussed techniques. We conclude by discussing open challenges in the field and the social aspects associated with the usage of the reviewed methods.

In this paper, a convolution sparse coding method based on global structure characteristics and spectral correlation is proposed for the reconstruction of compressive spectral images. The proposed method uses the convolution kernel to operate the global image, which can better preserve image structure information in the spatial dimension. To take full exploration of the constraints between spectra, the coefficients corresponding to the convolution kernel are constrained by the norm to improve spectral accuracy. And, to solve the problem that convolutional sparse coding is insensitive to low frequency, the global total-variation (TV) constraint is added to estimate the low-frequency components. It not only ensures the effective estimation of the low-frequency but also transforms the convolutional sparse coding into a de-noising process, which makes the reconstructing process simpler. Simulations show that compared with the current mainstream optimization methods (DeSCI and Gap-TV), the proposed method improves the reconstruction quality by up to 7 dB in PSNR and 10% in SSIM, and has a great improvement in the details of the reconstructed image.

Neural network related methods, due to their unprecedented success in image processing, have emerged as a new set of tools in CT reconstruction with the potential to change the field. However, the lack of high-quality training data and theoretical guarantees, together with increasingly complicated network structures, make its implementation impractical. In this paper, we present a new framework (RBP-DIP) based on Deep Image Prior (DIP) and a special residual back projection (RBP) connection to tackle these challenges. Comparing to other pre-trained neural network related algorithms, the proposed framework is closer to an iterative reconstruction (IR) algorithm as it requires no training data or training process. In that case, the proposed framework can be altered (e.g, different hyperparameters and constraints) on demand, adapting to different conditions (e.g, different imaged objects, imaging instruments, and noise levels) without retraining. Experiments show that the proposed framework has significant improvements over other state-of-the-art conventional methods, as well as pre-trained and untrained models with similar network structures, especially under sparse-view, limited-angle, and low-dose conditions.

Detection of out-of-distribution samples is one of the critical tasks for real-world applications of computer vision. The advancement of deep learning has enabled us to analyze real-world data which contain unexplained samples, accentuating the need to detect out-of-distribution instances more than before. GAN-based approaches have been widely used to address this problem due to their ability to perform distribution fitting; however, they are accompanied by training instability and mode collapse. We propose a simple yet efficient reconstruction-based method that avoids adding complexities to compensate for the limitations of GAN models while outperforming them. Unlike previous reconstruction-based works that only utilize reconstruction error or generated samples, our proposed method simultaneously incorporates both of them in the detection task. Our model, which we call "Connective Novelty Detection" has two subnetworks, an autoencoder, and a binary classifier. The autoencoder learns the representation of the positive class by reconstructing them. Then, the model creates negative and connected positive examples using real and generated samples. Negative instances are generated via manipulating the real data, so their distribution is close to the positive class to achieve a more accurate boundary for the classifier. To boost the robustness of the detection to reconstruction error, connected positive samples are created by combining the real and generated samples. Finally, the binary classifier is trained using connected positive and negative examples. We demonstrate a considerable improvement in novelty detection over state-of-the-art methods on MNIST and Caltech-256 datasets.

The study of Markov processes and broadcasting on trees has deep connections to a variety of areas including statistical physics, graphical models, phylogenetic reconstruction, Markov Chain Monte Carlo, and community detection in random graphs. Notably, the celebrated Belief Propagation (BP) algorithm achieves Bayes-optimal performance for the reconstruction problem of predicting the value of the Markov process at the root of the tree from its values at the leaves. Recently, the analysis of low-degree polynomials has emerged as a valuable tool for predicting computational-to-statistical gaps. In this work, we investigate the performance of low-degree polynomials for the reconstruction problem on trees. Perhaps surprisingly, we show that there are simple tree models with $N$ leaves and bounded arity where (1) nontrivial reconstruction of the root value is possible with a simple polynomial time algorithm and with robustness to noise, but not with any polynomial of degree $N^{c}$ for $c > 0$ a constant depending only on the arity, and (2) when the tree is unknown and given multiple samples with correlated root assignments, nontrivial reconstruction of the root value is possible with a simple Statistical Query algorithm but not with any polynomial of degree $N^c$. These results clarify some of the limitations of low-degree polynomials vs. polynomial time algorithms for Bayesian estimation problems. They also complement recent work of Moitra, Mossel, and Sandon who studied the circuit complexity of Belief Propagation. As a consequence of our main result, we show that for some $c' > 0$ depending only on the arity, $\exp(N^{c'})$ many samples are needed for RBF kernel regression to obtain nontrivial correlation with the true regression function (BP). We pose related open questions about low-degree polynomials and the Kesten-Stigum threshold.

The use of low-resolution images adopting more relaxed acquisition conditions such as mobile phones and surveillance videos is becoming increasingly common in iris recognition nowadays. Concurrently, a great variety of single image super-resolution techniques are emerging, especially with the use of convolutional neural networks (CNNs). The main objective of these methods is to try to recover finer texture details generating more photo-realistic images based on the optimisation of an objective function depending basically on the CNN architecture and training approach. In this work, the authors explore single image super-resolution using CNNs for iris recognition. For this, they test different CNN architectures and use different training databases, validating their approach on a database of 1.872 near infrared iris images and on a mobile phone image database. They also use quality assessment, visual results and recognition experiments to verify if the photo-realism provided by the CNNs which have already proven to be effective for natural images can reflect in a better recognition rate for iris recognition. The results show that using deeper architectures trained with texture databases that provide a balance between edge preservation and the smoothness of the method can lead to good results in the iris recognition process.

High-resolution images are prevalent in various applications, such as autonomous driving and computer-aided diagnosis. However, training neural networks on such images is computationally challenging and easily leads to out-of-memory errors even on modern GPUs. We propose a simple method, Iterative Patch Selection (IPS), which decouples the memory usage from the input size and thus enables the processing of arbitrarily large images under tight hardware constraints. IPS achieves this by selecting only the most salient patches, which are then aggregated into a global representation for image recognition. For both patch selection and aggregation, a cross-attention based transformer is introduced, which exhibits a close connection to Multiple Instance Learning. Our method demonstrates strong performance and has wide applicability across different domains, training regimes and image sizes while using minimal accelerator memory. For example, we are able to finetune our model on whole-slide images consisting of up to 250k patches (>16 gigapixels) with only 5 GB of GPU VRAM at a batch size of 16.

Facial expression is one of the most external indications of a person's feelings and emotions. In daily conversation, according to the psychologist, only 7\% and 38\% of information is communicated through words and sounds respective, while up to 55\% is through facial expression. It plays an important role in coordinating interpersonal relationships. Ekman and Friesen recognized six essential emotions in the nineteenth century depending on a cross-cultural study, which indicated that people feel each basic emotion in the same fashion despite culture. As a branch of the field of analyzing sentiment, facial expression recognition offers broad application prospects in a variety of domains, including the interaction between humans and computers, healthcare, and behavior monitoring. Therefore, many researchers have devoted themselves to facial expression recognition. In this paper, an effective hybrid data augmentation method is used. This approach is operated on two public datasets, and four benchmark models see some remarkable results.

Electrical properties (EP), namely permittivity and electric conductivity, dictate the interactions between electromagnetic waves and biological tissue. EP can be potential biomarkers for pathology characterization, such as cancer, and improve therapeutic modalities, such radiofrequency hyperthermia and ablation. MR-based electrical properties tomography (MR-EPT) uses MR measurements to reconstruct the EP maps. Using the homogeneous Helmholtz equation, EP can be directly computed through calculations of second order spatial derivatives of the measured magnetic transmit or receive fields $(B_{1}^{+}, B_{1}^{-})$. However, the numerical approximation of derivatives leads to noise amplifications in the measurements and thus erroneous reconstructions. Recently, a noise-robust supervised learning-based method (DL-EPT) was introduced for EP reconstruction. However, the pattern-matching nature of such network does not allow it to generalize for new samples since the network's training is done on a limited number of simulated data. In this work, we leverage recent developments on physics-informed deep learning to solve the Helmholtz equation for the EP reconstruction. We develop deep neural network (NN) algorithms that are constrained by the Helmholtz equation to effectively de-noise the $B_{1}^{+}$ measurements and reconstruct EP directly at an arbitrarily high spatial resolution without requiring any known $B_{1}^{+}$ and EP distribution pairs.

Implicit neural 3D representation has achieved impressive results in surface or scene reconstruction and novel view synthesis, which typically uses the coordinate-based multi-layer perceptrons (MLPs) to learn a continuous scene representation. However, existing approaches, such as Neural Radiance Field (NeRF) and its variants, usually require dense input views (i.e. 50-150) to obtain decent results. To relive the over-dependence on massive calibrated images and enrich the coordinate-based feature representation, we explore injecting the prior information into the coordinate-based network and introduce a novel coordinate-based model, CoCo-INR, for implicit neural 3D representation. The cores of our method are two attention modules: codebook attention and coordinate attention. The former extracts the useful prototypes containing rich geometry and appearance information from the prior codebook, and the latter propagates such prior information into each coordinate and enriches its feature representation for a scene or object surface. With the help of the prior information, our method can render 3D views with more photo-realistic appearance and geometries than the current methods using fewer calibrated images available. Experiments on various scene reconstruction datasets, including DTU and BlendedMVS, and the full 3D head reconstruction dataset, H3DS, demonstrate the robustness under fewer input views and fine detail-preserving capability of our proposed method.