Deep latent variable models (DLVMs) are designed to learn meaningful representations in an unsupervised manner, such that the hidden explanatory factors are interpretable by independent latent variables (aka disentanglement). The variational autoencoder (VAE) [1], [2] is a popular DLVM widely studied in disentanglement analysis due to the modeling of the posterior distribution using a factorized Gaussian distribution [3] that encourages the alignment of the latent factors with the latent axes. Several metrics have been proposed recently, assuming that the latent variables explaining the variation in data are aligned with the latent axes (cardinal directions). However, there are other DLVMs, such as the AAE and WAE-MMD (matching the aggregate posterior to the prior), where the latent variables might not be aligned with the latent axes. In this work, we propose a statistical method to evaluate disentanglement for any DLVMs in general. The proposed technique discovers the latent vectors representing the generative factors of a dataset that can be different from the cardinal latent axes. We empirically demonstrate the advantage of the method on two datasets.

The variational autoencoder (VAE) [19], [41] is a popular, deep, latent-variable model (DLVM) due to its simple yet effective formulation for modeling the data distribution. Moreover, optimizing the VAE objective function is more manageable than other DLVMs. The bottleneck dimension of the VAE is a crucial design choice, and it has strong ramifications for the model's performance, such as finding the hidden explanatory factors of a dataset using the representations learned by the VAE. However, the size of the latent dimension of the VAE is often treated as a hyperparameter estimated empirically through trial and error. To this end, we propose a statistical formulation to discover the relevant latent factors required for modeling a dataset. In this work, we use a hierarchical prior in the latent space that estimates the variance of the latent axes using the encoded data, which identifies the relevant latent dimensions. For this, we replace the fixed prior in the VAE objective function with a hierarchical prior, keeping the remainder of the formulation unchanged. We call the proposed method the automatic relevancy detection in the variational autoencoder (ARD-VAE)11https://github.com/Surojit-Utah/ARD-VAE. We demonstrate the efficacy of the ARD-VAE on multiple benchmark datasets in finding the relevant latent dimensions and their effect on different evaluation metrics, such as FID score and disentanglement analysis.

Automated interpretation of seismic images using deep learning methods is challenging because of the limited availability of training data. Few-shot learning is a suitable learning paradigm in such scenarios due to its ability to adapt to a new task with limited supervision (small training budget). Existing few-shot semantic segmentation (FSSS) methods fix the number of target classes. Therefore, they do not support joint training on multiple datasets varying in the number of classes. In the context of the interpretation of seismic facies, fixing the number of target classes inhibits the generalization capability of a model trained on one facies dataset to another, which is likely to have a different number of facies. To address this shortcoming, we propose a few-shot semantic segmentation method for interpreting seismic facies that can adapt to the varying number of facies across the dataset, dubbed theAdaSemSeg. In general, the backbone network of FSSS methods is initialized with the statistics learned from the ImageNet dataset for better performance. The lack of such a huge annotated dataset for seismic images motivates using a self-supervised algorithm on seismic datasets to initialize the backbone network. We have trained the AdaSemSeg on three public seismic facies datasets with different numbers of facies and evaluated the proposed method on multiple metrics. The performance of the AdaSemSeg on unseen datasets (not used in training) is better than the prototype-based few-shot method and baselines. Code is available at https://github.com/Surojit-Utah/AdaSemSeg.

This paper proposes multi-task learning as a regularization method for segmentation tasks in seismic images. We examine application-specific auxiliary tasks, such as the estimation/detection of horizons, dip angle, and amplitude that geophysicists consider relevant for identification of channels (a geological feature), which is currently done through painstaking outlining by qualified experts. We show that multi-task training helps in better generalization on test datasets with very similar and different structure/statistics. In such settings, we also show that multi-task learning performs better on unseen datasets relative to the baseline.

3D scan registration is a classical, yet a highly useful problem in the context of 3D sensors such as Kinect and Velodyne. While there are several existing methods, the techniques are usually incremental where adjacent scans are registered first to obtain the initial poses, followed by motion averaging and bundle-adjustment refinement. In this paper, we take a different approach and develop minimal solvers for jointly computing the initial poses of cameras in small loops such as 3-, 4-, and 5-cycles. Note that the classical registration of 2 scans can be done using a minimum of 3 point matches to compute 6 degrees of relative motion. On the other hand, to jointly compute the 3D registrations in n-cycles, we take 2 point matches between the first n-1 consecutive pairs (i.e., Scan 1 & Scan 2, ... , and Scan n-1 & Scan n) and 1 or 2 point matches between Scan 1 and Scan n. Overall, we use 5, 7, and 10 point matches for 3-, 4-, and 5-cycles, and recover 12, 18, and 24 degrees of transformation variables, respectively. Using simulations and real-data we show that the 3D registration using mini n-cycles are computationally efficient, and can provide alternate and better initial poses compared to standard pairwise methods.