TTVD: Towards a Geometric Framework for Test-Time Adaptation Based on Voronoi Diagram

Deep learning models often struggle with generalization when deploying on real-world data, due to the common distributional shift to the training data. Test-time adaptation (TTA) is an emerging scheme used at inference time to address this issue. In TTA, models are adapted online at the same time when making predictions to test data. Neighbor-based approaches have gained attention recently, where prototype embeddings provide location information to alleviate the feature shift between training and testing data. However, due to their inherit limitation of simplicity, they often struggle to learn useful patterns and encounter performance degradation. To confront this challenge, we study the TTA problem from a geometric point of view. We first reveal that the underlying structure of neighbor-based methods aligns with the Voronoi Diagram, a classical computational geometry model for space partitioning. Building on this observation, we propose the Test-Time adjustment by Voronoi Diagram guidance (TTVD), a novel framework that leverages the benefits of this geometric property. Specifically, we explore two key structures: 1) Cluster-induced Voronoi Diagram (CIVD): This integrates the joint contribution of self-supervision and entropy-based methods to provide richer information. 2) Power Diagram (PD): A generalized version of the Voronoi Diagram that refines partitions by assigning weights to each Voronoi cell. Our experiments under rigid, peer-reviewed settings on CIFAR-10-C, CIFAR-100-C, ImageNet-C, and ImageNet-R shows that TTVD achieves remarkable improvements compared to state-of-the-art methods. Moreover, extensive experimental results also explore the effects of batch size and class imbalance, which are two scenarios commonly encountered in real-world applications. These analyses further validate the robustness and adaptability of our proposed framework.

Continual Domain Adversarial Adaptation via Double-Head Discriminators

Domain adversarial adaptation in a continual setting poses a significant challenge due to the limitations on accessing previous source domain data. Despite extensive research in continual learning, the task of adversarial adaptation cannot be effectively accomplished using only a small number of stored source domain data, which is a standard setting in memory replay approaches. This limitation arises from the erroneous empirical estimation of $\gH$-divergence with few source domain samples. To tackle this problem, we propose a double-head discriminator algorithm, by introducing an addition source-only domain discriminator that are trained solely on source learning phase. We prove that with the introduction of a pre-trained source-only domain discriminator, the empirical estimation error of $\gH$-divergence related adversarial loss is reduced from the source domain side. Further experiments on existing domain adaptation benchmark show that our proposed algorithm achieves more than 2$\%$ improvement on all categories of target domain adaptation task while significantly mitigating the forgetting on source domain.

Progressive Voronoi Diagram Subdivision: Towards A Holistic Geometric Framework for Exemplar-free Class-Incremental Learning

Exemplar-free Class-incremental Learning (CIL) is a challenging problem because rehearsing data from previous phases is strictly prohibited, causing catastrophic forgetting of Deep Neural Networks (DNNs). In this paper, we present iVoro, a holistic framework for CIL, derived from computational geometry. We found Voronoi Diagram (VD), a classical model for space subdivision, is especially powerful for solving the CIL problem, because VD itself can be constructed favorably in an incremental manner -- the newly added sites (classes) will only affect the proximate classes, making the non-contiguous classes hardly forgettable. Further, in order to find a better set of centers for VD construction, we colligate DNN with VD using Power Diagram and show that the VD structure can be optimized by integrating local DNN models using a divide-and-conquer algorithm. Moreover, our VD construction is not restricted to the deep feature space, but is also applicable to multiple intermediate feature spaces, promoting VD to be multi-centered VD (CIVD) that efficiently captures multi-grained features from DNN. Importantly, iVoro is also capable of handling uncertainty-aware test-time Voronoi cell assignment and has exhibited high correlations between geometric uncertainty and predictive accuracy (up to ~0.9). Putting everything together, iVoro achieves up to 25.26%, 37.09%, and 33.21% improvements on CIFAR-100, TinyImageNet, and ImageNet-Subset, respectively, compared to the state-of-the-art non-exemplar CIL approaches. In conclusion, iVoro enables highly accurate, privacy-preserving, and geometrically interpretable CIL that is particularly useful when cross-phase data sharing is forbidden, e.g. in medical applications. Our code is available at https://machunwei.github.io/ivoro.

A Bayesian Detect to Track System for Robust Visual Object Tracking and Semi-Supervised Model Learning

Object tracking is one of the fundamental problems in visual recognition tasks and has achieved significant improvements in recent years. The achievements often come with the price of enormous hardware consumption and expensive labor effort for consecutive labeling. A missing ingredient for robust tracking is achieving performance with minimal modification on network structure and semi-supervised learning intermittent labeled frames. In this paper, we ad-dress these problems in a Bayesian tracking and detection framework parameterized by neural network outputs. In our framework, the tracking and detection process is formulated in a probabilistic way as multi-objects dynamics and network detection uncertainties. With our formulation, we propose a particle filter-based approximate sampling algorithm for tracking object state estimation. Based on our particle filter inference algorithm, a semi-supervised learn-ing algorithm is utilized for learning tracking network on intermittent labeled frames by variational inference. In our experiments, we provide both mAP and probability-based detection measurements for comparison between our algorithm with non-Bayesian solutions. We also train a semi-supervised tracking network on M2Cai16-Tool-Locations Dataset and compare our results with supervised learning on fully labeled frames.

Few-shot Learning as Cluster-induced Voronoi Diagrams: A Geometric Approach

Few-shot learning (FSL) is the process of rapid generalization from abundant base samples to inadequate novel samples. Despite extensive research in recent years, FSL is still not yet able to generate satisfactory solutions for a wide range of real-world applications. To confront this challenge, we study the FSL problem from a geometric point of view in this paper. One observation is that the widely embraced ProtoNet model is essentially a Voronoi Diagram (VD) in the feature space. We retrofit it by making use of a recent advance in computational geometry called Cluster-induced Voronoi Diagram (CIVD). Starting from the simplest nearest neighbor model, CIVD gradually incorporates cluster-to-point and then cluster-to-cluster relationships for space subdivision, which is used to improve the accuracy and robustness at multiple stages of FSL. Specifically, we use CIVD (1) to integrate parametric and nonparametric few-shot classifiers; (2) to combine feature representation and surrogate representation; (3) and to leverage feature-level, transformation-level, and geometry-level heterogeneities for a better ensemble. Our CIVD-based workflow enables us to achieve new state-of-the-art results on mini-ImageNet, CUB, and tiered-ImagenNet datasets, with ${\sim}2\%{-}5\%$ improvements upon the next best. To summarize, CIVD provides a mathematically elegant and geometrically interpretable framework that compensates for extreme data insufficiency, prevents overfitting, and allows for fast geometric ensemble for thousands of individual VD. These together make FSL stronger.

Improving Uncertainty Calibration of Deep Neural Networks via Truth Discovery and Geometric Optimization

Deep Neural Networks (DNNs), despite their tremendous success in recent years, could still cast doubts on their predictions due to the intrinsic uncertainty associated with their learning process. Ensemble techniques and post-hoc calibrations are two types of approaches that have individually shown promise in improving the uncertainty calibration of DNNs. However, the synergistic effect of the two types of methods has not been well explored. In this paper, we propose a truth discovery framework to integrate ensemble-based and post-hoc calibration methods. Using the geometric variance of the ensemble candidates as a good indicator for sample uncertainty, we design an accuracy-preserving truth estimator with provably no accuracy drop. Furthermore, we show that post-hoc calibration can also be enhanced by truth discovery-regularized optimization. On large-scale datasets including CIFAR and ImageNet, our method shows consistent improvement against state-of-the-art calibration approaches on both histogram-based and kernel density-based evaluation metrics. Our codes are available at https://github.com/horsepurve/truly-uncertain.

Scribble-based Hierarchical Weakly Supervised Learning for Brain Tumor Segmentation

The recent state-of-the-art deep learning methods have significantly improved brain tumor segmentation. However, fully supervised training requires a large amount of manually labeled masks, which is highly time-consuming and needs domain expertise. Weakly supervised learning with scribbles provides a good trade-off between model accuracy and the effort of manual labeling. However, for segmenting the hierarchical brain tumor structures, manually labeling scribbles for each substructure could still be demanding. In this paper, we use only two kinds of weak labels, i.e., scribbles on whole tumor and healthy brain tissue, and global labels for the presence of each substructure, to train a deep learning model to segment all the sub-regions. Specifically, we train two networks in two phases: first, we only use whole tumor scribbles to train a whole tumor (WT) segmentation network, which roughly recovers the WT mask of training data; then we cluster the WT region with the guide of global labels. The rough substructure segmentation from clustering is used as weak labels to train the second network. The dense CRF loss is used to refine the weakly supervised segmentation. We evaluate our approach on the BraTS2017 dataset and achieve competitive WT dice score as well as comparable scores on substructure segmentation compared to an upper bound when trained with fully annotated masks.

Neural Style Transfer Improves 3D Cardiovascular MR Image Segmentation on Inconsistent Data

Three-dimensional medical image segmentation is one of the most important problems in medical image analysis and plays a key role in downstream diagnosis and treatment. Recent years, deep neural networks have made groundbreaking success in medical image segmentation problem. However, due to the high variance in instrumental parameters, experimental protocols, and subject appearances, the generalization of deep learning models is often hindered by the inconsistency in medical images generated by different machines and hospitals. In this work, we present StyleSegor, an efficient and easy-to-use strategy to alleviate this inconsistency issue. Specifically, neural style transfer algorithm is applied to unlabeled data in order to minimize the differences in image properties including brightness, contrast, texture, etc. between the labeled and unlabeled data. We also apply probabilistic adjustment on the network output and integrate multiple predictions through ensemble learning. On a publicly available whole heart segmentation benchmarking dataset from MICCAI HVSMR 2016 challenge, we have demonstrated an elevated dice accuracy surpassing current state-of-the-art method and notably, an improvement of the total score by 29.91\%. StyleSegor is thus corroborated to be an accurate tool for 3D whole heart segmentation especially on highly inconsistent data, and is available at https://github.com/horsepurve/StyleSegor.