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Topological simplification is the process of reducing complexity of a function while maintaining its essential features. Its goal is to find a new filter function, which reorders cells of the input complex in a way which eliminates some…

Additive models can be used for interpretable machine learning for their clarity and simplicity. However, In the classical models for high-order data, the vectorization operation disrupts the data structure, which may lead to degenerated…

While conventional computer vision emphasizes pixel-level and feature-based objectives, medical image analysis of intricate biological structures necessitates explicit representation of their complex topological properties. Despite their…

Data augmentation aims to generate new and synthetic features from the original data, which can identify a better representation of data and improve the performance and generalizability of downstream tasks. However, data augmentation for…

In this paper, we present new incremental algorithms for maintaining data structures that represent all connectivity cuts of size one in directed graphs (digraphs), and the strongly connected components that result by the removal of each of…

Despite topology optimization producing high-performance structures, late-stage localized revisions remain brittle: direct density-space edits (e.g., warping pixels, inserting holes, swapping infill) can sever load paths and sharply degrade…

Tomography is a widely used tool for analyzing microstructures in three dimensions (3D). The analysis, however, faces difficulty because the constituent materials produce similar grey-scale values. Sometimes, this prompts the image…

The transformer architecture has shown remarkable success in various domains, such as natural language processing and computer vision. When it comes to graph learning, transformers are required not only to capture the interactions between…

We propose a novel data augmentation method `GridMask' in this paper. It utilizes information removal to achieve state-of-the-art results in a variety of computer vision tasks. We analyze the requirement of information dropping. Then we…

We propose to employ scale spaces of mathematical morphology to hierarchically simplify fracture surfaces of complementarity fitting archaeological fragments. This representation preserves complementarity and is insensitive to different…

In medical image analysis, feature engineering plays an important role in the design and performance of machine learning models. Persistent homology (PH), from the field of topological data analysis (TDA), demonstrates robustness and…

Cross-graph node classification, utilizing the abundant labeled nodes from one graph to help classify unlabeled nodes in another graph, can be viewed as a domain generalization problem of graph neural networks (GNNs) due to the structure…

Mapping is an essential task for mobile robots and topological representation often works as a basis for the various applications. In this paper, a novel framework that can build topological maps incrementally is proposed. The algorithm is…

In this paper, we investigate the problem of Semantic Segmentation for agricultural aerial imagery. We observe that the existing methods used for this task are designed without considering two characteristics of the aerial data: (i) the…

In spacetime dimensions of 4 (i.e., 3+1) and higher, topological orders exhibit spatially extended excitations like loops and membranes, which support diverse topological data characterizing braiding, fusion, and shrinking processes,…

Vision-language models have shown strong performance, but they often generalize poorly to specialized domains. While semi-supervised vision-language learning mitigates this limitation by leveraging a small set of labeled image-text pairs…

We consider ad-hoc networks consisting of $n$ wireless nodes that are located on the plane. Any two given nodes are called neighbors if they are located within a certain distance (communication range) from one another. A given node can be…

In this paper, we introduce a novel parametric method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford-Shah and the Chan-Vese functionals and perform a region-based segmentation of 3D…

The ability to dynamically extend a model to new data and classes is critical for multiple organ and tumor segmentation. However, due to privacy regulations, accessing previous data and annotations can be problematic in the medical domain.…

Data augmentation (DA) is an essential technique for training state-of-the-art deep learning systems. In this paper, we empirically show data augmentation might introduce noisy augmented examples and consequently hurt the performance on…