Related papers: Efficient computation of topological integral tran…
Euler's elastica constitute an appealing variational image inpainting model. It minimises an energy that involves the total variation as well as the level line curvature. These components are transparent and make it attractive for shape…
Accurate classification of computed tomography (CT) images is essential for diagnosis and treatment planning, but existing methods often struggle with the subtle and spatially diverse nature of pathological features. Current approaches…
We introduce a novel class of explicit feature maps based on topological indices that represent each graph by a compact feature vector, enabling fast and interpretable graph classification. Using radial basis function kernels on these…
Many adaptations of transformers have emerged to address the single-modal vision tasks, where self-attention modules are stacked to handle input sources like images. Intuitively, feeding multiple modalities of data to vision transformers…
Multiple instance learning (MIL) is a powerful tool to solve the weakly supervised classification in whole slide image (WSI) based pathology diagnosis. However, the current MIL methods are usually based on independent and identical…
Real-world clinical data is inherently multimodal, providing complementary evidence that mirrors the practical necessity of jointly assessing multiple related outcomes. Although multi-task learning can improve efficiency by sharing…
The use of topology for visualisation applications has become increasingly popular due to its ability to summarise data at a high level. Criticalities in scalar field data are used by visualisation methods such as the Reeb graph and contour…
The published literature on topology optimization has exploded over the last two decades to include methods that use shape and topological derivatives or evolutionary algorithms formulated on various geometric representations and…
Computing topological invariants of 3-manifolds is generally intractable, yet specialized algebraic structures can enable efficient algorithms. For Witten-Reshetikhin-Turaev (WRT) invariants of torus bundles, we exploit the non-commutative…
We provide a new approach for computing integrals over hypersurfaces in the level set framework. The method is based on the discretization (via simple Riemann sums) of the classical formulation used in the level set framework, with the…
Implicit neural representations (INRs), which leverage neural networks to represent signals by mapping coordinates to their corresponding attributes, have garnered significant attention. They are extensively utilized for image…
Efficient algorithms for computing linear convolutions based on the fast Fourier transform are developed. A hybrid approach is described that combines the conventional practice of explicit dealiasing (explicitly padding the input data with…
Classical unsupervised learning methods like clustering and linear dimensionality reduction parametrize large-scale geometry when it is discrete or linear, while more modern methods from manifold learning find low dimensional representation…
The Euler Characteristic Transform (ECT) is an efficiently-computable geometrical-topological invariant that characterizes the global shape of data. In this paper, we introduce the Local Euler Characteristic Transform ($\ell$-ECT), a novel…
Optimization-based solvers play a central role in a wide range of signal processing and communication tasks. However, their applicability in latency-sensitive systems is limited by the sequential nature of iterative methods and the high…
This paper introduces an adaptive convolutional neural network (CNN) architecture capable of automating various topology optimization (TO) problems with diverse underlying physics. The proposed architecture has an encoder-decoder-type…
We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic…
Mathematical morphology is a theory and technique to collect features like geometric and topological structures in digital images. Given a target image, determining suitable morphological operations and structuring elements is a cumbersome…
Mapping complex input data into suitable lower dimensional manifolds is a common procedure in machine learning. This step is beneficial mainly for two reasons: (1) it reduces the data dimensionality and (2) it provides a new data…
Elliptic curves have a well-known and explicit theory for the construction and application of endomorphisms, which can be applied to improve performance in scalar multiplication. Recent work has extended these techniques to hyperelliptic…