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A tangent category is a categorical abstraction of the tangent bundle construction for smooth manifolds. In that context, Cockett and Cruttwell develop the notion of differential bundle which, by work of MacAdam, generalizes the notion of…

We develop an alternative view on the concept of connections over a vector bundle map, which consists of a horizontal lift procedure to a prolonged bundle. We further focus on prolongations to an affine bundle and introduce the concept of…

The paper glosses different forms of an introducing of higher order tangent-like functors, especially functors derived from higher order nonholonomic tangent functors. A special attention is devoted to higher order osculating bundles: their…

We propose a new notion of the formal tangent space to the Wasserstein space $\mathcal{P}(X)$ at a given measure. Modulo an integrability condition, we say that this tangent space is made of functions over $X$ which are valued in the…

Object Navigation (ObjectNav) has made great progress with large language models (LLMs), but still faces challenges in memory management, especially in long-horizon tasks and dynamic scenes. To address this, we propose TopoNav, a new…

Traditional learning from demonstration (LfD) generally demands a cumbersome collection of physical demonstrations, which can be time-consuming and challenging to scale. Recent advances show that robots can instead learn from human videos…

Topological transforms have been very useful in statistical analysis of shapes or surfaces without restrictions that the shapes are diffeomorphic and requiring the estimation of correspondence maps. In this paper we introduce two…

Accurate segmentation of aortic vascular structures is critical for diagnosing and treating cardiovascular diseases.Traditional Transformer-based models have shown promise in this domain by capturing long-range dependencies between vascular…

Multi-modal medical image segmentation plays an essential role in clinical diagnosis. It remains challenging as the input modalities are often not well-aligned spatially. Existing learning-based methods mainly consider sharing trainable…

We study complex compact Kaehler manifolds $X$ carrying a contact structure. If $X$ is almost homogeneous and $b_2(X) \geq 2$, then $X$ is a projectivised tangent bundle (this was known in the projective case even without assumption on the…

Feature maps in deep neural network generally contain different semantics. Existing methods often omit their characteristics that may lead to sub-optimal results. In this paper, we propose a novel end-to-end deep saliency network which…

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…

Semantic segmentation from very fine resolution (VFR) urban scene images plays a significant role in several application scenarios including autonomous driving, land cover classification, and urban planning, etc. However, the tremendous…

Curvature and torsion of linear transports along paths in, respectively, vector bundles and the tangent bundle to a differentiable manifold are defined and certain their properties are derived.

Functions correspond to one of the key concepts in mathematics and science, allowing the representation and modeling of several types of signals and systems. The present work develops an approach for characterizing the coverage and…

For intelligent robots to interact in meaningful ways with their environment, they must understand both the geometric and semantic properties of the scene surrounding them. The majority of research to date has addressed these mapping…

The theory of frames normal for general connections on differentiable bundles is developed. Links with the existing theory of frames normal for covariant derivative operators (linear connections) in vector bundles are revealed. The…

Transformers are built upon multi-head scaled dot-product attention and positional encoding, which aim to learn the feature representations and token dependencies. In this work, we focus on enhancing the distinctive representation by…

Local connection forms provide a very useful tool for handling connections on principal bundles, because they ignore any complexities of the total space and, essentially, involve only two fundamental features of the structure group, namely…

High-definition (HD) maps provide essential semantic information of road structures for autonomous driving systems, yet current HD map construction methods require calibrated multi-camera setups and either implicit or explicit 2D-to-BEV…