# GeloVec: Higher Dimensional Geometric Smoothing for Coherent Visual Feature Extraction in Image Segmentation

arXiv: https://arxiv.org/abs/2505.01057 · HTML: https://mlsanity.com/paper/2505.01057/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 47 references that are in the map.
- First posted on arXiv 2 May 2025.

## Builds on (most cited first, 30 of 35)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Spatial Pyramid Pooling in Deep Convolutional Networks for Visual Recognition](https://mlsanity.com/paper/1406.4729/) (2014)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Image Segmentation Using Deep Learning: A Survey](https://mlsanity.com/paper/2001.05566/) (2020)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [RefineNet: Multi-Path Refinement Networks for High-Resolution Semantic Segmentation](https://mlsanity.com/paper/1611.06612/) (2016)
- [Context Encoding for Semantic Segmentation](https://mlsanity.com/paper/1803.08904/) (2018)
- [Attention Mechanisms in Computer Vision: A Survey](https://mlsanity.com/paper/2111.07624/) (2021)
- [A Review on Deep Learning Techniques Applied to Semantic Segmentation](https://mlsanity.com/paper/1704.06857/) (2017)
- [Semantic Segmentation using Vision Transformers: A survey](https://mlsanity.com/paper/2305.03273/) (2023)
- [A General Survey on Attention Mechanisms in Deep Learning](https://mlsanity.com/paper/2203.14263/) (2022)
- [Look Closer to Segment Better: Boundary Patch Refinement for Instance Segmentation](https://mlsanity.com/paper/2104.05239/) (2021)
- [ContextNet: Exploring Context and Detail for Semantic Segmentation in Real-time](https://mlsanity.com/paper/1805.04554/) (2018)
- [A Survey of Semantic Segmentation](https://mlsanity.com/paper/1602.06541/) (2016)
- [A Survey on Deep Learning-based Architectures for Semantic Segmentation on 2D images](https://mlsanity.com/paper/1912.10230/) (2019)
- [Semantic Image Segmentation: Two Decades of Research](https://mlsanity.com/paper/2302.06378/) (2023)
- [From CNN to Transformer: A Review of Medical Image Segmentation Models](https://mlsanity.com/paper/2308.05305/) (2023)
- [Semantic Segmentation Refinement by Monte Carlo Region Growing of High Confidence Detections](https://mlsanity.com/paper/1802.07789/) (2018)
- [A singular Riemannian geometry approach to Deep Neural Networks I. Theoretical foundations](https://mlsanity.com/paper/2201.09656/) (2021)
- [Attention Mechanisms in Medical Image Segmentation: A Survey](https://mlsanity.com/paper/2305.17937/) (2023)
- [Deep Manifold Learning for Dynamic MR Imaging](https://mlsanity.com/paper/2104.01102/) (2021)
- [A singular Riemannian geometry approach to Deep Neural Networks II. Reconstruction of 1-D equivalence classes](https://mlsanity.com/paper/2112.10583/) (2021)
- [A Deep Semantic Segmentation Network with Semantic and Contextual Refinements](https://mlsanity.com/paper/2412.08671/) (2024)

## Built on by (most cited first, 2 of 2)

- [PSTNet: Physically-Structured Turbulence Network](https://mlsanity.com/paper/2603.07957/) (2026)
- [AlphaJet: Automated Conceptual Aircraft Synthesis via Disentangled Generative Priors and Topology-Preserving Evolutionary Search](https://mlsanity.com/paper/2604.26337/) (2026)

## Abstract (arXiv)

This paper introduces GeloVec, a new CNN-based attention smoothing framework for semantic segmentation that addresses critical limitations in conventional approaches. While existing attention-backed segmentation methods suffer from boundary instability and contextual discontinuities during feature mapping, our framework implements a higher-dimensional geometric smoothing method to establish a robust manifold relationships between visually coherent regions. GeloVec combines modified Chebyshev distance metrics with multispatial transformations to enhance segmentation accuracy through stabilized feature extraction. The core innovation lies in the adaptive sampling weights system that calculates geometric distances in n-dimensional feature space, achieving superior edge preservation while maintaining intra-class homogeneity. The multispatial transformation matrix incorporates tensorial projections with orthogonal basis vectors, creating more discriminative feature representations without sacrificing computational efficiency. Experimental validation across multiple benchmark datasets demonstrates significant improvements in segmentation performance, with mean Intersection over Union (mIoU) gains of 2.1%, 2.7%, and 2.4% on Caltech Birds-200, LSDSC, and FSSD datasets respectively compared to state-of-the-art methods. GeloVec's mathematical foundation in Riemannian geometry provides theoretical guarantees on segmentation stability. Importantly, our framework maintains computational efficiency through parallelized implementation of geodesic transformations and exhibits strong generalization capabilities across disciplines due to the absence of information loss during transformations.