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

TL;DR

GeloVec introduces a higher-dimensional geometric smoothing framework for CNN-based image segmentation, improving boundary stability and feature coherence through advanced manifold relationships and multispatial transformations.

Contribution

It presents a novel geometric smoothing method using n-dimensional distances and tensorial projections, enhancing segmentation accuracy and stability over existing attention-based approaches.

Findings

Achieves up to 2.7% mIoU improvement on benchmark datasets.

Provides theoretical guarantees on segmentation stability via Riemannian geometry.

Maintains computational efficiency with parallelized geodesic transformations.

Abstract

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.