arXiv subjects

Jakob Geipel

Publications and source records attributed to Jakob Geipel.

4 recordsLinked to original sources

arXiv2026

Registration-Free Hyperspectral Reconstruction from RGB via a Permutation-Invariant Gram-Matrix Principle

Reconstructing a spatially and spectrally high-resolution hyperspectral image (HR-HSI) from a low-resolution HSI (LR-HSI) and a high-resolution RGB image (HR-RGB) usually assumes precise registration and a known camera response function (CRF). Both assumptions are difficult to satisfy with different sensors. We remove both through a permutation-invariant supervision principle: the Gram matrix of an unmixed abundance map depends on shared material composition but not on pixel ordering. Matching abundance Gram matrices therefore allows RGB-to-HSI mapping to be learned without spatial correspondence and without a predefined CRF. Under a full random permutation of HR-RGB pixels, a state-of-the-art fusion method collapses, whereas our reconstruction is unchanged after inverse reindexing for evaluation. Building on this principle, a residual spectral super-resolution function maps HR-RGB directly to HR-HSI without registration, known CRF, or paired supervision. Across indoor, natural-scene, and remote-sensing benchmarks, the method achieves accuracy comparable to approaches that require these assumptions while remaining robust when they are violated. Loss ablations further show that reconstruction accuracy is largely insensitive to the specific discrepancy used to match the Gram matrices, indicating that performance arises primarily from the permutation-invariant principle rather than loss tuning.

cs.CV↗

arXiv2026

From Implicit Ambiguity to Explicit Solidity: Diagnosing Interior Geometric Degradation in Neural Radiance Fields for Dense 3D Scene Understanding

Neural Radiance Fields (NeRFs) have emerged as a powerful paradigm for multi-view reconstruction, complementing classical photogrammetric pipelines based on Structure-from-Motion (SfM) and Multi-View Stereo (MVS). However, their reliability for quantitative 3D analysis in dense, self-occluding scenes remains poorly understood. In this study, we identify a fundamental failure mode of implicit density fields under heavy occlusion, which we term Interior Geometric Degradation (IGD). We show that transmittance-based volumetric optimization satisfies photometric supervision by reconstructing hollow or fragmented structures rather than solid interiors, leading to systematic instance undercounting. Through controlled experiments on synthetic datasets with increasing occlusion, we demonstrate that state-of-the-art mask-supervised NeRFs saturate at approximately 89% instance recovery in dense scenes, despite improved surface coherence and mask quality. To overcome this limitation, we introduce an explicit geometric pipeline based on Sparse Voxel Rasterization (SVRaster), initialized from SfM feature geometry. By projecting 2D instance masks onto an explicit voxel grid and enforcing geometric separation via recursive splitting, our approach preserves physical solidity and achieves a 95.8% recovery rate in dense clusters. A sensitivity analysis using degraded segmentation masks further shows that explicit SfM-based geometry is substantially more robust to supervision failure, recovering 43% more instances than implicit baselines. These results demonstrate that explicit geometric priors are a prerequisite for reliable quantitative analysis in highly self-occluding 3D scenes.

cs.CV↗

arXiv2025

InvNeRF-Seg: Fine-Tuning a Pre-Trained NeRF for 3D Object Segmentation

Neural Radiance Fields (NeRF) have been widely adopted for reconstructing high quality 3D point clouds from 2D RGB images. However, the segmentation of these reconstructed 3D scenes is more essential for downstream tasks such as object counting, size estimation, and scene understanding. While segmentation on raw 3D point clouds using deep learning requires labor intensive and time-consuming manual annotation, directly training NeRF on binary masks also fails due to the absence of color and shading cues essential for geometry learning. We propose Invariant NeRF for Segmentation (InvNeRFSeg), a two step, zero change fine tuning strategy for 3D segmentation. We first train a standard NeRF on RGB images and then fine tune it using 2D segmentation masks without altering either the model architecture or loss function. This approach produces higher quality, cleaner segmented point clouds directly from the refined radiance field with minimal computational overhead or complexity. Field density analysis reveals consistent semantic refinement: densities of object regions increase while background densities are suppressed, ensuring clean and interpretable segmentations. We demonstrate InvNeRFSegs superior performance over both SA3D and FruitNeRF on both synthetic fruit and real world soybean datasets. This approach effectively extends 2D segmentation to high quality 3D segmentation.

cs.CV↗

arXiv2017

Generalised Calibrations in AdS backgrounds from Exceptional Sasaki-Einstein Structures

We study generalised calibrations described by Exceptional Sasaki-Einstein structures on AdS backgrounds in type IIB and M-theory, placing the focus on the generalised Reeb vectors. The inequalities for the energy bound are derived by decomposing a $\kappa$-symmetry condition and equivalently, bispinors in calibration conditions from existing literature. We explain how the closure of the calibration forms is related to the integrability conditions of the Exceptional Sasaki-Einstein structure, in particular for AdS space-filling or point-like branes. Doing so, we show that the form parts of the twisted vector structure in M-theory provides generalised calibrations, reproducing the result conjectured in a recent paper. The IIB case yields analogous results. Finally, we discuss briefly the extension of the conjecture to hypermultiplet structures and other brane configurations.

hep-th↗