arXiv subjects

Markus Gross

Publications and source records attributed to Markus Gross.

At least 19 recordsLinked to original sources

arXiv2026

Flow map learning in nonlinear vector autoregressive models: influence of the feature-library structure on the training error

Time series forecasting often requires learning nonlinear and time-delayed dependencies. A paradigmatic class of forecasting models are nonlinear vector autoregressive processes (NVAR), also known as next-generation reservoir computers (NG-RCs). These models approximate the Koopman operator on the space spanned by their explicit feature library. We consider the identifiability problem for learning Markovian nonlinear dynamical systems and show that the training error as a function of time resolution follows characteristic (pre-)asymptotic scaling laws. These laws depend on whether the feature library can represent the early Lie-series coefficients of the flow map (propagator) exactly or merely approximately. For dynamical systems governed by polynomial vector fields, we demonstrate the mechanism for NVAR/NG-RC models with monomial and Fourier feature libraries. We determine the dependence of the training error on the temporal resolution, the involved nonlinear degree, and the number of delay terms. While delay terms reduce the optimal one-step training error, they improve long-horizon forecasts only when the library provides sufficient nonlinearity. Thus, small training error coexists with weak generalization as the model class is mismatched to the true data-generating process. Numerical experiments on various chaotic dynamical systems confirm the theoretical predictions.

cs.LG↗

arXiv2026

{\alpha}Depth: Learning Single-Pass Soft Boundary Decomposition for Stereo Conversion

Accurately modeling soft boundaries, e.g., hair and defocus blur, is a fundamental challenge in stereo conversion due to the ambiguous blending of foreground and background. Existing depth models primarily predict single-layer depth, leading to ambiguity in depth correspondence at soft boundaries. While matting techniques can capture opacity for layered modeling, they often struggle in complex scenes with multiple targets and usually require user intervention. This paper introduces {\alpha}Depth, a layered representation that decomposes soft boundaries for high-fidelity stereo conversion. Specifically, we first resolve mixed color and depth ambiguity by estimating layered color and depth values at soft boundaries. Considering complex multi-target scenes, we design a Circular Alpha Representation (CAR) that shifts the paradigm from global target extraction to local boundary decomposition. Unlike prior matting methods restricted to a single foreground/background, CAR enables efficient scene-level inference without manual guidance. Extensive evaluations demonstrate that {\alpha}Depth achieves state-of-the-art performance in stereo conversion, eliminating background bleeding and structural distortions at soft boundaries.

cs.CV↗

arXiv2026

CoCo-InEKF: State Estimation with Learned Contact Covariances in Dynamic, Contact-Rich Scenarios

Robust state estimation for highly dynamic motion of legged robots remains challenging, especially in dynamic, contact-rich scenarios. Traditional approaches often rely on binary contact states that fail to capture the nuances of partial contact or directional slippage. This paper presents CoCo-InEKF, a differentiable invariant extended Kalman filter that utilizes continuous contact velocity covariances instead of binary contact states. These learned covariances allow the method to dynamically modulate contact confidence, accounting for more nuanced conditions ranging from firm contact to directional slippage or no contact. To predict these covariances for a set of predefined contact candidate points, we employ a lightweight neural network trained end-to-end using a state-error loss. This approach eliminates the need for heuristic ground-truth contact labels. In addition, we propose an automated contact candidate selection procedure and demonstrate that our method is insensitive to their exact placement. Experiments on a bipedal robot demonstrate a superior accuracy-efficiency tradeoff for linear velocity estimation, as well as improved filter consistency compared to baseline methods. This enables the robust execution of challenging motions, including dancing and complex ground interactions -- both in simulation and in the real world.

cs.RO↗

arXiv2026

ConFixGS: Learning to Fix Feedforward 3D Gaussian Splatting with Confidence-Aware Diffusion Priors in Driving Scenes

Feedforward 3D Gaussian Splatting (3DGS) often struggles in trajectory-based sparse-view driving scenes. Existing Gaussian repair methods mainly target optimization-based 3DGS, while diffusion-based repair is typically restricted to iterative refinement near observed viewpoints, leaving feedforward 3DGS repair underexplored. We propose ConFixGS, a plug-and-play method that learns to fix feedforward 3DGS with confidence-aware diffusion priors. Starting from a pretrained feedforward model, ConFixGS generates diffusion-enhanced local pseudo-targets and validates them through reprojection-based cross-checking against support views. The resulting dense confidence maps guide refinement, enhancing reliable details while suppressing hallucinated or inconsistent evidence. On Waymo, nuScenes, and KITTI, ConFixGS improves challenging novel view synthesis, with PSNR gains of up to 3.68 dB and FID reduced by nearly half. Our results highlight confidence-aware fusion of generative priors and support-view consistency as a key principle for robust feedforward 3D driving scene reconstruction.

cs.CV↗

arXiv2026

EnerGS: Energy-Based Gaussian Splatting with Partial Geometric Priors

3D Gaussian Splatting (3DGS) has been widely adopted for scene reconstruction, where training inherently constitutes a highly coupled and non-convex optimization problem. Recent works commonly incorporate geometric priors, such as LiDAR measurements, either for initialization or as training constraints, with the goal of improving photometric reconstruction quality. However, in large-scale outdoor scenarios, such geometric supervision is often spatially incomplete and uneven, which limits its effectiveness as a reliable prior and can even be detrimental to the final reconstruction. To address this challenge, we model partially observable geometry as a continuous energy field induced by geometric evidence and propose EnerGS. Rather than enforcing geometry as a hard constraint, EnerGS provides a soft geometric guidance for the optimization of Gaussian primitives, allowing geometric information to steer the optimization process without directly restricting the solution space. Extensive experiments on large-scale outdoor scenes demonstrate that, under both sparse multi-view and monocular settings, EnerGS consistently improves photometric quality and geometric stability, while effectively mitigating overfitting during 3DGS training.

cs.CV↗

arXiv2026

DiV-INR: Extreme Low-Bitrate Diffusion Video Compression with INR Conditioning

We present a perceptually-driven video compression framework integrating implicit neural representations (INRs) and pre-trained video diffusion models to address the extremely low bitrate regime (<0.05 bpp). Our approach exploits the complementary strengths of INRs, which provide a compact video representation, and diffusion models, which offer rich generative priors learned from large-scale datasets. The INR-based conditioning replaces traditional intra-coded keyframes with bit-efficient neural representations trained to estimate latent features and guide the diffusion process. Our joint optimization of INR weights and parameter-efficient adapters for diffusion models allows the model to learn reliable conditioning signals while encoding video-specific information with minimal parameter overhead. Our experiments on UVG, MCL-JCV, and JVET Class-B benchmarks demonstrate substantial improvements in perceptual metrics (LPIPS, DISTS, and FID) at extremely low bitrates, including improvements on BD-LPIPS up to 0.214 and BD-FID up to 91.14 relative to HEVC, while also outperforming VVC and previous strong state-of-the-art neural and INR-only video codecs. Moreover, our analysis shows that INR-conditioned diffusion-based video compression first composes the scene layout and object identities before refining textural accuracy, exposing the semantic-to-visual hierarchy that enables perceptually faithful compression at extremely low bitrates.

eess.IV↗

arXiv2026

Region-Adaptive Generative Compression with Spatially Varying Diffusion Models

Generative image codecs aim to optimize perceptual quality, producing realistic and detailed reconstructions. However, they often overlook a key property of human vision: our tendency to focus on particular aspects of a visual scene (e.g., salient objects) while giving less importance to other regions. An ideal perceptual codec should be able to exploit this property by allocating more representational capacity to perceptually important areas. To this end, we propose a region-adaptive diffusion-based image codec that supports non-uniform bit allocation within an image. We design a novel spatially varying diffusion model capable of denoising varying amounts of noise per pixel according to arbitrary importance maps. We further identify that these maps can serve as effective priors on the latent representation, and integrate them into our entropy model, improving rate-distortion performance. Built on these contributions, our spatially-adaptive diffusion-based codec outperforms state-of-the-art ROI-controllable baselines in both full-image and ROI-masked perceptual quality.

eess.IV↗

arXiv2026

SafeLand: Safe Autonomous Landing in Unknown Environments with Bayesian Semantic Mapping

Autonomous landing of uncrewed aerial vehicles (UAVs) in unknown, dynamic environments poses significant safety challenges, particularly near people and infrastructure, as UAVs transition to routine urban and rural operations. Existing methods often rely on prior maps, heavy sensors like LiDAR, static markers, or fail to handle non-cooperative dynamic obstacles like humans, limiting generalization and real-time performance. To address these challenges, we introduce SafeLand, a lean, vision-based system for safe autonomous landing (SAL) that requires no prior information and operates only with a camera and a lightweight height sensor. Our approach constructs an online semantic ground map via deep learning-based semantic segmentation, optimized for embedded deployment and trained on a consolidation of seven curated public aerial datasets (achieving 70.22% mIoU across 20 classes), which is further refined through Bayesian probabilistic filtering with temporal semantic decay to robustly identify metric-scale landing spots. A behavior tree then governs adaptive landing, iteratively validates the spot, and reacts in real time to dynamic obstacles by pausing, climbing, or rerouting to alternative spots, maximizing human safety. We extensively evaluate our method in 200 simulations and 60 end-to-end field tests across industrial, urban, and rural environments at altitudes up to 100m, demonstrating zero false negatives for human detection. Compared to the state of the art, SafeLand achieves sub-second response latency, substantially lower than previous methods, while maintaining a superior success rate of 95%. To facilitate further research in aerial robotics, we release SafeLand's segmentation model as a plug-and-play ROS package, available at https://github.com/markus-42/SafeLand.

cs.RO↗

arXiv2026

SegFly: A Dataset and 2D-3D-2D Paradigm for Aerial RGB-Thermal Semantic Segmentation at Scale

Semantic segmentation for uncrewed aerial vehicles (UAVs) is fundamental for aerial scene understanding, yet existing RGB and RGB-T datasets remain limited in scale, diversity, and annotation efficiency due to the high cost of manual labeling and the difficulties of accurate RGB-T alignment on off-the-shelf UAVs. To address these challenges, we propose a scalable geometry-driven 2D-3D-2D paradigm that leverages multi-view redundancy in high-overlap aerial imagery to automatically propagate labels from a small subset of manually annotated RGB images to both RGB and thermal modalities within a unified framework. By lifting less than 3% of RGB images into a semantic 3D point cloud and rendering it into all views, our approach enables dense pseudo ground-truth generation across large image collections, automatically producing 97% of RGB labels and 100% of thermal labels while achieving 91% and 88% annotation accuracy without any 2D manual refinement. We further extend this 2D-3D-2D paradigm to cross-modal image registration, using 3D geometry as an intermediate alignment space to obtain fully automatic, strong pixel-level RGB-T alignment with 87% registration accuracy and no hardware-level synchronization. Applying our framework to existing geo-referenced aerial imagery, we construct SegFly, a large-scale benchmark with over 20,000 high-resolution RGB images and more than 15,000 geometrically aligned RGB-T pairs spanning diverse urban, industrial, and rural environments across multiple altitudes and seasons. On SegFly, we establish the Firefly baseline for RGB and thermal semantic segmentation and show that both conventional architectures and vision foundation models benefit substantially from SegFly supervision, highlighting the potential of geometry-driven 2D-3D-2D pipelines for scalable multi-modal aerial scene understanding. Data and Code available at https://github.com/markus-42/SegFly.

cs.CV↗

arXiv2026

Theory and interpretability of Quantum Extreme Learning Machines: a Pauli-transfer matrix approach

Quantum reservoir computers (QRCs) have emerged as a promising approach to quantum machine learning, since they utilize the natural dynamics of quantum systems for data processing and are simple to train. Here, we consider $n$-qubit quantum extreme learning machines (QELMs) with initial-state encoding and continuous-time reservoir dynamics. We apply the Pauli transfer matrix (PTM) formalism to theoretically analyze the influence of encoding, reservoir dynamics, and measurement operations (including temporal multiplexing) on the QELM performance. This formalism reveals the complete set of (nonlinear) features generated by the encoding, and shows how the subsequent quantum channels linearly transform these Pauli features before they are probed by the chosen measurement operators. Optimizing such a QELM can therefore be cast as a decoding problem in which one shapes the channel-induced transformations such that task-relevant features become available to the regressor, effectively reversing the information scrambling of a unitary. Operator spreading under unitary evolution determines decodability of Pauli features, which underlies the nonlinear processing capacity of the reservoir. When paired with certain observables, structured Hamiltonians can reduce model expressivity, as reflected in a low readout rank. We trace this effect to Hamiltonian symmetries and derive asymptotic rank estimates for symmetry-resolved observable families. The PTM formalism yields a nonlinear vector (auto-)regression model as an interpretable classical representation of a QELM. As a specific application, we focus on forecasting nonlinear dynamical systems and show that a QELM trained on such trajectories learns a surrogate-approximation to the underlying flow map.

quant-ph↗

arXiv2026

Kernel-based optimization of measurement operators for quantum reservoir computers

Finding optimal measurement operators is crucial for the performance of quantum reservoir computers (QRCs), since they employ a fixed quantum feature map. We formulate the training of both stateless (quantum extreme learning machines, QELMs) and stateful (memory dependent) QRCs in the framework of kernel ridge regression. We thus extend the kernel viewpoint of supervised quantum models to recurrent QRCs by deriving an exact Hilbert--Schmidt kernel representation of the optimal readout observable on history space. This approach renders an optimal measurement operator that minimizes prediction error for a given reservoir and training dataset. For large qubit numbers, this method is more efficient than the conventional training of QRCs. We discuss efficiency and practical implementation strategies, including Pauli basis decomposition and operator diagonalization, to adapt the optimal observable to hardware constraints. To demonstrate the effectiveness of this approach, we present numerical experiments on image classification and time series prediction tasks, including chaotic and strongly non-Markovian systems. The developed method can also be applied to other quantum machine learning models.

quant-ph↗

arXiv2026

StableDPT: Temporal Stable Monocular Video Depth Estimation

Applying single image Monocular Depth Estimation (MDE) models to video sequences introduces significant temporal instability and flickering artifacts. We propose a novel approach that adapts any state-of-the-art image-based (depth) estimation model for video processing by integrating a new temporal module - trainable on a single GPU in a few days. Our architecture StableDPT builds upon an off-the-shelf Vision Transformer (ViT) encoder and enhances the Dense Prediction Transformer (DPT) head. The core of our contribution lies in the temporal layers within the head, which use an efficient cross-attention mechanism to integrate information from keyframes sampled across the entire video sequence. This allows the model to capture global context and inter-frame relationships leading to more accurate and temporally stable depth predictions. Furthermore, we propose a novel inference strategy for processing videos of arbitrary length avoiding the scale misalignment and redundant computations associated with overlapping windows used in other methods. Evaluations on multiple benchmark datasets demonstrate improved temporal consistency, competitive state-of-the-art performance and on top 2x faster processing in real-world scenarios.

cs.CV↗

arXiv2026

RelightAnyone: A Generalized Relightable 3D Gaussian Head Model

3D Gaussian Splatting (3DGS) has become a standard approach to reconstruct and render photorealistic 3D head avatars. A major challenge is to relight the avatars to match any scene illumination. For high quality relighting, existing methods require subjects to be captured under complex time-multiplexed illumination, such as one-light-at-a-time (OLAT). We propose a new generalized relightable 3D Gaussian head model that can relight any subject observed in a single- or multi-view images without requiring OLAT data for that subject. Our core idea is to learn a mapping from flat-lit 3DGS avatars to corresponding relightable Gaussian parameters for that avatar. Our model consists of two stages: a first stage that models flat-lit 3DGS avatars without OLAT lighting, and a second stage that learns the mapping to physically-based reflectance parameters for high-quality relighting. This two-stage design allows us to train the first stage across diverse existing multi-view datasets without OLAT lighting ensuring cross-subject generalization, where we learn a dataset-specific lighting code for self-supervised lighting alignment. Subsequently, the second stage can be trained on a significantly smaller dataset of subjects captured under OLAT illumination. Together, this allows our method to generalize well and relight any subject from the first stage as if we had captured them under OLAT lighting. Furthermore, we can fit our model to unseen subjects from as little as a single image, allowing several applications in novel view synthesis and relighting for digital avatars.

cs.CV↗

arXiv2026

Guardians of the Hair: Rescuing Soft Boundaries in Depth, Stereo, and Novel Views

Soft boundaries, like thin hairs, are commonly observed in natural and computer-generated imagery, but they remain challenging for 3D vision due to the ambiguous mixing of foreground and background cues. This paper introduces Guardians of the Hair (HairGuard), a framework designed to recover fine-grained soft boundary details in 3D vision tasks. Specifically, we first propose a novel data curation pipeline that leverages image matting datasets for training and design a depth fixer network to automatically identify soft boundary regions. With a gated residual module, the depth fixer refines depth precisely around soft boundaries while maintaining global depth quality, allowing plug-and-play integration with state-of-the-art depth models. For view synthesis, we perform depth-based forward warping to retain high-fidelity textures, followed by a generative scene painter that fills disoccluded regions and eliminates redundant background artifacts within soft boundaries. Finally, a color fuser adaptively combines warped and inpainted results to produce novel views with consistent geometry and fine-grained details. Extensive experiments demonstrate that HairGuard achieves state-of-the-art performance across monocular depth estimation, stereo image/video conversion, and novel view synthesis, with significant improvements in soft boundary regions.

cs.CV↗

arXiv2026

A Platform for Interactive AI Character Experiences

From movie characters to modern science fiction - bringing characters into interactive, story-driven conversations has captured imaginations across generations. Achieving this vision is highly challenging and requires much more than just language modeling. It involves numerous complex AI challenges, such as conversational AI, maintaining character integrity, managing personality and emotions, handling knowledge and memory, synthesizing voice, generating animations, enabling real-world interactions, and integration with physical environments. Recent advancements in the development of foundation models, prompt engineering, and fine-tuning for downstream tasks have enabled researchers to address these individual challenges. However, combining these technologies for interactive characters remains an open problem. We present a system and platform for conveniently designing believable digital characters, enabling a conversational and story-driven experience while providing solutions to all of the technical challenges. As a proof-of-concept, we introduce Digital Einstein, which allows users to engage in conversations with a digital representation of Albert Einstein about his life, research, and persona. While Digital Einstein exemplifies our methods for a specific character, our system is flexible and generalizes to any story-driven or conversational character. By unifying these diverse AI components into a single, easy-to-adapt platform, our work paves the way for immersive character experiences, turning the dream of lifelike, story-based interactions into a reality.

cs.HC↗

arXiv2025

OccuFly: A 3D Vision Benchmark for Semantic Scene Completion from the Aerial Perspective

Semantic Scene Completion (SSC) is essential for 3D perception in mobile robotics, as it enables holistic scene understanding by jointly estimating dense volumetric occupancy and per-voxel semantics. Although SSC has been widely studied in terrestrial domains such as autonomous driving, aerial settings like autonomous flying remain largely unexplored, thereby limiting progress on downstream applications. Furthermore, LiDAR sensors are the primary modality for SSC data generation, which poses challenges for most uncrewed aerial vehicles (UAVs) due to flight regulations, mass and energy constraints, and the sparsity of LiDAR point clouds from elevated viewpoints. To address these limitations, we propose a LiDAR-free, camera-based data generation framework. By leveraging classical 3D reconstruction, our framework automates semantic label transfer by lifting <10% of annotated images into the reconstructed point cloud, substantially minimizing manual 3D annotation effort. Based on this framework, we introduce OccuFly, the first real-world, camera-based aerial SSC benchmark, captured across multiple altitudes and all seasons. OccuFly provides over 20,000 samples of images, semantic voxel grids, and metric depth maps across 21 semantic classes in urban, industrial, and rural environments, and follows established data organization for seamless integration. We benchmark both SSC and metric monocular depth estimation on OccuFly, revealing fundamental limitations of current vision foundation models in aerial settings and establishing new challenges for robust 3D scene understanding in the aerial domain. Visit https://github.com/markus-42/occufly.

cs.CV↗

arXiv2025

Spline Deformation Field

Trajectory modeling of dense points usually employs implicit deformation fields, represented as neural networks that map coordinates to relate canonical spatial positions to temporal offsets. However, the inductive biases inherent in neural networks can hinder spatial coherence in ill-posed scenarios. Current methods focus either on enhancing encoding strategies for deformation fields, often resulting in opaque and less intuitive models, or adopt explicit techniques like linear blend skinning, which rely on heuristic-based node initialization. Additionally, the potential of implicit representations for interpolating sparse temporal signals remains under-explored. To address these challenges, we propose a spline-based trajectory representation, where the number of knots explicitly determines the degrees of freedom. This approach enables efficient analytical derivation of velocities, preserving spatial coherence and accelerations, while mitigating temporal fluctuations. To model knot characteristics in both spatial and temporal domains, we introduce a novel low-rank time-variant spatial encoding, replacing conventional coupled spatiotemporal techniques. Our method demonstrates superior performance in temporal interpolation for fitting continuous fields with sparse inputs. Furthermore, it achieves competitive dynamic scene reconstruction quality compared to state-of-the-art methods while enhancing motion coherence without relying on linear blend skinning or as-rigid-as-possible constraints.

cs.CV↗

arXiv2025

IPFormer: Visual 3D Panoptic Scene Completion with Context-Adaptive Instance Proposals

Semantic Scene Completion (SSC) has emerged as a pivotal approach for jointly learning scene geometry and semantics, enabling downstream applications such as navigation in mobile robotics. The recent generalization to Panoptic Scene Completion (PSC) advances the SSC domain by integrating instance-level information, thereby enhancing object-level sensitivity in scene understanding. While PSC was introduced using LiDAR modality, methods based on camera images remain largely unexplored. Moreover, recent Transformer-based approaches utilize a fixed set of learned queries to reconstruct objects within the scene volume. Although these queries are typically updated with image context during training, they remain static at test time, limiting their ability to dynamically adapt specifically to the observed scene. To overcome these limitations, we propose IPFormer, the first method that leverages context-adaptive instance proposals at train and test time to address vision-based 3D Panoptic Scene Completion. Specifically, IPFormer adaptively initializes these queries as panoptic instance proposals derived from image context and further refines them through attention-based encoding and decoding to reason about semantic instance-voxel relationships. Extensive experimental results show that our approach achieves state-of-the-art in-domain performance, exhibits superior zero-shot generalization on out-of-domain data, and achieves a runtime reduction exceeding 14x. These results highlight our introduction of context-adaptive instance proposals as a pioneering effort in addressing vision-based 3D Panoptic Scene Completion. Code available at https://github.com/markus-42/ipformer.

cs.CV↗