Octree

Generating compact, artist-style meshes with explicit topology typically relies on autoregressive models which incur prohibitive sequential per-token costs, or continuous flow models that depend on heuristic connectivity decoders. Next-scale generation paradigms offer a compelling alternative by enabling parallel intra-scale token prediction and coarse-to-fine refinement from global structure to local topology; yet, existing methods derive hierarchical scales via progressive mesh simplification and invert them sequentially. This eliminates intra-scale parallelism and scales generation steps linearly with face count. In this paper, we propose MeshOctave, which instead defines scale through dyadic spatial grid resolutions, framing coarsening as a deterministic collapse that merges vertices sharing a voxel cell and inherits connectivity. Its inverse operation, split-and-rewire, determines which octant sub-vertices are instantiated for each coarse face and resolves local connectivity using discrete structural tokens. These per-face operations require no serialization, each scale transition is modeled as an unordered set that adds one bit of coordinate precision, naturally supporting dynamic-length meshes and adaptive resolution refinement. We construct a scale-conditioned masked-uniform discrete diffusion model to learn split-and-rewire operation from resolution collapse hierarchies. MeshOctave outperforms strong baselines in geometric fidelity and topological validity by a non-trivial margin, while supporting adaptive resolution refinement and extending naturally to mesh subdivision tasks.

We present a new class of near-linear algorithms for efficiently integrating general tensor fields defined on trees with distance dependent kernels, the Structure-Adaptive Tree Field Integrators (STAD-TFIs). STAD-TFIs exploit the tree's underlying structure through decompositions built around path backbones and single vertex separators, and use two-dimensional fast Fourier transforms to compute interactions jointly. By exploiting this structural information, STAD-TFIs achieve more computationally efficient integration than their regular efficient tree field integrators (TFI) counterparts. We provide a detailed theoretical analysis of our proposed approach and complement it with an exhaustive empirical evaluation, ranging from speed tests on synthetic trees, through accelerated Sinkhorn-based relaxations of the Optimal Transport algorithms on real meshes, to Topological Attention Transformers for vision tasks. To the best of our knowledge, we provide some of the first results showing that efficient to compute and accurate relaxations of the geodesic Sinkhorn-based solutions of the Optimal Transport problem can be derived by applying fast TFI methods.

To achieve general-purpose autonomy over long horizons, a robot needs to maintain spatial environment information that supports a variety of tasks: geometry for planning and control, radiance for rendering and relocalization, and vision-language features for open-vocabulary grounding. Existing methods represent and estimate each modality separately, multiplying memory and compute cost while forgoing potential synergy among the representations. We develop OREN-X, an online mapping method that uses an octree in 3D space as a shared data structure for indexing and storing a multi-modal field, capturing geometric, radiance, and vision-language information. OREN-X provides efficient unified storage and retrieval of these data in explicit/implicit and full/compressed form. Our unified representation yields cross-modality synergy: SDF estimates are sharpened by occupancy and radiance, while GPU-based ray-octree traversal and octree query enable real-time rendering. We also use online dictionary learning to compress the vision-language features, shrinking them 3.7x below full per-vertex storage while raising the query accuracy. On Replica, OREN-X maps in real time (80+ fps for SDF and 30+ fps for all four modalities), improves near-surface SDF accuracy by 33% over single-modality baselines, and improves mean open-vocabulary 3D mIoU by 71% and mean accuracy by 61% over the best prior method.

Aerial Object Goal Navigation (ObjectNav) requires an unmanned aerial vehicle (UAV) to locate a described target in an unknown outdoor environment using onboard visual observations. Vision-language models (VLMs) can interpret open-ended target descriptions and visual observations, but their frame-level outputs are often noisy, sparse, and spatially transient. We propose AeroBelief, a dual-layer semantic-spatial belief mapping framework that transforms transient VLM observations into persistent spatial guidance. It separates broad contextual plausibility from target-specific evidence: an intuition layer accumulates scene-level semantic cues for exploration, while an evidence layer preserves qualified target-specific observations for approach and confirmation. Evidence-gated fusion combines the two layers into spatial belief hotspots. We further introduce object-conditioned visual reasoning with conservative evidence qualification to improve observation reliability before spatial accumulation. In parallel, egocentric regional guidance converts quadtree coverage into UAV-centered, yaw-aligned directional proposals and stabilizes them through temporal commitment. Its regional scoring is independent of semantic belief values, maintaining exploration pressure and reducing repeated low-gain search. Experiments on the UAV-ON benchmark show that AeroBelief achieves the best reported overall SR, OSR, and SPL among the compared methods, reaching 21.61%, 35.57%, and 10.62, respectively. These results support the effectiveness of persistent semantic-spatial belief, conservative evidence qualification, and temporally stable regional guidance for aerial ObjectNav.

In real pigsty environments, pig point clouds often come into close contact with background structures, resulting in blurred target boundaries, local adhesion, and background mis-segmentation. This reduces the accuracy of subsequent point cloud completion and body size measurement. To address these challenges, this study proposes a pig point cloud segmentation method based on boundary feature analysis. The proposed method adopts Octree Transformer as the backbone network and integrates local geometric details with global semantic context through octree convolution, self-attention encoding, and multi-scale feature fusion. Furthermore, soft-distance boundary pseudo-labels are generated to provide continuous boundary supervision, and a bidirectional cross-boundary semantic module is designed to enable explicit interaction between boundary and semantic features. Experiments conducted on a comprehensive dataset demonstrate that the proposed method significantly outperforms various state-of-the-art models in terms of segmentation accuracy, mean intersection over union, and boundary delineation. The results indicate that the method effectively alleviates boundary adhesion, providing reliable point cloud inputs for downstream precision livestock farming tasks.

Numerous 3D assets are discarded due to low texture resolution, while current super-resolution models ignore texture maps and focus on natural images. An efficient and generalizable texture super-resolution model can revitalize a large corpus of aging yet valuable assets across industries such as film and video games. We present Texture++, a novel framework for texture super-resolution, which enhances the low-resolution textures of assets to produce high-resolution, high-quality results. Specifically, we reformulate the task of super-resolution in UV space into performing it across multiple rendered views and merging the outputs. Firstly, to achieve more complete and continuous textures in the view space, we propose an adaptive view selection strategy to integrate textures dispersed across UV texture patches. Furthermore, we introduce a quadtree-based texture region organization method for combining super-resolved textures from different viewpoints, providing masks to distinguish regions that require improvement. Finally, we design a diffusion-based super-resolution model that enhances the texture resolution for specified masked regions, seamlessly integrating with surrounding regions. Through comprehensive evaluations, we demonstrate that our approach yields textures with substantially improved detail and coherence over existing methods.

Constructing octrees for mobile robots that process continuous point streams in real time poses significant computational and memory challenges. Standard global structures often suffer from high latency and unbalanced tree growth. We introduce the Ego-Centric Octree (ECO), a spatial data structure that acts as a 3D sliding window, dynamically bounding the mapping space to the robot's immediate surroundings. ECO uses an efficient incremental update algorithm that categorizes the environment into shift-out, shift-in, and overlap regions, eliminating redundant global coordinate transformations. Evaluations on the KITTI benchmark demonstrate that ECO reduces update times by up to 25.60% (24.87% on average) compared to full static reconstruction and by up to 67.52% (54.60% on average) compared to a bounded incremental baseline. Furthermore, ECO substantially lowers the total system latency of downstream tasks, running up to 34.17% faster than full reconstruction in voxel-map generation. In dynamic scenes, ECO naturally retains a short-term temporal memory of moving objects, providing useful temporal context while keeping update cost bounded and the tree balanced for real-time spatial perception.

Reconstructing dynamic urban scenes remains challenging due to the unbounded nature of driving environments and the presence of multiple dynamic objects. Currently, potentially faster sparse voxel methods are mainly designed for static scenarios. On the other hand, dynamic approaches based on 3D Gaussian Splatting, despite their high-fidelity, are often time-consuming for driving scenarios and exhibit uncontrollable memory growth in large scenes. To address these limitations, we present DrivingVoxels, a compositional sparse voxel rendering framework for dynamic driving scenes. Our method jointly rasterizes sparse voxels from multiple independent octrees within a single rendering pass. Each rigid dynamic object is represented by an octree defined in its local coordinate frame, while a separate static octree models the stationary background. DrivingVoxels adopts a fully explicit, neural-free representation together with a LiDAR-guided structural initialization that efficiently captures scene geometry. We evaluate our framework on the PandaSet benchmark, demonstrating that DrivingVoxels performs on par on perceptual metrics and better on structural metrics for NVS and reconstruction while requiring shorter training times than previous 3DGS-base methods to an efficient optimization workflow anchored by a strong LiDAR prior.

Neural order-independent transparency delivers high-quality rendering of overlapping transparent surfaces, but its geometry passes and network input generation remain costly, particularly on mobile and legacy hardware. We present a spatiotemporal acceleration framework that exploits spatial and temporal coherence to reduce this overhead while preserving visual quality. Spatially, we use adaptive quadtree-based screen-space subdivision to scale geometry pass resolution according to local color variance. Temporally, selected frames reuse the previous transparency result through depth-based reprojection instead of full rendering. Together, these optimizations reduce rendering cost and integrate efficiently into existing real-time rendering pipelines.

Modeling high-frequency outgoing radiance distributions remains a fundamental challenge in global illumination, especially for glossy and specular materials. Existing neural-based radiance caching methods commonly rely on positional feature encodings or spatially organized caches, which makes it difficult to represent sharp directional radiance variations without increasing the model complexity or sampling cost. To address this challenge, we propose OctaOctree, an efficient spatial-angular radiance representation for global illumination. OctaOctree organizes outgoing radiance with an adaptive octree in 3D space, and associates each spatial node with an octahedral directional map. By coupling the spatial hierarchy with direction-dependent storage, our representation allocates fine spatial resolution to local illumination and visibility changes, while using coarser spatial levels with richer angular resolution to capture glossy and specular radiance distributions. This design embeds a reflectance-aware spatial-angular prior directly into the radiance representation, reducing the burden on neural networks or reconstruction modules to recover high-frequency view-dependent effects from positional features alone. As a result, OctaOctree provides a compact and expressive neural encoding for a wide range of indirect illumination effects, from diffuse interreflection to sharp glossy reflections. Experiments demonstrate that our method produces high-quality, direction-aware global illumination with single network query at primary intersections, achieving improved fidelity and real-time performance compared with baseline neural radiosity and radiance caching approaches.

We present CrossLift, a technique for computing cross fields on meshes guided by visual features in images. We leverage powerful text-to-image priors that are capable of synthesizing images of feature-aligned quad meshes in 2D. We extract this signal as explicit per-pixel directions in the 2D images, which we then back-project to the mesh surface. We aggregate these candidate surface directions by performing two smooth interpolations on the mesh surface (first within each view and second across multiple views). We propose custom confidence-based weights for the candidate directions in each interpolation that allow us to resolve conflicts between candidates on the same face and smoothly interpolate our field to occluded faces. Our method is modular and can be used with many different 2D visual priors. We show additional applications to texture-aligned quad meshing as well as interactive cross-field design using coarse, user-drawn lines as signal. We demonstrate the effectiveness of CrossLift on a diverse set of both organic and mechanical shapes and produce quad meshes that exhibit superior semantic alignment as compared to existing methods. Project page at: https://crosslift.github.io/

Large Multimodal Models (LMMs) have recently emerged as promising backbones for GUI-agent models, where high-resolution GUI screenshots are introduced to the prompts at each iteration step. However, these screenshots exhibit highly non-uniform spatial information density: large regions may carry little information and are visually homogeneous, while key text and icons may require high visual fidelity. Existing approaches to this problem either require additional training or rely on attention-based token compression, ignoring the structured layout and spatial redundancy of GUI screenshots. To fill the gap, this paper proposes AquaUI, a training-free inference-time token reduction method for GUI agent models that utilizes the non-uniform information density in screenshots. AQuaUI constructs an adaptive quadtree on each screenshot input and keeps one representative merged token per leaf of the quadtree. AQuaUI preserves the spatial positions of retained tokens throughout the pipeline to ensure that all position-encoding stages remain consistent. To further improve temporal consistency across multi-step GUI interactions, we propose a conditional quadtree algorithm that leverages the continuity between consecutive screenshots within a single request. Specifically, it refines the current quadtree using previous quadtrees as references, helping preserve fine-grained regions across static or mildly shifted GUI states. We implement AQuaUI on state-of-the-art GUI agent models and conduct experiments on standard grounding and navigational benchmarks. AQuaUI consistently shows improved accuracy-efficiency trade-offs over prior baselines. Notably, on GUI-Owl-1.5-32B-Instruct, AQuaUI achieves up to 13.22% speedup and 29.52% fewer visual tokens while retaining 99.06% of full-token performance, suggesting that the spatial redundancy of GUI screenshots can be exploited at inference without retraining.

This paper addresses the problem of image denoising for grayscale images. We propose a probabilistic image generative model that combines a quadtree region-partitioning model with a mixture autoregressive model, and propose a framework that reduces MAP (maximum a posteriori)-estimation-based denoising to the maximization of a variational lower bound. To maximize this lower bound, we develop an algorithm that alternately applies variational Bayes and gradient methods. We particularly demonstrate that the gradient-based update rule can be computed analytically without numerical computation or approximation. We carried out some experiments to verify that the proposed algorithm actually removes image noise and to identify directions for future improvement.

We present AQMP, a novel image codec combining Adaptive Quadtree Refinement with Matching Pursuit. Unlike conventional Matching Pursuit methods that operate on fixed-size sub-images, AQMP dynamically adapts block sizes to local image structure, allocating finer partitions where the image is complex and coarser ones where it is smooth. This adaptivity yields superior compression ratios compared to fixed-size block Matching Pursuit at equivalent image quality, while offering significant parallelization opportunities at both the tree-leaf level and during compression of individual nodes. The algorithm is governed by user-specified accuracy and sparsity parameters alongside a small set of additional hyperparameters. To navigate the trade-off between compression efficiency and visual quality, we perform multi-objective hyperparameter optimization using the Tree-Structured Parzen Estimator, producing comprehensive Pareto fronts. Experimental results show that AQMP achieves up to $4\times$ higher compression rates than JPEG at comparable SSIM values, while maintaining competitive quality across a broad range of compression regimes. Performance evaluation is provided using a representative set of test images. To ensure reproducibility and promote adoption, we have made our implementation publicly available on GitHub under the MIT license.

LiDAR point cloud compression is vital for autonomous systems to handle massive data from high-resolution sensors. While learned entropy modeling built upon octree structures yields high compression gains, it faces two critical bottlenecks: 1) prohibitive latency, particularly during decoding, caused by causal, multi-stage context modeling; and 2) a rigid performance-latency trade-off, preventing a single model from adapting to varying constraints. These limitations stem from the tight coupling between the context aggregation backbone and probability prediction. To address this, we propose PACE, a new framework that reformulates ancestral context aggregation as a non-causal backbone and confines causality to a lightweight, stage-scalable predictor, eliminating repetitive backbone executions and reducing computational overhead. The predictor supports an arbitrary number of prediction stages, enabling seamless adaptation across diverse performance-latency trade-offs without reloading parameters. Experiments demonstrate that PACE sets a new state-of-the-art in compression efficiency, achieving notable BD-BR savings and reducing decoding latency by over 90% in autoregressive mode, making it attractive for practical applications.

The development of 3D scanning technology has enabled the acquisition of massive point cloud models with diverse structures and large scales, thereby presenting significant challenges in point cloud processing. Fast neighboring points search is one of the most common problems, which is frequently used in model reconstruction, classification, retrieval and feature visualization. Hash function is well known for its high-speed and accurate performance in searching high-dimensional data, which is also the core of the proposed 2L-LSH. Specifically, the 2L-LSH algorithm adopts a two-step hash function strategy, in which the popular step divides the bounding box of the point cloud model and the second step constructs a generalized table-based data structure. The proposed 2L-LSH offers a highly efficient and accurate solution for fast neighboring points search in large-scale 3D point cloud models, making it a promising technique for various applications in the field. The proposed algorithm is compared with the well-known methods including Kd-tree and Octree; the obtained results demonstrated that the proposed method outperforms Kd-tree and Octree in terms of speed, i.e. the time consumption of kNN search can be 51.111% and 94.159% lower than Kd-tree and Octree, respectively. And the RN search time can be 54.519% and 41.840% lower than Kd-tree and Octree, respectively.

3D Gaussian Splatting (3DGS) has emerged as an efficient approach for achieving photorealistic rendering. Recent MLP-based variants further improve visual fidelity but introduce substantial decoding overhead during rendering. To alleviate computation cost, several pruning strategies and level-of-detail (LOD) techniques have been introduced, aiming to effectively reduce the number of Gaussian primitives in large-scale scenes. However, our analysis reveals that significant redundancy still remains due to the lack of occlusion awareness. In this work, we propose Proxy-GS, a novel pipeline that exploits a proxy to introduce Gaussian occlusion awareness from any view. At the core of our approach is a fast proxy system capable of producing precise occlusion depth maps at a resolution of 1000x1000 under 1ms. This proxy serves two roles: first, it guides the culling of anchors and Gaussians to accelerate rendering speed. Second, it guides the densification towards surfaces during training, avoiding inconsistencies in occluded regions, and improving the rendering quality. In heavily occluded scenarios, such as the MatrixCity Streets dataset, Proxy-GS not only equips MLP-based Gaussian splatting with stronger rendering capability but also achieves faster rendering speed. Specifically, it achieves more than 2.5x speedup over Octree-GS, and consistently delivers substantially higher rendering quality. Code will be public upon acceptance.