This book presents a code-first introduction to computer vision, spanning classical 2D image processing, classical 3D vision, and deep learning. Organized as 44 short chapters across three parts, the book builds each topic from first principles: image arithmetic and morphology; convolution, pyramids, and frequency-domain filtering; feature detection, optical flow, and stereo; projective geometry, camera calibration, and structure from motion; and the full arc of modern deep learning, from a single neuron through convolutional networks, backpropagation, classic architectures, transfer learning, object detection, and semantic and instance segmentation, concluding with engineering considerations like mixed-precision and parallel training. Every technique is implemented directly in Python and NumPy or PyTorch and checked numerically against the corresponding OpenCV or PyTorch library function, so readers see not just the mathematics but its concrete behavior on real and synthetic data. The material was distilled with AI assistance from freely available online course notes, condensing extensive working code into concise mathematical exposition while preserving verified, reproducible results throughout. It is intended as a self-contained reference for students and practitioners who want to understand computer vision algorithms and their Python implementations.
https://arxiv.org/abs/2609.39627
While Vision-Language-Action (VLA) models excel in static tasks, they struggle in dynamic environments where objects are in motion (e.g., conveyor belt manipulation). We identify three fundamental limitations hindering current VLAs in these scenarios: the \textbf{perception gap}, where static visual inputs lack temporal motion cues; the \textbf{latency gap}, where inference delays render actions obsolete; and the \textbf{control gap}, caused by the open-loop action chunk execution without real-time adjustment. In this work, we propose \textbf{DSDyn-VLA}, a Slow-Fast \textbf{D}ual-\textbf{S}tream \textbf{Dyn}amic manipulation framework that integrates motion-aware foresighted planning with real-time residual correction. The slow \textbf{Flow-Planner} serves as a macro-planner. By enhancing the VLA with optical flow for temporal perception and a future state awareness mechanism to preemptively offset inference latency, it produces globally consistent, motion-aware action chunks. Complementing this, the fast \textbf{Res-Refiner} employs a lightweight RL policy to inject high-frequency, closed-loop corrections into the planned action chunks based on real-time observations. In addition, we introduce \textbf{DynBench}, a MuJoCo-based benchmark for dynamic object manipulation that comprises nine tasks. Extensive experiments demonstrate that DSDyn-VLA reduces the failure rate by over 76\% compared to current SOTA method in high-latency setting on the Kinetix dynamic benchmark, while achieving about 6$\times$ the success rate of PI0.5 in real-world dynamic settings and about 5$\times$ on DynBench. We will open-source all the code and weights.
https://arxiv.org/abs/2609.39198
Accurate dynamic scene reconstruction is important for robotic perception, where temporally consistent representations of dynamic environments are essential. Deformable 3D Gaussian Splatting (3DGS) models dynamic scenes through deformation fields, and recent methods incorporate motion supervision by aligning rendered Gaussian flow with optical flow. However, we find that such Gaussian-flow-based supervision provides only limited improvements in motion modeling. We identify a fundamental limitation of this supervision paradigm, namely a domain gap between rendered Gaussian flow and optical flow. To address this limitation, we propose a motion supervision framework built on Displacement Flow, which splats per-Gaussian 3D displacements onto the image plane to provide direct and stable optimization signals. We further disentangle scene motion from camera motion via intermediate-view rendering, enabling more reliable motion priors and targeted constraints on deformation and geometry. We also observe a discrepancy between motion fidelity and image-based evaluation, where improved motion awareness does not necessarily translate into better rendered image quality or higher image-based metric scores. Motivated by this mismatch, we introduce Deformation-Rendering Consistency (DRC), a motion-aware metric that measures the alignment between predicted deformation and rendering improvement. Experiments on dynamic scene benchmarks show substantial improvements in motion localization and motion--rendering consistency, reaching up to 39% and 6%, respectively, while image-based metrics change by only about 0.1%. These results confirm the observed mismatch between motion fidelity and image-based evaluation, demonstrating the significance of DRC for motion-aware evaluation.
https://arxiv.org/abs/2609.36940
The honeybee waggle dance motivates a communication mechanism in which one agent's motion guides the subsequent work of other agents. For aerial robots, realizing this mechanism requires a link from observed movement to a complete message, local task selection, and execution. This paper presents a MuJoCo system for comparing RGB and synthetic event vision within that link. One performer broadcasts six-bit task offers to one to three observers, each of which independently decodes both offers before selecting a task. The RGB receiver extracts trajectories using sparse optical flow; the event receiver uses only local event support and packet timing. Both use a common motion alphabet and explicit null delimiters. Because event silence does not establish target visibility, the event version includes a physical acquisition motion and continuity-qualified null confirmation. In the nominal three-observer case, each version produced 12 complete message receptions, six completed work units, and reassignment after withdrawal of a depleted task. Six paired functional cases produced the same message and work counts; an additional event-stream dropout case preserved inactivity of the affected observer. Replaying 42,060,633 recorded synthetic events reproduced all 12 event-message payloads and completion timestamps. Total nominal mission time was 493.80 s for RGB and 517.40 s for events, with the difference dominated by the event acquisition schedule. These fixed simulation results establish functional feasibility across two receiver implementations, rather than a sensor-performance advantage or hardware validation.
https://arxiv.org/abs/2609.37464
High dynamic range (HDR) video reconstruction from al\-ter\-na\-ting-exposure sequences remains challenging, especially in regions with extreme luminance variation. We propose a novel HDR reconstruction framework based on dual-stream registration and accurate pyramid fusion. Given three consecutive frames, our method computes optical flow directly with the central frame, while introducing a complementary midpoint displacement strategy to handle cases with severe overexposition. A pyramid fusion stage then merges the resulting radiance and LDR images into a final HDR output. Experimental results demonstrate that our approach consistently outperforms state-of-the-art methods.
https://arxiv.org/abs/2609.31108
Recent advances in text-to-video generation have enabled high-fidelity visual synthesis, yet realistic motion remains challenging. Generated videos may exhibit temporal discontinuities, inconsistent action progression, and structural distortions during complex movements. Even when individual frames appear realistic, the underlying motion may evolve in inconsistent or implausible ways. Standard generative objectives provide limited motion-specific supervision, leaving motion evolution insufficiently constrained. In this paper, we propose MotionSpec, a motion supervision framework centered on Spectral Trajectory Consistency (STC). STC constructs dense anchor-relative motion trajectories and transforms them into motion spectral volumes via a temporal Fourier transform. By aligning the spectral amplitude and phase of predicted and target trajectories, STC constrains both motion strength across temporal frequencies and the temporal organization of motion. To complement this trajectory-level supervision, we introduce Local Flow Consistency (LFC), which aligns consecutive-frame optical flow between predicted and target videos to stabilize local motion transitions. Experiments demonstrate that MotionSpec consistently improves motion consistency, temporal coherence, and plausibility while preserving visual fidelity.
https://arxiv.org/abs/2609.28095
Stereo visual SLAM systems built on local descriptors suffer from semantic ambiguity, instance-level confusion, and independently moving objects, each corrupting data association and accumulating as trajectory drift. Prevailing semantic and dynamic SLAM methods address this through binary feature rejection, sacrificing correspondence density for outlier suppression. We contend that contextual implausibility is better expressed as a graded quantity than an exclusion criterion. We present Know-Your-Scene (KYS)-SLAM, a modular extension of ORB-SLAM3 that supplants feature rejection with continuous correspondence modulation. The contribution is the reframing of contextual evidence as correspondence cost, applied within feature matching and leaving the geometric backend unmodified. Each keypoint is augmented with semantic, panoptic, and motion priors fused through a hierarchical compatibility formulation, in which semantic class and instance identity enforce structural plausibility while a zero-shot motion score down-weights features on independently moving objects. That score comes from a training-free module fitting a depth-aware ego-motion model to background optical flow and classifying panoptic segments via self-calibrating, coverage-aware thresholds, so only segments with sufficient motion evidence are penalized and static structure is left unpenalized. Penalizing correspondences rather than discarding them preserves the geometric support bundle adjustment depends on. Under one fixed configuration, no coefficient retuned per sequence or dataset, KYS-SLAM reduces per-sequence ATE RMSE by 17.4% on outdoor KITTI and 27.7% on indoor EuRoC across 21 stereo sequences with no regressions, and by 6.6% on dynamic subsets of KITTI Tracking and 17.8%, up to 31.2%, on Virtual KITTI 2 -- cross-domain transfer across outdoor driving, indoor flight, and synthetic imagery under one set of constants.
https://arxiv.org/abs/2609.27509
General-purpose robot control requires models to understand task intent, identify where to interact, capture how the scene evolves, and generate precise actions. Vision-language-action models provide strong semantic priors but typically do not explicitly model scene dynamics, while world-action models couple visual prediction with control without necessarily exposing the task-relevant semantic and spatial structure needed for fine-grained manipulation. We present MachEmbodied-U0 (ME-U0), a unified embodied foundation model connecting understanding and generation experts through a Mixture-of-Transformers architecture. Subtask prediction and affordance grounding guide joint visual-dynamics and action generation via flow matching. Visual dynamics encompass future RGB, depth, surface normals, and optical flow, providing complementary supervision for appearance, geometry, and motion. Multi-rate Rotary Position Encoding (MRPE) aligns visual dynamics with fine-grained control. We pretrain ME-U0 on approximately 4,200 hours of curated demonstrations from robotic datasets and egocentric datasets. Using only the supervision natively available in each downstream benchmark, ME-U0 achieves an average score of 17.66 on the RoboDojo simulation benchmark and average success rates of 99.0\% and 82.5\% on LIBERO and LIBERO-Plus, respectively. We additionally validate ME-U0 on real-world robotic manipulation tasks, demonstrating its effectiveness beyond simulation. Without corresponding downstream supervision, ME-U0 further demonstrates zero-shot subtask prediction, affordance grounding, and visual dynamics on simulated and real-world observations. Overall, ME-U0 combines competitive downstream control performance with transferable task-grounding and visual-dynamics capabilities across simulation and the real world.
https://arxiv.org/abs/2609.25627
In frame interpolation tasks, motion ambiguity in the training set causes models to generate blurry intermediate frames. Moreover, the assumption of uniform motion between frames during inference further leads to inaccuracies in the generated intermediate frames. To tackle these challenges, we propose an Accurate motion estimation algorithm with Bézier Control point, ABC-Inter, for efficient frame Interpolation. Specifically, ABC-Inter designs an Accurate Flow estimation Module (AFM) by decoupling two-frame features and mapping to corresponding coordinates to better estimate the optical flow between the two frames. Furthermore, ABC-Inter eliminates motion ambiguity in the training set by introducing Bézier control points that are computed using the input frames and the intermediate ground-truth (gt) frames. This allows the model to estimate accurate optical flow between two frames during the training process, thereby solving the blurriness problem in the generated intermediate frames during inference. Benefiting from the more accurate flow estimation between two frames, we can introduce additional frames and directly use multiple flows to calculate Bézier control points for modeling non-uniform motion without retraining the model. Simultaneously, to realize the estimation of non-linear motion using only two frames, we also introduce a new Bézier control point estimation module which achieves better motion estimation between the two frames by performing fine-tuning on the model in the second stage. Experimental results demonstrate that our ABC-Inter achieves state-of-the-art performance on multiple benchmark datasets and exhibits excellent visual perception.
https://arxiv.org/abs/2609.23408
Dynamic object segmentation and ego-motion estimation are closely coupled problems in autonomous driving, as accurate ego-motion estimation typically requires static scene observations, while identifying static observations requires knowledge of the ego motion. We present Radar-Dot, a radar--RGB framework that exploits radar Doppler measurements to address this coupling. Radar returns are first used to estimate ego velocity through a linear Doppler constraint, with residual-based static/dynamic segmentation and robust estimation used to reduce the influence of moving objects. The estimated motion is then combined with metric depth and dense optical flow to identify image regions whose observed motion is inconsistent with the rigid scene motion. Experiments on 10 nuScenes scenes (part of nuscenes-mini) demonstrate that the resulting geometric pipeline achieves 20.24% dynamic IoU and 33.67% F1-score over 394 frame pairs, while radar-based static-point filtering improves ego-velocity estimation compared with using all radar returns. These results demonstrate the potential of radar as a modality for jointly improving ego-motion estimation and dynamic object segmentation.
https://arxiv.org/abs/2609.22857
The performance of learned robot visuomotor policies depends heavily on the size and quality of their training data, yet collecting high-quality demonstrations remains costly for robots in the real world. Although large-scale robot and human datasets are increasingly available, embodiment gaps and mismatched action spaces make them difficult to leverage directly. Cross-embodiment transfer, reusing experience from other embodiments to improve learning on a target embodiment, is therefore crucial for scaling robot learning beyond per-robot data collection. In this work, we find that efficient transfer can be achieved by learning from what is shared across embodiments, the visual dynamics of how the world responds to motion, and by effectively exploiting the scarce target-embodiment data at test time. The proposed framework, called Latent Policy Steering (LPS), implements an embodiment-agnostic pretraining phase, which trains an image-based World Model (WM) with optical flow across diverse embodiments. The resulting WM is finetuned on the target embodiment with robot actions. It then steers the base policy toward better actions by searching in the WM's latent space for plans that stay close to the finetuning data. LPS is a policy-agnostic framework: it can flexibly accommodate different policies without having to retrain them. In Robomimic and real-world evaluations, LPS improves the average performance of Diffusion Policy relatively by 16% and 62%, and Pi0.5 by 8% and 14%, with only 50 demonstrations on an unseen target embodiment.
https://arxiv.org/abs/2609.22521
Deep learning-based visual odometry (VO) has achieved significant progress, yet most existing methods focus on a monocular approach, which suffers from scale ambiguity. Stereo VO provides real metric by its nature, but remains less studied in deep learning VO due to its high computational cost and modeling complexity. Recent advances in stereo matching and optical flow estimation have made dense visual correspondence increasingly accurate and reliable, but their complementary geometric information has not been fully exploited for VO. In this paper, we present SFVO, a correspondence-driven stereo VO framework that directly builds upon pretrained stereo matching and optical flow models. SFVO exploits pretrained stereo matching and optical flow models to estimate stereo and temporal correspondences. Instead of learning pose directly from images, SFVO maps learned correspondences into geometric constraints and predicts which points are trustworthy. To improve the reliability of visual correspondence-based geometric constraints, we introduce decoupled confidence maps for rotation and translation. This design better aligns the characteristics of visual correspondence and 6-DoF transformations. Extensive experiments on outdoor and indoor datasets demonstrate that SFVO achieves robust and accurate pose estimation with strong generalization capability. The code will be released.
https://arxiv.org/abs/2609.21754
Embodied visual perception relies on temporally coherent visual experience accumulated through continuous engagement with the environment. However, collecting large-scale egocentric binocular observations together with dense annotations remains costly and difficult. Moreover, visual experience is shaped not only by the environment but also by the embodiment of the observer, including viewing height, field of view, binocular geometry, and motion through the scene. To address these challenges, we present BinoGen, an automated framework for generating large-scale, embodiment-aware egocentric binocular visual experiences in indoor environments. BinoGen jointly models environmental and observer variation through generative scene synthesis, probabilistic object instantiation, appearance randomization, stochastic trajectory generation, and configurable binocular camera setups. The framework produces synchronized binocular videos together with dense multimodal supervision, including depth maps, optical flow, surface normals, semantic maps, object coordinates, and camera poses. Using BinoGen, we construct a dataset comprising more than 20 million annotated images for supervised learning. We demonstrate two complementary utilities of BinoGen. First, incorporating BinoGen data consistently improves real-world visual perception, including depth estimation, object detection, and video object tracking. Second, paired human-inspired and mouse-inspired observations from the same environments enable controlled investigation of how observer embodiment affects perceptual learning. Embodiment-specific adaptation substantially improves performance, while joint training enables a single model to perform competitively across both embodiments. Together, these results demonstrate that large-scale, controllable visual experience can improve embodied perception...
https://arxiv.org/abs/2609.19881
Sparse optical flow provides stable inter-frame correspondence, playing a key role in Visual Odometry (VO) and Visual-Inertial Odometry (VIO). Classical optimization-based methods, such as Lucas-Kanade (LK), perform well under small displacements but are sensitive to large motions and illumination changes. Modern regression-based learning methods, while more robust in complex scenes, are often computationally heavy and lack explicit geometric consistency, making them less suitable for efficient VO/VIO front-ends. To bridge this gap, we propose a hybrid neuro-symbolic framework that combines the strengths of both paradigms. Our method uses a Convolutional Neural Network (CNN) to extract robust feature representations, which is fed into a differentiable LK optimizer to estimate optical flow in an end-to-end trainable manner. Through implicit differentiation, gradients are propagated across the iterative solver, enabling joint optimization of feature extraction and flow estimation. The resulting system integrates seamlessly into existing VO/VIO pipelines and runs in real-time on embedded platforms. Experiments show that our method outperforms conventional optimization-based flow in challenging conditions such as dynamic lighting and low texture, while also achieving higher accuracy and lower latency than purely regression-based alternatives. When deployed in a VIO system, our method demonstrates significant performance improvement, achieving an average error reduction of 42\% on challenging datasets while enhancing tracking stability. The code is publicly available.
https://arxiv.org/abs/2609.06074
Visual monitoring of flapping-wing vehicles requires distinguishing individual wingbeats from motion strength and average frequency. This paper presents a controlled MuJoCo evaluation of wingbeat counting from signed optical flow observed by virtual cameras mounted on Crazyflie vehicles. Three flapping-wing models were recorded at optical distances of 1.5 and 3.0 m, producing 1,440 clips from 240 paired scene configurations with a scene-level 3:1 training-test split. A common spatial convolutional encoder was combined with a causal temporal convolutional network, a recurrent leaky integrate-and-fire spiking network, or causal self-attention. Each model predicted phase and activity, followed by the same directed-crossing event counter. The six existing convolutional models were retained, and all twelve new models were frozen before their test predictions were generated. Exact-count accuracies at 1.5 m were 96.67%, 95.00%, and 96.67%, respectively; at 3.0 m they were 94.44%, 92.22%, and 95.00%. All paired scene-bootstrap intervals for differences in exact-count accuracy included zero. Seven far-distance spiking-model clips had correct totals despite event-timing mismatches, demonstrating why total-count and event-level measurements must be reported together. The results support the feasibility of causal optical-flow counting in the tested setting and identify boundary-sensitive errors. They do not establish an architecture ranking across repeated training, real-flight robustness, or hardware efficiency.
https://arxiv.org/abs/2609.17308
Autonomous nano-UAV navigation requires accurate ego-motion estimation under stringent size, weight, power, and computing (SWaP-C) constraints, where visual sensors and LiDARs exceed payload limits, optical flow degrades in low-texture scenes, and inertial-only state estimation is susceptible to accumulated drift. While multi-zone time-of-flight (ToF) arrays provide a lightweight metric complement, 6-DoF estimation from merely 384 ranges per frame is challenged by invalid returns, anisotropic observability, and temporal computational scaling. We propose TIO-FORMER, a camera-free, optical-flow-free, and mapless range-inertial odometry framework driven by an IMU and an ultra-lightweight (15 g) payload of six orthogonal 8 x 8 ToF arrays. Our frontend pairs consecutive range grids with a bilateral gated difference, while IMU-guided cross-attention dynamically routes directional features conditioned on platform kinematics. A Streaming Causal Transformer couples an uncompressed Local KV cache with compressed Chunk-FIFO memory, maintaining bounded inference cost and memory footprint independent of flight duration. In real-flight evaluations, TIO-FORMER reduces open-loop position error by 54.4% compared to nano-UAV optical flow and by 66.4%-89.1% over learned inertial baselines. We also evaluate performance across multiple environments and robustness under severe sensing degradation. Deployed on an edge RISC-V companion computer, TIO-FORMER achieves a P95 latency of 10.466 ms and peak resident memory of 6.324 MiB (less than 5 percent system RAM), demonstrating that sparse range sensing provides practical geometric anchoring for resource-constrained micro-aerial robots. Code is available at this https URL.
https://arxiv.org/abs/2609.17198
Sparse-view 3D scene reconstruction with 3D Gaussian Splatting (3DGS) is inherently underconstrained. Plausible renderings can also coexist with erroneous Gaussian geometry, as errors in positions or depths may be concealed by opacity, scale, and appearance; we term this failure mode Geometry Cheating. Existing regularization methods constrain geometry but remain limited to observed views, while video-diffusion-based methods complete unseen views yet mainly use them as RGB pseudo-supervision, underusing motion and temporal priors and lacking explicit geometry supervision. We present Bi-FlowGS, which uses optical flow to bridge generative view completion and Gaussian geometry regularization. Our plug-and-play Video-to-Geometry Flow Distillation (V2G) distills temporal correspondence priors from restored videos into Gaussian geometry to alleviate Geometry Cheating. Conversely, Geometry-to-Video Flow-Guided Restoration (G2V) uses the current 3DGS geometry to guide temporally consistent video restoration, providing more reliable generative supervision. Together, V2G and G2V form an implicit bidirectional co-refinement process, enabling restored videos and the optimized 3DGS scene to iteratively improve each other. Experiments demonstrate improved rendering quality and geometric consistency across wide-baseline and unbounded 360° benchmarks.
https://arxiv.org/abs/2609.17039
Streaming 4D reconstruction has been demonstrated only indoors, on dense camera rigs surrounding subjects that move at human pace. Outdoor 4D reconstruction exists but relies either on cameras mounted on the moving vehicle itself, or on limited-coverage arrays observing quasi-static subjects offline. The case that actually matters for spectators is a fast-moving subject, watched from a sparse ring of allocentric cameras, streaming. No method targets this, and no benchmark exists to evaluate one. To this end, we introduce FastFlowGS, a streaming 4D Gaussian Splatting method for reconstructing fast-moving subjects from a small set of fixed external cameras, and Monaco4D, a photorealistic Unreal Engine 5 benchmark for high-speed outdoor reconstruction. FastFlowGS fuses sparse matches, semi-dense tracks, and dense optical flow by lifting each signal to 3D with geometric uncertainty and combining them through a Kalman-style temporal update. Monaco4D provides Formula 1 sequences under varied illumination from trackside, onboard, and drone viewpoints with dense ground truth. On CMU-Panoptic, FastFlowGS exceeds the strongest baseline by 12.6% VMAF at 35% greater efficiency. On Monaco4D, where existing streaming methods degrade severely, it improves dynamic-region PSNR by up to 18.6% with 28.3% lower per-frame optimization time. Dataset and additional details can be found at this https URL.
https://arxiv.org/abs/2609.16310
Video segmentation models recognize and track objects over time, but they do not indicate whether each segmented region moves independently of the observing camera. This dynamicity attribute cannot be inferred from semantics alone and is confounded by camera ego-motion. We introduce \method, an online framework that augments query-based video segmentation with region-level dynamicity prediction. It jointly produces the original segmentation outputs and a dynamic or static state for each predicted region. At inference, DynEoMT uses only the current frame and propagated queries, without optical flow, depth, camera pose, previous RGB frames, or feature maps. Because established video segmentation benchmarks do not annotate this attribute, we also introduce a class-agnostic offline supervision pipeline using camera-compensated optical flow and confidence-aware temporal filtering. Across VIPSeg, OVIS, YouTube-VIS 2022, and VSPW, DynEoMT achieves balanced accuracies of 84.3, 68.0, 68.6, and 87.6, respectively, while largely preserving segmentation performance. These results show that segmentation-region dynamicity can be learned from propagated queries, enabling its online prediction without a dedicated motion-processing pipeline at inference. The complete code will be released as open source to enable full reproduction of the method and experiments.
https://arxiv.org/abs/2609.14466
Optical flow methods typically rely on task-specific inductive biases, such as correlation volumes, feature warping, and iterative refinement, among others, to reach high accuracy. While effective, such biases constrain the model to predefined heuristics, which can limit its expressivity and lead to more complex pipelines and additional computational cost. We present FreeFlow, a hierarchical transformer built without any flow-specific components, using instead a single feed-forward encoder--decoder. FreeFlow combines three attention variants: window attention for local processing, shifted-window attention for cross-window information exchange, and a global attention operating at a reduced resolution. The resulting architecture scales naturally with model capacity, enabling a consistent accuracy gain from small to large variants. Despite the absence of standard inductive biases, FreeFlow achieves state-of-the-art results on major benchmarks, including Sintel (0.68/1.48 EPE on Clean/Final), KITTI-2015 (3.23 Fl-all), and Spring (3.192 1px), while remaining memory efficient at 1080p inference.
https://arxiv.org/abs/2609.11486