FlowSeek: Optical Flow & Airflow Algorithms

• FlowSeek is a dual framework combining an optical flow estimation model with a sensor-based airflow localization system, each optimized for efficient, real-world use.
• The optical flow variant fuses pretrained depth foundation models with low-dimensional motion basis encoding in a RAFT-derived backbone to enhance accuracy and reduce domain gaps.
• The airflow variant employs a sensor system with finite-state control and PD yaw adjustments to enable rapid, upwind plume detection on micro aerial vehicles.

FlowSeek denotes two distinct frameworks in recent literature: a compact, high-accuracy optical flow estimation system based on the fusion of depth foundation models and classical motion bases (Poggi et al., 5 Sep 2025); and a practical source-seeking algorithm and hardware solution for airflow plume localization on micro aerial vehicles using a single-directional flow sensor (Thomas et al., 22 Jan 2026). Both employ fundamentally different underlying principles, architectures, and operational domains, but are united by their focus on sparse sensing and algorithmic simplicity to enable efficient real-world deployment.

1. Optical FlowSeek: Model Architecture and Algorithmic Components

The optical flow variant of FlowSeek advances the design space for deep optical flow estimation through the integration of (1) a pretrained depth foundation model, and (2) low-dimensional rigid-motion basis parametrization, within an efficient RAFT-derived backbone. The architecture comprises the following key modules:

• Feature Extraction (FeatNet): Produces deep feature maps $F_0 = \mathrm{FeatNet}(I_0)$ and $F_1 = \mathrm{FeatNet}(I_1)$ for input images $I_0,I_1$.
• Depth Foundation Model: Supplies dense inverse depth maps $D_0,D_1$ and decoder features $\Phi_0,\Phi_1$ using models such as Depth Anything v2, embedded in both feature and context streams.
• Motion Basis Encoding (BasesNet): Encodes eight rigid-motion basis flow fields $\mathcal{B}_{\rm motion}$ (three translation plus five rotation, split to eliminate focal length dependence) using Heeger–Jepson subspace parametrization as determined by $D_0$.
• All-Pair Correlation Pyramid: Constructs a multiscale correlation volume $\{V^s\}_{s=1}^S$, where $$V^s(i,j,u,v) = \sum_k F_0(i,j,k) \cdot F^s_1(u,v,k)$$.
• Context Network (ContextNet): Builds an initial context feature set incorporating $I_0,I_1$ and optionally $F_1 = \mathrm{FeatNet}(I_1)$0.
• Iterative Update Operator (UpdNet) and FlowHead: The hidden state, initialized with context and motion bases, is iteratively refined via correlation lookups and recurrent updates to yield the accumulated flow $F_1 = \mathrm{FeatNet}(I_1)$1.

The loss function for supervision is a per-iteration log-likelihood over a Laplace mixture applied to residual flows, decayed across time steps:

$F_1 = \mathrm{FeatNet}(I_1)$2

where $F_1 = \mathrm{FeatNet}(I_1)$3 is the temporal decay weight.

2. Motion Basis Parametrization and Depth-Driven Priors

Integrating classical motion subspace theory, FlowSeek encodes scene motion via a set of depth-derived basis fields. Each pixel $F_1 = \mathrm{FeatNet}(I_1)$4 receives a basis vector:

• $F_1 = \mathrm{FeatNet}(I_1)$5
• $F_1 = \mathrm{FeatNet}(I_1)$6
• $F_1 = \mathrm{FeatNet}(I_1)$7
• Five analogous rotation components, with split forms for focal length invariance.

This rigid-motion embedding constrains the iterative optimizer, accelerating convergence and disambiguating large motions, leveraging structural priors traceable to the 3D scene geometry inferred from depth. Basis encoding is performed once per input, yielding $F_1 = \mathrm{FeatNet}(I_1)$8 for recurrent flow-update initialization.

3. Depth Foundation Models and Cross-Domain Generalization

The embedded single-image depth model (locked weights) provides both geometric priors and high-level cues. Depth decoder bottleneck features are injected into the correlation computation, while depth maps permeate the context representation. This design yields substantial domain gap reduction:

• On the Sintel Final and KITTI 2015 datasets (zero-shot, synthetic-real gap), FlowSeek achieves 10--15% lower endpoint error compared to the SEA-RAFT baseline under an identical training regime (Poggi et al., 5 Sep 2025).

This integration enables FlowSeek to maintain robustness across varied datasets without the need for domain-specific fine-tuning.

4. Training Strategy, Efficiency, and Quantitative Performance

FlowSeek is optimized for resource-constrained learning:

• Hardware: Trained on a single NVIDIA RTX 3090 GPU, contrasting with SEA-RAFT L's eight-GPU requirement.
• Curriculum: Initial training on TartanAir, then FlyingChairs ("C"), followed by FlyingThings3D ("T"), then further fine-tuning on Spring and LayeredFlow (TSKH mix), following the established "C→T→TSKH" protocol.
• Backbone Efficiency: FlowSeek runs effectively with small backbones (ResNet-18, ResNet-34) and significantly fewer iterative updates (4 vs. 12).
• MACs: FlowSeek (T) uses ~435 G MACs; the largest variant (L) uses 1859 G MACs, yet still trains on a single card and outperforms multi-GPU competitors.

Performance Comparison Table: Zero-Shot Results (Poggi et al., 5 Sep 2025)

Model	Sintel Clean↓	Sintel Final↓	KITTI Fl-All↓
SEA-RAFT (L)	1.19	4.11	12.9
FlowSeek (L)	1.07	2.21	12.5

Comparable trends hold for the Spring and LayeredFlow benchmarks. This suggests that geometric and motion-basis priors confer strong inductive bias, driving accuracy and sample efficiency.

5. FlowSeek (Airflow) on Micro Quadrotors: Sensor and Algorithm Design

In its alternative instantiation, FlowSeek designates a finite-state machine and sensor system for airflow source seeking (Thomas et al., 22 Jan 2026):

• Sensor System: A flexible fin with an attached permanent magnet is suspended above a 3-axis magnetometer. Fin bending under airflow is mapped to 2D (in-plane) airflow vector estimation via calibrated linear mapping:

$F_1 = \mathrm{FeatNet}(I_1)$9

where $I_0,I_1$0 is the body-frame airflow, $I_0,I_1$1 the magnetometer readings, $I_0,I_1$2 a sensitivity matrix, $I_0,I_1$3 a static offset, and $I_0,I_1$4 Gaussian noise. Flow magnitude and direction are computed after applying a 10-point moving average filter to magnetometer output.

• Algorithmic Logic (Vector Surge): Modifies classical "Cast and Surge" by exploiting real-time flow direction for efficient upwind reorientation. The algorithm toggles between casting (lateral sweeps), reorientation (yaw alignment upwind via PD control), and surging (direct upwind movement)—terminating when the local flow field crests (detected by a maximal flow threshold $I_0,I_1$5).
• Control Stability: PD yaw control stabilizes heading corrections, with closed-loop dynamics yielding $I_0,I_1$6 for chosen gain parameters ($I_0,I_1$7), robust at sampling rates ($I_0,I_1$8 Hz) and latencies ($I_0,I_1$9 ms) compared to gust/settling time ($D_0,D_1$0 s).

6. Experimental Validation and System Limitations

Sensor and Algorithmic Performance:

• The sensor reliably detects flows as low as 0.2 m/s above quadrotor-generated background, with $D_0,D_1$1 accuracy in directional tracking over full yaw rotations.
• In repeated trials within a 10×10 m environment, the system achieves first flow detection 3–4 m from the fan and source localization missions in 38–55 seconds for successful runs; 8 out of 10 trials reached the stop criterion.
• Primary failure modes: loss of plume during surge (flow magnitude below detection threshold) and manual aborts near obstacles (no built-in avoidance).

System Constraints:

• Sensing is planar, unable to resolve vertical flow components.
• Disturbances from prop wash and quadrotor body motion may mask ambient airflows at or below 0.2 m/s.
• No obstacle avoidance; sensor fusion with inertial measurements or the addition of multiple fins/arrays is identified as potential future improvement.
• Integration with chemical (gas) sensors is not yet realized but identified as a direction for richer plume tracking capabilities.

7. Comparative Significance and Future Directions

Both instantiations of FlowSeek emphasize the induction of strong, domain-relevant priors—depth for vision, precise vector-direction for physical plume seeking—while retaining algorithmic and hardware frugality. For the optical flow model, the synergy of depth foundation models and classical motion bases enables state-of-the-art generalization without large-scale compute. For the quadrotor domain, real-time airflow vector sensing substantially shortens source-localization trajectories over traditional cast-and-surge, albeit with the limitation to 2D flow environments.

Potential future directions include the extension to 3D sensor arrays for airborne robotics, integration of chemotactic cues with aerodynamic localization, and further exploitation of fused foundation models in visual correspondence estimation for broader generalization. In both cases, the FlowSeek framework illustrates the impact of embedding structure-exploiting priors into otherwise data-driven iterative estimation procedures (Poggi et al., 5 Sep 2025, Thomas et al., 22 Jan 2026).