P2P: Perception-to-Pursuit Systems

• P2P is defined as the integration of sensory data into actionable plans, uniting perception with pursuit for coherent scene interpretation.
• The framework employs differentiable context reasoning modules (e.g., graph CNNs, CRFs) to map raw images to strategic actions with measurable performance gains.
• P2P systems enhance biologically inspired control and robotics by jointly optimizing perception and pursuit, yielding improvements in prediction accuracy and interception feasibility.

Perception-to-Pursuit (P2P) frameworks unify the processes of sensing, interpreting, and acting upon perceptual input for the purpose of interaction or tracking in both biological and artificial systems. P2P systems span multiple domains—from multi-agent animal behavior and biologically inspired control to visual scene interpretation and autonomous robotic interception. Central to P2P is the tight coupling between “perception” (transforming sensory data into mid-level representations) and “pursuit” (using those representations to drive goal-directed, contextually consistent actions or interpretations).

1. Core Concepts and Formal Definitions

P2P architectures are characterized by an explicit interface that turns perceptual input into actionable plans or interpretations. In visual scene understanding, P2P refers to the tightly integrated pipeline wherein deep neural networks first “perceive” raw images into semantic units (e.g., region proposals or pixel labels) and then “pursue” a global, coherent scene interpretation through structured reasoning modules (Liu et al., 2019). In pursuit and tracking contexts, P2P formalizes the link from raw sensor measurements or detection streams to the generation of kinematically feasible interception strategies or behavioral responses (Oruganti, 27 Jan 2026).

Mathematically, the P2P paradigm in visual semantic interpretation seeks to jointly maximize the posterior over all scene variables $x^* = \arg\max_{x\in X} P(x|I,B_I)$, where $I$ is the image, $B_I$ the proposal set, and $x$ the collection of object classes, locations, and relationships. The joint energy formulation combines unary (perceptual) terms with structured (contextual) energy components:

$$E_\theta(x;I,B_I) = \sum_i \psi_u(x_i;I,B_I) + \sum_{i\neq j}\psi_b(x_i, x_j)$$

where $\psi_u$ encodes perceptual evidence and $\psi_b$ encodes contextual consistency (Liu et al., 2019).

In pursuit and tracking, P2P maps tracks or detection sequences to a compact state representation (e.g., velocity, acceleration, smoothness), which is then temporally reasoned upon (e.g., via a causal transformer) to output future position forecasts and actionable interception plans (Oruganti, 27 Jan 2026).

2. P2P in Biologically Inspired Control and Animal Behavior

The P2P formalism has been instrumental in modeling animal behavior, particularly in studies of group coordination and leader-follower dynamics. For instance, in paired bat flight, the follower’s trajectory cannot be fully explained by classical pursuit laws (e.g., direct pursuit, constant bearing, or motion camouflage). Instead, a virtual loom variable $\Lambda(t)$ is defined as a function of the relative headings and positions:

$$\Lambda(t) = \frac{\left[1 - x_f(t) \cdot x_l(t)\right] v_f}{r(t) \cdot x_f(t)}$$

where $x_f(t)$ and $x_l(t)$ are the follower’s and leader’s headings, $r(t)$ is the follower-to-leader vector, and $v_f$ is the follower’s speed (Kong et al., 2013). The virtual loom-based steering law

$u_f = k (x_l \cdot y_f) = -k \sin\alpha$

drives the follower to align with the leader without explicit interception, resulting in parallel, offset trajectories. The P2P control pipeline concatenates modular vision-based primitives: following (virtual loom), distance maintenance, and circling. Behavioral switching is state-driven, not stack-weighted (Kong et al., 2013).

3. Joint Perception–Action Learning in Autonomous Agents

Efficient P2P frameworks for autonomous agents have been formalized as coupled sparse coding and reinforcement learning systems. In vision-based pursuit tasks, an active “eye” agent develops both motion-selective neural encodings and smooth pursuit control by maximizing a unified, intrinsic reward tied to encoding fidelity and sparsity (Zhang et al., 2014). At each time $t$, the agent observes patches $x_i(t)$, encodes them with a learned overcomplete dictionary $D$, and selects actions through a policy $\pi(\cdot|f;\theta)$ based on pooled complex-cell features $f(t)$. The shared objective,

$$r(t) = -\sum_{i=1}^P \left[\|x_i(t) - D a_i(t)\|_2^2 + \lambda \|a_i(t)\|_1\right]$$

jointly optimizes perception ($D$) and pursuit control ($\theta$). Continuous online adaptation leads to emergent, V1-like motion coding and human-equivalent pursuit gain (Zhang et al., 2014).

4. Temporal Reasoning and Feasibility in Actionable Pursuit

In open-world robotic pursuit, P2P frameworks emphasize not just prediction, but the actionable feasibility of the forecast. P2P in drone interception encodes detections as 8-dimensional motion tokens $(x, y,$ $v_x, v_y,$ $a_x, a_y,$ scale, smoothness), aggregates tokens in a temporal window, and inputs these into a causal transformer. The network produces multi-task outputs: predicted locations, behavioral intent, and forecast trajectories. Pursuit feasibility is quantified by the Intercept Success Rate (ISR), defined as the proportion of predictions that can be intercepted by a bang-bang controller with speed/acceleration limits:

$$\mathrm{ISR} = \frac{1}{N}\sum_{i=1}^N \mathbf{1}\big[t_{\rm reach}(\| \hat p_i - p_0 \| ) \leq t_i^* \big]$$

where $t_{\rm reach}$ is computed under kinematic constraints (Oruganti, 27 Jan 2026). This approach delivers 77% lower average displacement error and nearly three orders-of-magnitude increase in actionable pursuit feasibility over baseline trackers.

5. Unified P2P Paradigms in Visual Semantic Interpretation

P2P frameworks in vision research formalize the end-to-end mapping from raw pixels through semantic unit extraction to globally coherent scene interpretation. The “pursuit” stage is realized via differentiable context reasoning modules—graph CNNs, RNNs, CRFs, or global attention—that propagate constraints or relational information over object or region variables (Liu et al., 2019). Training is end-to-end, with joint loss terms for both perception (e.g., cross-entropy, smooth-L1) and reasoning (e.g., margin-based, KL-divergence), possibly with regularization across embeddings.

Four main categories of deep P2P approaches include:

Category	Key Modules	Typical Strengths
Two-Stage Detectors + Graph	Proposal + box/cls + graph CNN/RNN	Modularity, parallel inference
End-to-End Context Networks	Unified backbone + context layer	Full backprop, efficient
Probabilistic Graphical Models	MRF/CRF, mean-field/loopy BP layers	Arbitrary structure, flexibility
Scene Graph Generation	Global graph, relational embedding	Higher-order relations, accuracy

Empirical gains in detection (mAP), segmentation (mIoU), and scene graph Recall@50/100 metrics consistently reflect the value of tightly integrating reasoning into the P2P pipeline (Liu et al., 2019).

6. Empirical Evaluation and Domain-Specific Outcomes

Domain-specific implementation details highlight the versatility of P2P:

• In bat flight studies, trajectory smoothing (cubic-spline, $F=0.85$), real-time optical-flow, and primitive switching generate synthetic trajectories closely matching empirical bat data, with Pearson $R=0.8894$ between group size and mean $y$-excursion (Kong et al., 2013).
• In pursuit learning, policies and encoding dictionaries co-develop, with motion-selective bases (spatiotemporal Gabor-like filters, residual MSE $\approx 0.06$) and pursuit gain approaching unity after $10^5$ frames (Zhang et al., 2014).
• In drone chasing, a P2P transformer achieves average displacement error of $28.12$ pixels and ISR of $0.597$ (60% feasible trajectories), compared to baseline trackers at ISR $\approx 0.001$ (Oruganti, 27 Jan 2026).

7. Challenges, Generalization, and Future Directions

Prominent challenges include weakly supervised P2P (relaxing the need for strong labels), scaling variational inference beyond mean-field, efficiently encoding higher-order contextual constraints, and domain-adapting graph knowledge across visual and non-visual modalities (Liu et al., 2019). In control contexts, advancing modular primitive architectures to three-dimensional pursuit, integrating multi-sensory fusion, and autonomous learning of state-to-primitive boundaries remain open lines of research (Kong et al., 2013). P2P’s generality has been evidenced in domains from animal behavior modeling to practical drone interception and vision systems, with ongoing research focusing on enhancing robustness, scalability, and explainability in both engineered and natural systems.