Cross-View Goal Specification

Updated 4 August 2025

Cross-view goal specification is a methodology for formalizing and operationalizing objectives across diverse sensor and representational views using information-theoretic decomposition.
It leverages unique, shared, and synergistic information components to align goals, driving robust decision-making in robotics, navigation, and spatial AI.
The approach integrates neural, symbolic, and multi-modal techniques to overcome representation gaps, ensuring effective goal transfer across heterogeneous domains.

Cross-view goal specification denotes the formalization, inference, and operationalization of desired outcomes or objectives in environments where observations, requirements, or targets are provided or realized under differing sensor, informational, or representational perspectives. This concept is central across domains such as neural information processing, robotics, autonomous systems, and spatial AI, where the semantic alignment of goals between contrasting domains—be they anatomical motifs, camera viewpoints, symbolic-physical abstractions, or sensor modalities—is critical to robust, context-independent reasoning and effective action.

1. Theoretical Foundations: Information Decomposition and Domain-Independence

A unifying theoretical basis for cross-view goal specification is provided by partial information decomposition (PID) (Wibral et al., 2015). Classical information theory—embodied in Shannon’s mutual information—quantifies the total information shared between variables as a scalar I(Y; X). However, in multi-input systems (e.g., neurons or circuits with several afferents), cross-domain unification necessitates explicit decomposition of information transmission into distinct contributions:

Unique information from each input, $I_{\text{unq}}(Y : X_1 \setminus X_2)$ , conveying information available only from $X_1$ ,
Redundant (shared) information, $I_{\text{shd}}(Y : X_1;X_2)$ , accessible from each input alone,
Synergistic information, $I_{\text{syn}}(Y : X_1;X_2)$ , which can be inferred only from their combination.

This decomposition enables the domain-independent ("view-independent") declaration of neural or system goals:

$I(Y : X_1, X_2) = I_{\text{unq}}(Y : X_1 \setminus X_2) + I_{\text{unq}}(Y : X_2 \setminus X_1) + I_{\text{shd}}(Y : X_1;X_2) + I_{\text{syn}}(Y : X_1;X_2)$

Specification of generic neural goal functions becomes a parametric optimization:

$G = \Gamma_0 I_{\text{unq}}(Y : X_1 \setminus X_2) + \Gamma_1 I_{\text{unq}}(Y : X_2 \setminus X_1) + \Gamma_2 I_{\text{shd}}(Y : X_1;X_2) + \Gamma_3 I_{\text{syn}}(Y : X_1;X_2) + \Gamma_4 H(Y|X_1,X_2)$

where the $\Gamma_i$ coefficients tune emphasis between the unique, shared, and synergistic components, yielding an information-theoretic meta-language for cross-view goal specification in neural and engineered systems.

Cross-view goal specification also manifests in spatial, multi-modal, or viewpoint-sensitive contexts where target state or location must be defined across disparate sensor geometries.

Semantic Cross-View Matching (Castaldo et al., 2015) operationalizes cross-view goal localization by transforming both ground-level images and top-down GIS representations into structured, semantically segmented descriptors (semantic segment layout, SSL), capturing both semantic class presence and spatial arrangement. Descriptors are compared (e.g., via Hellinger distance of Gaussian models for segments and pooling regions) across modalities. This enables matching of a query image (e.g., a photograph) to candidate locations in a GIS, specifying a spatial goal despite severe changes in appearance, resolution, and perspective. The method was shown to reduce search areas in urban ground-to-map localization to under 5% of total area for many queries.
Cross-View Policy Learning for Navigation (Li et al., 2019) employs multi-modal joint embedding and policy distillation losses to couple agent policies observed in ground and aerial views, enabling the use of goal specifications in one view (e.g., bird's-eye satellites) to drive actions in another, even in tasks involving zero-shot transfer to novel environments.
XVTP3D (Song et al., 2023) further unifies goal prediction in autonomous driving by projecting view-specific features (from BEV and first-person view) into a shared set of 3D queries representing goal hypotheses. Cross-view consistency is enforced both through architectural information fusion (coarse-to-fine cross-attention, random mask augmentation) and through prediction losses, ensuring view-invariant trajectory intent and reducing divergence of predicted goals between sensor modalities.

3. Symbolic-Abstraction and Model-Based Planning Across Views

In robot-manipulation and symbolic-AI settings, cross-view goal specification requires bridging abstract, often linguistic or property-based, goal definitions to executable low-level actions under uncertainty.

Belief-Space Specification for Manipulation (Kaelbling et al., 2021) demonstrates this by formalizing goals as probabilistic predicates over world properties:
- $B(\phi, p)$ encodes belief with probability $p$ that property $\phi$ is true,
- $B(\text{Den}(\lambda x. expr, o), p)$ encodes that $o$ satisfies description $expr$ probabilistically.

Planning operates in belief-space, with regression-based, STRIPS-like reasoning and probabilistic cost minimization, integrating resolution of ambiguous goal references and low-level sensorimotor execution in a unified hierarchy.

Goal-Oriented Requirements and Evolution (Nguyen et al., 2016, Botangen et al., 2019) provide a software engineering analogue, representing requirements and preferences as graph-structured models (and/or DAGs, annotated with logical and contextual conditions). "Cross-view" here denotes mapping specification and evolution of goals across stakeholders, implementation strategies, and contexts—enabling trade-off analysis, constraint satisfaction, and optimization of minimal effort transformations during system evolution, using hybrid constraint/optimization solvers and answer set programming.

Recent advances in cross-modal embedding and correspondence learning empower specification and recognition of goals across fundamentally distinct observation domains, such as language, images, or simulated sensors.

Foundation Model-Based Specification (Cui et al., 2022) uses large pretrained models—ResNet, MoCo, CLIP—to embed both robot observations and goal descriptions (whether images, hand-drawn sketches, or language instructions) into a shared space. Goals can thus be specified via modalities orthogonal to the robot's native sensor input (e.g., an internet image or text description), with goal attainment measured by embedding similarity $\varphi^{\text{raw}}$ or "delta" features. This approach yields up to 14-fold improvements in zero-shot goal identification versus random selection in diverse manipulation tasks.
End-to-End Cross-View Correspondence (Bono et al., 2023) addresses navigation with goal images from disparate viewpoints. The architecture, built on binocular ViTs and a sequential duo of pretext tasks (cross-view completion and relative pose+visibility estimation), induces patch-level correspondence using early cross-attention, allowing robust goal localization and navigation even under extreme wide-baseline and occlusion scenarios. The emergent alignment in attention maps is a key outcome of this methodology.
Cross-View Goal Alignment Frameworks in Visuomotor Policies (Cai et al., 4 Mar 2025) and Cross-View Multi-Modal Segmentation (Fu et al., 6 Jun 2025) adopt similar strategies, leveraging segmentation masks, residual fusion of textual and visual cues, and object-level alignment modules to robustly match and locate goals across ego-exo perspectives. Metrics such as IoU, visibility accuracy, and centroid error are used to assess alignment fidelity and operational efficacy.

5. Practical Implications and Applications

Applications of cross-view goal specification span:

Autonomous Navigation: Efficient localization in GPS-denied environments by cross-referencing semantic cues from street-level imagery and GIS (e.g., forensics, disaster response).
Robotics: Zero-shot instruction following and task specification via natural language, sketches, or cross-view images, lowering barriers for human–robot interaction.
Requirement Engineering: Specification, optimization, and evolution of requirements models that adapt to stakeholder contexts and evolving environments.
Multimodal Perception: Object correspondence and robust segmentation for surveillance, AR/VR content mapping, and multicamera collaborative scenarios.
Autonomous Driving: Consistent trajectory prediction across heterogeneous sensor suites for safety and planning.

The fundamental benefit is the decoupling of specification and observation views: systems can interpret, plan, and achieve goals despite representational, sensory, or contextual heterogeneity.

6. Limitations, Challenges, and Future Directions

Challenges in cross-view goal specification include:

Representation Gap: Mapping between high-level (symbolic, linguistic, or abstract) and low-level (physical, sensor) state descriptions remains nontrivial. Approaches rely on embedding alignment, probabilistic inference, or hierarchical symbol grounding.
Ambiguity and Multi-Modality: Goals described in different modalities or under uncertainty may be ambiguous or contextually underdetermined. Recent methods address this via contextual preference modeling, multimodal fusion, or uncertainty-aware planning.
Safety and Interpretability: Ensuring that cross-view alignment does not lead to catastrophic misinterpretation or unintended behaviors, especially in safety-critical systems (autonomous driving, robotics), is an open research imperative.

A plausible implication is that future research will further integrate foundation models and multi-view perceptual learning, emphasizing generalization, robustness, and explainability in cross-view goal interpretation and fulfiLLMent scenarios. Integration of spatial, temporal, and semantic consistency checks, as well as ongoing benchmarking on real-world cross-view datasets, will be essential for continued progress.

The cross-view goal specification paradigm thus encapsulates a suite of methodologies for defining, reasoning about, and achieving objectives across representational, modal, or sensory domains, supported by advances in information theory, learning algorithms, symbolic models, and joint embedding architectures.