Glossary

84 terms across 10 categories. The canonical source is docs/typst/shared/glossary.typ; generated Quarto, Typst, YAML, KG, and shortcode artifacts share the same definitions.

Tier counts: 53 core, 15 support, and 16 background terms. Core terms are the thesis math lookup; background terms remain linkable but are visually demoted.

Use {{< gls term-id >}} for the linked short label and {{< glsfull term-id >}} for the linked full label in QMD pages.

Core Math Lookup

Concept Meaning Symbols Equations
NBV - Next-Best-View Selection of a sensor viewpoint to improve reconstruction under a limited acquisition budget.
\(\mathcal{M}_{\mathrm{NBV}}\)rl.mdp_nbv
\(\mathcal{M}_{\mathrm{NBV}}=(\mathcal{S},\mathcal{A},\mathcal{T},r^e,\gamma,H)\)rl.nbv_mdp
RRI - Relative Reconstruction Improvement Reduction in reconstruction error relative to the error before one acquisition.
\(\mathrm{RRI}\)oracle.rri
\(\mathrm{RRI}_t(q)=\frac{D(\mathcal{P}_t,\mathcal{M}^{\mathrm{GT}})-D(\mathcal{P}_{t\mid q},\mathcal{M}^{\mathrm{GT}})}{D(\mathcal{P}_t,\mathcal{M}^{\mathrm{GT}})+\varepsilon_{\mathrm{err}}}\)rri.rri
CD - Chamfer Distance Bidirectional discrepancy between two point clouds, formed by averaging nearest-neighbour distances in each direction.
\(\mathcal{P}\)oracle.points
\(D_{\mathrm{PS-Chamfer}}(\mathcal{P},\mathcal{Q})=\frac{1}{|\mathcal{P}|}\sum_{\boldsymbol{p}\in\mathcal{P}}\min_{\boldsymbol{q}\in\mathcal{Q}}\lVert\boldsymbol{p}-\boldsymbol{q}\rVert_2^2+\frac{1}{|\mathcal{Q}|}\sum_{\boldsymbol{q}\in\mathcal{Q}}\min_{\boldsymbol{p}\in\mathcal{P}}\lVert\boldsymbol{q}-\boldsymbol{p}\rVert_2^2\)rri.point_sampled_chamfer
target RRI - Target-Specific RRI State-relative reconstruction improvement restricted to the selected target.
\(\mathrm{RRI}^e\)entity.rri_e \(\mathcal{M}_e^{\mathrm{GT}}\)ase.mesh_target
\(\mathrm{RRI}_{t,i}^e=\frac{D(\mathcal{P}_t^e,\mathcal{M}_e^{\mathrm{GT}})-D(\mathcal{P}_{t\mid i}^e,\mathcal{M}_e^{\mathrm{GT}})}{D(\mathcal{P}_t^e,\mathcal{M}_e^{\mathrm{GT}})+\varepsilon_{\mathrm{err}}}\)rri.target_rri
target - Target of Interest Object whose reconstruction is to be improved during a rollout.
\(e\)rl.target \(\mathcal{M}_e^{\mathrm{GT}}\)ase.mesh_target
-
PC - Point Cloud Collection of sampled three-dimensional points representing geometry.
\(\mathcal{P}\)oracle.points \(\mathcal{P}_q\)oracle.points_q
-
candidate - Candidate View Proposed rigid camera pose that could be selected for the next acquisition.
\(\mathcal{Q}_t\)rl.candidate_table \(q_{t,i}\)rl.candidate_qti
-
oracle RRI - Oracle RRI RRI measured using privileged reference geometry.
\(\mathrm{RRI}\)oracle.rri \(\mathcal{M}^{\mathrm{GT}}\)ase.mesh
\(\mathrm{RRI}_t(q)=\frac{D(\mathcal{P}_t,\mathcal{M}^{\mathrm{GT}})-D(\mathcal{P}_{t\mid q},\mathcal{M}^{\mathrm{GT}})}{D(\mathcal{P}_t,\mathcal{M}^{\mathrm{GT}})+\varepsilon_{\mathrm{err}}}\)rri.rri
collection policy - Collection Policy Selection rule used to choose the acquisitions recorded for training.
\(\pi\)rl.pi
-
target-conditioned scorer - Target-Conditioned Scorer Model that predicts candidate utility from scene evidence, a proposed camera pose, and a target descriptor.
\(\hat{r}\)vin.rri_hat
\(\rho=\operatorname{corr}(\operatorname{rank}(\hat{r}_i),\operatorname{rank}(r_i))\)metrics.spearman \(\mathrm{TopKAcc}(k)=\frac{1}{N}\sum_i\mathbb{1}[y_i\in\mathrm{TopK}(\boldsymbol{\pi}_i,k)]\)metrics.topk_acc
OBS-SEL - Observed Target Selection Selection of a target using actor-visible evidence. - -
PRED-Q - Predicted-Target Q Candidate-value prediction conditioned on an observed or predicted target descriptor.
\(Q_H\)rl.qh
\(\begin{aligned}Q_{h,e}^{\star,\Xi}(\mathcal{H}_t,q_{t,i})&=\sup_{\pi\in\Pi^{\mathrm{act}}}\mathbb{E}_{\pi, a_t:=i}\left[G_{t,e}^{(h)}\mid\mathcal{H}_t\right],\\&\quad i\in\mathcal{A}_t,\quad 1\le h\le b_t\le H_{\max},\\Q_{0,e}^{\star,\Xi}(\mathcal{H}_t,q_{t,i})&=0\end{aligned}\)rl.q_h
GT-EVAL - Ground-Truth Target Evaluation Measurement of target reconstruction quality against privileged reference geometry.
\(\mathcal{M}_e^{\mathrm{GT}}\)ase.mesh_target
-
cost - Acquisition Cost Resources consumed by acquiring observations.
\(C(\tau)\)rl.acquisition_cost
-
NBV MDP - Target-Conditioned NBV MDP Decision-process formulation for target-conditioned acquisition from generated candidate views.
\(\mathcal{M}_{\mathrm{NBV}}\)rl.mdp_nbv \(s\)rl.s \(\mathcal{A}(s_t)\)rl.action_set \(\mathcal{T}\)rl.transition \(r_t^e\)rl.target_reward \(\gamma\)rl.gamma \(H\)rl.H
\(\mathcal{M}_{\mathrm{NBV}}=(\mathcal{S},\mathcal{A},\mathcal{T},r^e,\gamma,H)\)rl.nbv_mdp
rollout state - Rollout State Representation of the information carried from one planning decision to the next.
\(s\)rl.s \(\mathcal{I}^{\mathrm{hist}}\)rl.s_hist \(s_t^{\mathrm{off}}\)rl.s_off \(s_t^{\mathrm{cf0}}\)rl.s_cf0 \(s_t^{\mathrm{S0-pose}}\)rl.s_pose \(s_t^{\mathrm{S1-surface}}\)rl.s_surface \(s_t^{\mathrm{S2-ray}}\)rl.s_ray \(s_t^{\mathrm{cf+}}\)rl.s_cf_geom \(\kappa_t^{\mathrm{oracle}}\)rl.s_oracle \(\mathcal{P}\)oracle.points \(\mathcal{Q}_t\)rl.candidate_table \(m_{t,i}^{\mathrm{act}}\)rl.action_mask \(\rho_{t,i}\)rl.invalid_reason \(e\)rl.target \(b_t\)rl.budget
\(\mathcal{I}^{\mathrm{hist}}=(\boldsymbol{I}^{\mathrm{rgb}},\boldsymbol{X},\mathcal{P}^{\mathrm{semi}},\boldsymbol{F}_v)\)rl.s_hist \(s_t^{\mathrm{off}}=(\mathcal{P}_t^{\mathrm{semi}},\boldsymbol{T}_{\mathsf{R}_t^{\mathrm{native}}}^{\mathsf{W}},\mathcal{Q}_t,\boldsymbol{m}_t^{\mathrm{act}},\boldsymbol{F}_v)\)rl.s_off \(s_t^{\mathrm{cf0}}=(\boldsymbol{\Phi}_t^{\mathrm{scene}},\boldsymbol{\phi}_e,\boldsymbol{H}_t^{\mathrm{pose}},b_t)\in\mathcal{S}^{\mathrm{cf0}}\)rl.s_cf0 \(s_t^{\mathrm{cf+}}=(s_t^{\mathrm{cf0}},(\boldsymbol{D},\boldsymbol{V},\mathcal{P}^{\mathrm{cf}},\boldsymbol{n})_{1:t})\)rl.s_cf_geom \(\kappa_t^{\mathrm{oracle}}=(s_t^{\mathrm{cf+}},\mathcal{M}^{\mathrm{GT}},\mathcal{M}_e^{\mathrm{GT}},\boldsymbol{D}_q,\mathcal{P}_q,\mathrm{RRI})\)rl.s_oracle
historical observations - Historical Observations Observations available from the logged trajectory before a counterfactual rollout begins.
\(\mathcal{I}^{\mathrm{hist}}\)rl.s_hist
\(\mathcal{I}^{\mathrm{hist}}=(\boldsymbol{I}^{\mathrm{rgb}},\boldsymbol{X},\mathcal{P}^{\mathrm{semi}},\boldsymbol{F}_v)\)rl.s_hist
offline state - Persisted Offline Sample State Stored record of a decision context and its associated training or diagnostic data.
\(s_t^{\mathrm{off}}\)rl.s_off
\(s_t^{\mathrm{off}}=(\mathcal{P}_t^{\mathrm{semi}},\boldsymbol{T}_{\mathsf{R}_t^{\mathrm{native}}}^{\mathsf{W}},\mathcal{Q}_t,\boldsymbol{m}_t^{\mathrm{act}},\boldsymbol{F}_v)\)rl.s_off
S0-pose - Pose-Only Counterfactual State Planning representation that retains initial observations and records subsequently selected camera poses and remaining budget.
\(s_t^{\mathrm{S0-pose}}\)rl.s_pose \(\boldsymbol{H}_t^{\mathrm{pose}}\)rl.selected_pose_prefix
\(s_t^{\mathrm{S0-pose}}=(\mathcal{S}_{\mathrm{root}}^{\mathrm{VIN}},\boldsymbol{F}_v^{\mathrm{root}},(\boldsymbol{T}_{\mathsf{E}_e}^{\mathsf{R}_0},\boldsymbol{l}_e),\boldsymbol{H}_t^{\mathrm{pose}},b_t)\)rl.s_pose
causal observation state - Causal Observation State Proposed actor representation that updates from observations at selected poses while retaining relevant historical evidence.
\(s_t^{\mathrm{cf0}}\)rl.s_cf0
\(s_t^{\mathrm{cf0}}=(\boldsymbol{\Phi}_t^{\mathrm{scene}},\boldsymbol{\phi}_e,\boldsymbol{H}_t^{\mathrm{pose}},b_t)\in\mathcal{S}^{\mathrm{cf0}}\)rl.s_cf0
S1-surface - Selected-Surface Privileged Control Privileged control that augments root evidence with surface measurements rendered at previously selected camera poses.
\(s_t^{\mathrm{S1-surface}}\)rl.s_surface
-
oracle context - Oracle Evaluation Context Privileged information used to render hypothetical observations and measure their reconstruction outcomes.
\(\kappa_t^{\mathrm{oracle}}\)rl.s_oracle
\(\kappa_t^{\mathrm{oracle}}=(s_t^{\mathrm{cf+}},\mathcal{M}^{\mathrm{GT}},\mathcal{M}_e^{\mathrm{GT}},\boldsymbol{D}_q,\mathcal{P}_q,\mathrm{RRI})\)rl.s_oracle
action set - Finite Candidate Action Set Set of admissible integer indices into the candidate-pose table at a decision state.
\(\mathcal{A}(s_t)\)rl.action_set \(q_{t,i}\)rl.candidate_qti \(\mathcal{Q}_t\)rl.candidate_table \(m_{t,i}^{\mathrm{act}}\)rl.action_mask
\(\begin{aligned}q_{t,i}&:=\boldsymbol{T}_{\widetilde{\mathsf{C}}_{t,i}}^{\mathsf{R}_0}\in\mathrm{SE}(3),\\\mathcal{Q}_t&=\{q_{t,i}\}_{i=1}^{N_q},\\\mathcal{A}_t&=\{i\in\{1,\ldots,N_q\}:m_{t,i}^{\mathrm{act}}=1\},\quad a_t\in\mathcal{A}_t\end{aligned}\)rl.finite_action_set
rollout transition - selected-action rollout transition Update obtained by selecting a candidate action and advancing a simulated or replayed trajectory.
\(\mathcal{T}\)rl.transition \(\mathcal{P}\)oracle.points \(\mathcal{P}_q\)oracle.points_q
\(\begin{aligned}\boldsymbol{T}_{\mathsf{C}_{t+1}}^{\mathsf{R}_0}&\leftarrow q_{t,a_t},\\\boldsymbol{H}_{t+1}^{\mathrm{pose}}&\leftarrow(\boldsymbol{H}_t^{\mathrm{pose}},q_{t,a_t}),\\b_{t+1}&\leftarrow b_t-1,\\(\mathcal{Q}_{t+1},\boldsymbol{m}_{t+1}^{\mathrm{act}})&\leftarrow g_{\Xi}(q_{t,a_t},\boldsymbol{H}_{t+1}^{\mathrm{pose}},e)\end{aligned}\)rl.replay_transition_expanded \(\mathcal{P}_t^e=\Phi_e(\operatorname{Concat}(\mathcal{P}_0^{\mathrm{root}},(\mathcal{P}_j^{\mathrm{sel}})_{j<t})),\quad\mathcal{P}_{t\mid i}^e=\Phi_e(\operatorname{Concat}(\mathcal{P}_0^{\mathrm{root}},(\mathcal{P}_j^{\mathrm{sel}})_{j<t},\mathcal{P}_{t,i}^{\mathrm{acq}}))\)rri.shared_transition_states
root-normalized reward - Root-Normalized Reward Signed target-error reduction from one acquisition, divided by the fixed initial target error plus a stabilizer.
\(r_t^e\)rl.target_reward \(\mathrm{RRI}^e\)entity.rri_e \(\mathcal{P}\)oracle.points \(\mathcal{M}_e^{\mathrm{GT}}\)ase.mesh_target
\(r_t^e=(\Delta_t^e-\Delta_{t+1}^e)/(\Delta_0^e+\varepsilon_{\mathrm{err}})\)rl.target_root_gain_reward \(J_t^e=\sum_{k=0}^{t-1}r_k^e=(\Delta_0^e-\Delta_t^e)/(\Delta_0^e+\varepsilon_{\mathrm{err}})\)rl.cumulative_target_root_gain \(\mathrm{RRI}_{t,i}^e=(\Delta_t^e-\Delta_{t\mid i}^e)/(\Delta_t^e+\varepsilon_{\mathrm{err}})\)rl.marginal_target_rri \(C_t^{\mathrm{RRI},e}=\sum_{k=0}^{t-1}\mathrm{RRI}_{k,a_k}^e\)rl.cumulative_target_rri
return - Finite-Horizon Return Sum of acquisition rewards over a specified prediction horizon, with discounting when specified.
\(G_{t,e}^{(h)}\)rl.return_h \(r_t^e\)rl.target_reward \(\gamma\)rl.gamma \(h\)rl.requested_horizon \(b_t\)rl.budget \(H_{\mathrm{max}}\)rl.H_max
\(G_{t,e}^{(h)}=\sum_{k=0}^{h-1}\gamma^k r_{t+k}^e,\quad 1\le h\le b_t\le H_{\max}\)rl.finite_horizon_return
Q_H - Finite-Horizon Q Function Expected finite-horizon return after taking a specified candidate action first.
\(Q_H\)rl.qh \(G_{t,e}^{(h)}\)rl.return_h \(s\)rl.s \(s_t^{\mathrm{S0-pose}}\)rl.s_pose \(s_t^{\mathrm{cf0}}\)rl.s_cf0 \(a\)rl.a
\(\begin{aligned}Q_{h,e}^{\star,\Xi}(\mathcal{H}_t,q_{t,i})&=\sup_{\pi\in\Pi^{\mathrm{act}}}\mathbb{E}_{\pi, a_t:=i}\left[G_{t,e}^{(h)}\mid\mathcal{H}_t\right],\\&\quad i\in\mathcal{A}_t,\quad 1\le h\le b_t\le H_{\max},\\Q_{0,e}^{\star,\Xi}(\mathcal{H}_t,q_{t,i})&=0\end{aligned}\)rl.q_h \(y_t^Q=r_t+\gamma V(s_{t+1})\)rl.q_backup
validity mask - Validity Mask Boolean indicator whose true entries identify admissible candidate actions.
\(m_{t,i}^{\mathrm{act}}\)rl.action_mask \(\rho_{t,i}\)rl.invalid_reason \(m\)vin.cand_valid
\(\begin{aligned}q_{t,i}&:=\boldsymbol{T}_{\widetilde{\mathsf{C}}_{t,i}}^{\mathsf{R}_0}\in\mathrm{SE}(3),\\\mathcal{Q}_t&=\{q_{t,i}\}_{i=1}^{N_q},\\\mathcal{A}_t&=\{i\in\{1,\ldots,N_q\}:m_{t,i}^{\mathrm{act}}=1\},\quad a_t\in\mathcal{A}_t\end{aligned}\)rl.finite_action_set
acquisition budget - Acquisition Budget Limit on the number of acquisitions allowed for a task. - -
action support - Action Support Candidate row indices admitted for selection under the declared action-validity rules.
\(\mathcal{A}_t\)rl.action_set_t \(m_{t,i}^{\mathrm{act}}\)rl.action_mask
-
Actor Information Information permitted to influence action selection under a specified observation protocol. - -
bootstrap target - Bootstrap Target Fitted training target combining measured immediate reward with estimated continuation value.
\(y_t^{(h,e)}\)rl.fitted_target \(B_t^{(h,e)}\)rl.continuation
-
candidate table - Candidate Table Finite collection of proposed camera poses and their aligned row data at one decision. - -
composite support mask - Composite Support Mask Voxelwise indicator that at least one of the specified source-support conditions is satisfied. - -
continuation policy - Continuation Policy Rule for choosing later actions after a specified first acquisition. - -
descriptor - Descriptor Quantity or collection of quantities describing relevant properties of a scene, target, history or candidate. - -
implemented oracle - Implemented Oracle Concrete privileged evaluator and collection or search procedure used to generate labels and trajectories.
\(\pi^{\mathrm{oracle}}\)rl.oracle_policy
-
label availability - Label Availability Presence of a usable measured training label for a candidate at a decision state. - -
learned encoding - Learned Encoding Model-produced representation of selected inputs. - -
observation modality - Observation Modality Type of acquired measurement, such as an image or a depth map. - -
optimal oracle value - Optimal Oracle Value The highest expected finite-horizon return achievable by a continuation policy admitted to privileged oracle information under the declared decision protocol.
\(Q_{h,e}^{*,\mathrm{oracle},\Xi}\)rl.ideal_oracle_q
-
relative endpoint-error reduction - Policy-Relative Endpoint-Error Reduction Reduction in endpoint reconstruction error relative to a named comparison policy. - -
prediction horizon - Prediction Horizon Number of future acquisition rewards included in a value query. - -
Project Aria Egocentric research-device and tooling ecosystem for calibrated, time-aligned multimodal sensing. - -
recording cutoff - Recording Cutoff End of data recording before the underlying acquisition task has necessarily ended. - -
representation aliasing - Representation Aliasing Mapping acquired histories with different action consequences to the same scorer representation.
\(z_t^{\sigma}\)rl.representation
-
Rollout Root Initial decision state from which a rollout and its comparison budget begin. - -
root-normalized endpoint gain - Root-Normalized Endpoint Gain Reduction from initial to endpoint target error, divided by the initial error plus a stabilizer. - -
sampled return - Sampled Return Realized sum of acquisition rewards along one trajectory over a stated horizon.
\(G_{t,e}^{(h,\mathrm{oracle})}\)rl.sampled_oracle_return
-
successor availability - Successor Availability Presence of a recorded successor linked to a selected acquisition. - -
Target Reconstruction Error Discrepancy between prepared reconstructed geometry and the fixed reference target mesh. - -
value calibration - Value Calibration Agreement of numerical return predictions with the expected return specified by a declared continuation policy and reference population.
\(\widehat{Q}_{\theta,h}^{\sigma,\Xi}\)rl.learned_q
-
volumetric fusion - Volumetric Fusion Integration of spatially aligned information from several observations or sources in a common voxel grid. - -

Core Concepts

Next-Best-View

NBV core planning.view_selection

Aliases next best view next-view selection

Symbols
\(\mathcal{M}_{\mathrm{NBV}}\)rl.mdp_nbv
Equations
\(\mathcal{M}_{\mathrm{NBV}}=(\mathcal{S},\mathcal{A},\mathcal{T},r^e,\gamma,H)\)rl.nbv_mdp

Selection of a sensor viewpoint to improve reconstruction under a limited acquisition budget.

A myopic selector ranks immediate improvement; a finite-horizon planner also values views that enable useful later acquisitions.

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Relative Reconstruction Improvement

RRI core metrics.reconstruction_quality

Aliases state-relative RRI immediate relative reconstruction improvement

Symbols
\(\mathrm{RRI}\)oracle.rri
Equations
\(\mathrm{RRI}_t(q)=\frac{D(\mathcal{P}_t,\mathcal{M}^{\mathrm{GT}})-D(\mathcal{P}_{t\mid q},\mathcal{M}^{\mathrm{GT}})}{D(\mathcal{P}_t,\mathcal{M}^{\mathrm{GT}})+\varepsilon_{\mathrm{err}}}\)rri.rri

Reduction in reconstruction error relative to the error before one acquisition.

Target-specific RRI measures this change on the selected object. Oracle RRI obtains the measurement from privileged reference geometry. Unlike the root-gain reward, its denominator changes with the current reconstruction.

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Chamfer Distance

CD core metrics.reconstruction_quality

Aliases Chamfer metric

Symbols
\(\mathcal{P}\)oracle.points
Equations
\(D_{\mathrm{PS-Chamfer}}(\mathcal{P},\mathcal{Q})=\frac{1}{|\mathcal{P}|}\sum_{\boldsymbol{p}\in\mathcal{P}}\min_{\boldsymbol{q}\in\mathcal{Q}}\lVert\boldsymbol{p}-\boldsymbol{q}\rVert_2^2+\frac{1}{|\mathcal{Q}|}\sum_{\boldsymbol{q}\in\mathcal{Q}}\min_{\boldsymbol{p}\in\mathcal{P}}\lVert\boldsymbol{q}-\boldsymbol{p}\rVert_2^2\)rri.point_sampled_chamfer

Bidirectional discrepancy between two point clouds, formed by averaging nearest-neighbour distances in each direction.

Its value depends on sampling density, distance norm and squaring convention. The thesis instead measures target reconstruction with an equal-face point-mesh error; historical use of CD for that metric is not an allowed synonym.

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Target-Specific RRI

target RRI core metrics.reconstruction_quality

Aliases entity RRI object RRI target RRI

Symbols
\(\mathrm{RRI}^e\)entity.rri_e \(\mathcal{M}_e^{\mathrm{GT}}\)ase.mesh_target
Equations
\(\mathrm{RRI}_{t,i}^e=\frac{D(\mathcal{P}_t^e,\mathcal{M}_e^{\mathrm{GT}})-D(\mathcal{P}_{t\mid i}^e,\mathcal{M}_e^{\mathrm{GT}})}{D(\mathcal{P}_t^e,\mathcal{M}_e^{\mathrm{GT}})+\varepsilon_{\mathrm{err}}}\)rri.target_rri

State-relative reconstruction improvement restricted to the selected target.

It specializes RRI to the target geometry and differs from the root-normalized reward used to accumulate gain across a rollout.

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Target of Interest

target core entity.targeting

Aliases target entity object of interest inspection target task target

Symbols
\(e\)rl.target \(\mathcal{M}_e^{\mathrm{GT}}\)ase.mesh_target

Object whose reconstruction is to be improved during a rollout.

The requested object remains fixed while camera poses and observations change. The actor receives an observed or predicted target descriptor; the oracle uses matched reference geometry to measure improvement on that object.

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Point Cloud

PC core reconstruction.representation

Aliases 3D point cloud

Symbols
\(\mathcal{P}\)oracle.points \(\mathcal{P}_q\)oracle.points_q

Collection of sampled three-dimensional points representing geometry.

Point coordinates may coincide while remaining distinct samples. The oracle concatenates observation clouds before shared fusion, cropping, and capping; treating this operation as set union would erase multiplicity.

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Candidate View

candidate core planning.action

Aliases candidate pose candidate viewpoint next-view candidate

Symbols
\(\mathcal{Q}_t\)rl.candidate_table \(q_{t,i}\)rl.candidate_qti

Proposed rigid camera pose that could be selected for the next acquisition.

The pose belongs to SE(3); the action is its integer index in the current candidate table. Selection makes that prospective pose the next realized pose. Its utility may include immediate improvement or longer-horizon return.

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Oracle RRI

oracle RRI core supervision.oracle

Aliases mesh-supervised RRI oracle-measured RRI

Symbols
\(\mathrm{RRI}\)oracle.rri \(\mathcal{M}^{\mathrm{GT}}\)ase.mesh
Equations
\(\mathrm{RRI}_t(q)=\frac{D(\mathcal{P}_t,\mathcal{M}^{\mathrm{GT}})-D(\mathcal{P}_{t\mid q},\mathcal{M}^{\mathrm{GT}})}{D(\mathcal{P}_t,\mathcal{M}^{\mathrm{GT}})+\varepsilon_{\mathrm{err}}}\)rri.rri

RRI measured using privileged reference geometry.

The current ASE protocol prepares the historical depth cloud together with selected and hypothetical rendered observations, then measures target point-mesh error against a fixed reference crop. These labels do not make candidate depth available to the main actor.

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Collection Policy

collection policy core planning.data_collection

Aliases collector data-collection policy behavior policy

Symbols
\(\pi\)rl.pi

Selection rule used to choose the acquisitions recorded for training.

It determines which candidate observations become selected successors. A scorer predicts values; a policy chooses actions, potentially using those values. The collection policy may use privileged oracle scores and need not match the learned policy evaluated later.

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Target-Conditioned Scorer

target-conditioned scorer core model.scoring

Aliases target-aware scorer

Symbols
\(\hat{r}\)vin.rri_hat
Equations
\(\rho=\operatorname{corr}(\operatorname{rank}(\hat{r}_i),\operatorname{rank}(r_i))\)metrics.spearman \(\mathrm{TopKAcc}(k)=\frac{1}{N}\sum_i\mathbb{1}[y_i\in\mathrm{TopK}(\boldsymbol{\pi}_i,k)]\)metrics.topk_acc

Model that predicts candidate utility from scene evidence, a proposed camera pose, and a target descriptor.

The predicted quantity can be immediate target reconstruction improvement or return over a specified number of future acquisitions.

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Observed Target Selection

OBS-SEL core protocol.targeting

Aliases observed-only target selection actor-visible target selection

Selection of a target using actor-visible evidence.

Under the observed-target profile, observed or predicted object descriptors guide the choice; privileged target annotations support matching and evaluation.

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Predicted-Target Q

PRED-Q core protocol.learning

Aliases predicted-target scorer predicted-target Q_H actor-visible Q

Symbols
\(Q_H\)rl.qh
Equations
\(\begin{aligned}Q_{h,e}^{\star,\Xi}(\mathcal{H}_t,q_{t,i})&=\sup_{\pi\in\Pi^{\mathrm{act}}}\mathbb{E}_{\pi, a_t:=i}\left[G_{t,e}^{(h)}\mid\mathcal{H}_t\right],\\&\quad i\in\mathcal{A}_t,\quad 1\le h\le b_t\le H_{\max},\\Q_{0,e}^{\star,\Xi}(\mathcal{H}_t,q_{t,i})&=0\end{aligned}\)rl.q_h

Candidate-value prediction conditioned on an observed or predicted target descriptor.

Under the observed-target profile, the descriptor identifies the requested object without supplying its ground-truth geometry to the actor.

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Ground-Truth Target Evaluation

GT-EVAL core protocol.evaluation

Aliases GT target evaluation GT target crop evaluation oracle target evaluation

Symbols
\(\mathcal{M}_e^{\mathrm{GT}}\)ase.mesh_target

Measurement of target reconstruction quality against privileged reference geometry.

Reference target boxes and mesh crops support matching, supervision, and evaluation. Under the observed-target profile, they are not actor inputs; privileged controls declare any exposure separately.

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Acquisition Cost

cost core planning.objective

Aliases observation acquisition cost

Symbols
\(C(\tau)\)rl.acquisition_cost

Resources consumed by acquiring observations.

The core comparison counts acquired views. An acquisition budget limits expenditure; it is not the cost already incurred. Motion distance and elapsed time are separate possible cost measures.

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Target-Conditioned NBV MDP

NBV MDP core planning.mdp

Aliases ARIA-NBV MDP rollout MDP finite-candidate NBV MDP

Symbols
\(\mathcal{M}_{\mathrm{NBV}}\)rl.mdp_nbv \(s\)rl.s \(\mathcal{A}(s_t)\)rl.action_set \(\mathcal{T}\)rl.transition \(r_t^e\)rl.target_reward \(\gamma\)rl.gamma \(H\)rl.H
Equations
\(\mathcal{M}_{\mathrm{NBV}}=(\mathcal{S},\mathcal{A},\mathcal{T},r^e,\gamma,H)\)rl.nbv_mdp

Decision-process formulation for target-conditioned acquisition from generated candidate views.

The acquisition protocol specifies observations, admissible actions, transitions and rewards. Finite-horizon queries value a bounded number of acquisitions; a recording cutoff need not end the underlying task. A finite actor representation is not automatically a sufficient Markov state.

ARIA-NBV MDP contract

\[ \mathcal{M}_{\mathrm{NBV}}=(\mathcal{S},\mathcal{A},\mathcal{T},r^e,\gamma,H) \]

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Rollout State

rollout state core planning.mdp

Aliases actor state representation information-state representation

Symbols
\(s\)rl.s \(\mathcal{I}^{\mathrm{hist}}\)rl.s_hist \(s_t^{\mathrm{off}}\)rl.s_off \(s_t^{\mathrm{cf0}}\)rl.s_cf0 \(s_t^{\mathrm{S0-pose}}\)rl.s_pose \(s_t^{\mathrm{S1-surface}}\)rl.s_surface \(s_t^{\mathrm{S2-ray}}\)rl.s_ray \(s_t^{\mathrm{cf+}}\)rl.s_cf_geom \(\kappa_t^{\mathrm{oracle}}\)rl.s_oracle \(\mathcal{P}\)oracle.points \(\mathcal{Q}_t\)rl.candidate_table \(m_{t,i}^{\mathrm{act}}\)rl.action_mask \(\rho_{t,i}\)rl.invalid_reason \(e\)rl.target \(b_t\)rl.budget
Equations
\(\mathcal{I}^{\mathrm{hist}}=(\boldsymbol{I}^{\mathrm{rgb}},\boldsymbol{X},\mathcal{P}^{\mathrm{semi}},\boldsymbol{F}_v)\)rl.s_hist \(s_t^{\mathrm{off}}=(\mathcal{P}_t^{\mathrm{semi}},\boldsymbol{T}_{\mathsf{R}_t^{\mathrm{native}}}^{\mathsf{W}},\mathcal{Q}_t,\boldsymbol{m}_t^{\mathrm{act}},\boldsymbol{F}_v)\)rl.s_off \(s_t^{\mathrm{cf0}}=(\boldsymbol{\Phi}_t^{\mathrm{scene}},\boldsymbol{\phi}_e,\boldsymbol{H}_t^{\mathrm{pose}},b_t)\in\mathcal{S}^{\mathrm{cf0}}\)rl.s_cf0 \(s_t^{\mathrm{cf+}}=(s_t^{\mathrm{cf0}},(\boldsymbol{D},\boldsymbol{V},\mathcal{P}^{\mathrm{cf}},\boldsymbol{n})_{1:t})\)rl.s_cf_geom \(\kappa_t^{\mathrm{oracle}}=(s_t^{\mathrm{cf+}},\mathcal{M}^{\mathrm{GT}},\mathcal{M}_e^{\mathrm{GT}},\boldsymbol{D}_q,\mathcal{P}_q,\mathrm{RRI})\)rl.s_oracle

Representation of the information carried from one planning decision to the next.

The rollout starts from a root with historical observations. Each selected action advances the camera pose, pose history, and budget; the chosen observation profile determines which new measurements also enter the actor representation. This representation is distinct from the physical environment and the privileged oracle context.

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Historical Observations

historical observations core planning.observation

Aliases historical observations logged historical evidence

Symbols
\(\mathcal{I}^{\mathrm{hist}}\)rl.s_hist
Equations
\(\mathcal{I}^{\mathrm{hist}}=(\boldsymbol{I}^{\mathrm{rgb}},\boldsymbol{X},\mathcal{P}^{\mathrm{semi}},\boldsymbol{F}_v)\)rl.s_hist

Observations available from the logged trajectory before a counterfactual rollout begins.

Images, poses, calibration, semidense points, and derived features form the initial evidence where available. Later selected synthetic observations extend this history only under profiles that admit them; ground-truth meshes and boxes remain separate oracle inputs.

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Persisted Offline Sample State

offline state core planning.state

Aliases offline sample state VIN offline state persisted VIN state

Symbols
\(s_t^{\mathrm{off}}\)rl.s_off
Equations
\(s_t^{\mathrm{off}}=(\mathcal{P}_t^{\mathrm{semi}},\boldsymbol{T}_{\mathsf{R}_t^{\mathrm{native}}}^{\mathsf{W}},\mathcal{Q}_t,\boldsymbol{m}_t^{\mathrm{act}},\boldsymbol{F}_v)\)rl.s_off

Stored record of a decision context and its associated training or diagnostic data.

It can contain both actor inputs and privileged labels. Storage in the same record does not grant the actor access to every field; the replay-store section defines their separation.

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Pose-Only Counterfactual State

S0-pose core planning.state

Aliases S0 pose-history state pose-only rollout state

Symbols
\(s_t^{\mathrm{S0-pose}}\)rl.s_pose \(\boldsymbol{H}_t^{\mathrm{pose}}\)rl.selected_pose_prefix
Equations
\(s_t^{\mathrm{S0-pose}}=(\mathcal{S}_{\mathrm{root}}^{\mathrm{VIN}},\boldsymbol{F}_v^{\mathrm{root}},(\boldsymbol{T}_{\mathsf{E}_e}^{\mathsf{R}_0},\boldsymbol{l}_e),\boldsymbol{H}_t^{\mathrm{pose}},b_t)\)rl.s_pose

Planning representation that retains initial observations and records subsequently selected camera poses and remaining budget.

Selecting another pose changes the pose history and available candidates but adds no new surface observations to the actor representation.

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Causal Observation State

causal observation state core planning.state

Aliases causal actor representation

Symbols
\(s_t^{\mathrm{cf0}}\)rl.s_cf0
Equations
\(s_t^{\mathrm{cf0}}=(\boldsymbol{\Phi}_t^{\mathrm{scene}},\boldsymbol{\phi}_e,\boldsymbol{H}_t^{\mathrm{pose}},b_t)\in\mathcal{S}^{\mathrm{cf0}}\)rl.s_cf0

Proposed actor representation that updates from observations at selected poses while retaining relevant historical evidence.

It should distinguish observed surface, observed free space, and unknown space, together with measurement support and uncertainty. This is a design objective, not a claim of proven minimality or Markov sufficiency.

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Selected-Surface Privileged Control

S1-surface core planning.state

Aliases selected-surface control S1-surface

Symbols
\(s_t^{\mathrm{S1-surface}}\)rl.s_surface

Privileged control that augments root evidence with surface measurements rendered at previously selected camera poses.

The implemented S1 control retains selected depth with camera calibration, poses, masks, and provenance. It reveals additional geometry to the control actor but does not establish that the same observations would be available to a deployable actor.

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Oracle Evaluation Context

oracle context core planning.supervision

Aliases oracle information privileged rollout context GT evaluation context

Symbols
\(\kappa_t^{\mathrm{oracle}}\)rl.s_oracle
Equations
\(\kappa_t^{\mathrm{oracle}}=(s_t^{\mathrm{cf+}},\mathcal{M}^{\mathrm{GT}},\mathcal{M}_e^{\mathrm{GT}},\boldsymbol{D}_q,\mathcal{P}_q,\mathrm{RRI})\)rl.s_oracle

Privileged information used to render hypothetical observations and measure their reconstruction outcomes.

Reference meshes, target crops, and candidate labels support supervision and bounded oracle lookahead. The oracle is distinct from actor information, and a bounded comparator need not attain the globally optimal return.

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Finite Candidate Action Set

action set core planning.mdp

Aliases candidate action set masked candidate set finite NBV action space

Symbols
\(\mathcal{A}(s_t)\)rl.action_set \(q_{t,i}\)rl.candidate_qti \(\mathcal{Q}_t\)rl.candidate_table \(m_{t,i}^{\mathrm{act}}\)rl.action_mask
Equations
\(\begin{aligned}q_{t,i}&:=\boldsymbol{T}_{\widetilde{\mathsf{C}}_{t,i}}^{\mathsf{R}_0}\in\mathrm{SE}(3),\\\mathcal{Q}_t&=\{q_{t,i}\}_{i=1}^{N_q},\\\mathcal{A}_t&=\{i\in\{1,\ldots,N_q\}:m_{t,i}^{\mathrm{act}}=1\},\quad a_t\in\mathcal{A}_t\end{aligned}\)rl.finite_action_set

Set of admissible integer indices into the candidate-pose table at a decision state.

Each row proposes a rigid camera pose; choosing an index selects that pose. The action mask excludes inadmissible rows independently of their predicted utility.

Masked finite action-index set

\[ \mathcal{Q}_t=\{q_{t,i}\}_{i=1}^{N_t},\quad \mathcal{A}(s_t)=\{i\in\{1,\ldots,N_t\}:m_{t,i}=1\},\quad q_t=q_{t,a_t} \]

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selected-action rollout transition

rollout transition core planning.mdp

Aliases rollout transition selected-action transition

Symbols
\(\mathcal{T}\)rl.transition \(\mathcal{P}\)oracle.points \(\mathcal{P}_q\)oracle.points_q
Equations
\(\begin{aligned}\boldsymbol{T}_{\mathsf{C}_{t+1}}^{\mathsf{R}_0}&\leftarrow q_{t,a_t},\\\boldsymbol{H}_{t+1}^{\mathrm{pose}}&\leftarrow(\boldsymbol{H}_t^{\mathrm{pose}},q_{t,a_t}),\\b_{t+1}&\leftarrow b_t-1,\\(\mathcal{Q}_{t+1},\boldsymbol{m}_{t+1}^{\mathrm{act}})&\leftarrow g_{\Xi}(q_{t,a_t},\boldsymbol{H}_{t+1}^{\mathrm{pose}},e)\end{aligned}\)rl.replay_transition_expanded \(\mathcal{P}_t^e=\Phi_e(\operatorname{Concat}(\mathcal{P}_0^{\mathrm{root}},(\mathcal{P}_j^{\mathrm{sel}})_{j<t})),\quad\mathcal{P}_{t\mid i}^e=\Phi_e(\operatorname{Concat}(\mathcal{P}_0^{\mathrm{root}},(\mathcal{P}_j^{\mathrm{sel}})_{j<t},\mathcal{P}_{t,i}^{\mathrm{acq}}))\)rri.shared_transition_states

Update obtained by selecting a candidate action and advancing a simulated or replayed trajectory.

Factual identifies the selected recorded branch in this simulated process, not physical deployment. The selected pose becomes the current pose, history and remaining budget advance, and a new candidate table is generated. Observation updates depend on the state profile: pose-only replay retains root evidence, whereas selected-observation profiles also incorporate the admitted measurements. Oracle reconstruction updates are evaluated separately.

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Root-Normalized Reward

root-normalized reward core metrics.reconstruction_quality

Aliases root-normalized reward fixed-root reward target root-gain reward

Symbols
\(r_t^e\)rl.target_reward \(\mathrm{RRI}^e\)entity.rri_e \(\mathcal{P}\)oracle.points \(\mathcal{M}_e^{\mathrm{GT}}\)ase.mesh_target
Equations
\(r_t^e=(\Delta_t^e-\Delta_{t+1}^e)/(\Delta_0^e+\varepsilon_{\mathrm{err}})\)rl.target_root_gain_reward \(J_t^e=\sum_{k=0}^{t-1}r_k^e=(\Delta_0^e-\Delta_t^e)/(\Delta_0^e+\varepsilon_{\mathrm{err}})\)rl.cumulative_target_root_gain \(\mathrm{RRI}_{t,i}^e=(\Delta_t^e-\Delta_{t\mid i}^e)/(\Delta_t^e+\varepsilon_{\mathrm{err}})\)rl.marginal_target_rri \(C_t^{\mathrm{RRI},e}=\sum_{k=0}^{t-1}\mathrm{RRI}_{k,a_k}^e\)rl.cumulative_target_rri

Signed target-error reduction from one acquisition, divided by the fixed initial target error plus a stabilizer.

For a complete chain measured consistently, its undiscounted sum equals the endpoint gain on that fixed scale. State-relative RRI instead divides by the error immediately before each acquisition.

Target root-gain reward

\[ r_t^e=(\Delta_t^e-\Delta_{t+1}^e)/(\Delta_0^e+\varepsilon_{\mathrm{err}}) \]

Marginal target RRI diagnostic

\[ \mathrm{RRI}_{t,i}^e=(\Delta_t^e-\Delta_{t\mid i}^e)/(\Delta_t^e+\varepsilon_{\mathrm{err}}) \]

Cumulative selected-chain RRI diagnostic

\[ C_t^{\mathrm{RRI},e}=\sum_{k=0}^{t-1}\mathrm{RRI}_{k,a_k}^e \]

Log-improvement follow-up

\[ r_t^{\log,e}=\log(D(\mathcal{P}_t^e,\mathcal{M}_e^{\mathrm{GT}})+\varepsilon_{\mathrm{err}})-\log(D(\mathcal{P}_{t+1}^e,\mathcal{M}_e^{\mathrm{GT}})+\varepsilon_{\mathrm{err}}) \]

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Finite-Horizon Return

return core planning.objective

Aliases h-step return

Symbols
\(G_{t,e}^{(h)}\)rl.return_h \(r_t^e\)rl.target_reward \(\gamma\)rl.gamma \(h\)rl.requested_horizon \(b_t\)rl.budget \(H_{\mathrm{max}}\)rl.H_max
Equations
\(G_{t,e}^{(h)}=\sum_{k=0}^{h-1}\gamma^k r_{t+k}^e,\quad 1\le h\le b_t\le H_{\max}\)rl.finite_horizon_return

Sum of acquisition rewards over a specified prediction horizon, with discounting when specified.

The core objective sums signed root-normalized rewards without discounting. A recorded return describes one realized continuation; an action value is an expected return under a specified continuation rule.

Finite-horizon return

\[ G_{t,e}^{(h)}=\sum_{k=0}^{h-1}\gamma^k r_{t+k}^e,\quad 1\le h\le b_t\le H_{\mathrm{max}} \]

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Finite-Horizon Q Function

Q_H core model.value

Aliases finite-horizon action value finite-horizon candidate value Q_H

Symbols
\(Q_H\)rl.qh \(G_{t,e}^{(h)}\)rl.return_h \(s\)rl.s \(s_t^{\mathrm{S0-pose}}\)rl.s_pose \(s_t^{\mathrm{cf0}}\)rl.s_cf0 \(a\)rl.a
Equations
\(\begin{aligned}Q_{h,e}^{\star,\Xi}(\mathcal{H}_t,q_{t,i})&=\sup_{\pi\in\Pi^{\mathrm{act}}}\mathbb{E}_{\pi, a_t:=i}\left[G_{t,e}^{(h)}\mid\mathcal{H}_t\right],\\&\quad i\in\mathcal{A}_t,\quad 1\le h\le b_t\le H_{\max},\\Q_{0,e}^{\star,\Xi}(\mathcal{H}_t,q_{t,i})&=0\end{aligned}\)rl.q_h \(y_t^Q=r_t+\gamma V(s_{t+1})\)rl.q_backup

Expected finite-horizon return after taking a specified candidate action first.

The continuation policy determines later choices. The ideal optimal value maximizes over policies using the admitted actor information; a learned scorer approximates it from a finite representation. A sampled return, the fitted training target and the predicted value are distinct. The Q function specifies neither encoder architecture nor training algorithm.

Finite-horizon candidate value

\[ Q_{h,e}^{\star,\Xi}(\mathcal{H}_t,q_{t,i})=\sup_{\pi\in\Pi^{\mathrm{act}}}\mathbb{E}_{\pi, a_t:=i}\left[G_{t,e}^{(h)}\mid\mathcal{H}_t\right] \]

Learned Q predictor

\[ \widehat{Q}_{\theta,h}^{\sigma,\Xi}(z_t^{\sigma},e,q_{t,i})\approx Q_{h,e}^{\star,\Xi}(\mathcal{H}_t,q_{t,i}) \]

Action-mask-independent scorer interface

\[ (\widehat{Q}_{\theta,h}^{\sigma,\Xi}(z_t^{\sigma},e,q_{t,i}),\ell_{t,i}^{\mathrm{feas}})=f_\theta(z_t^{\sigma},e,q_{t,i},h) \]

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Validity Mask

validity mask core planning.constraints

Aliases candidate validity mask action-admissibility mask action mask

Symbols
\(m_{t,i}^{\mathrm{act}}\)rl.action_mask \(\rho_{t,i}\)rl.invalid_reason \(m\)vin.cand_valid
Equations
\(\begin{aligned}q_{t,i}&:=\boldsymbol{T}_{\widetilde{\mathsf{C}}_{t,i}}^{\mathsf{R}_0}\in\mathrm{SE}(3),\\\mathcal{Q}_t&=\{q_{t,i}\}_{i=1}^{N_q},\\\mathcal{A}_t&=\{i\in\{1,\ldots,N_q\}:m_{t,i}^{\mathrm{act}}=1\},\quad a_t\in\mathcal{A}_t\end{aligned}\)rl.finite_action_set

Boolean indicator whose true entries identify admissible candidate actions.

It constrains selection separately from utility prediction. An invalid-action mask has the opposite polarity. Label availability and stored-successor availability require separate indicators.

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Acquisition Budget

acquisition budget core planning

Aliases view budget

Limit on the number of acquisitions allowed for a task.

The remaining budget counts acquisitions still available. Asking for a shorter prediction horizon does not change that budget.

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Action Support

action support core planning

Symbols
\(\mathcal{A}_t\)rl.action_set_t \(m_{t,i}^{\mathrm{act}}\)rl.action_mask

Candidate row indices admitted for selection under the declared action-validity rules.

Training-evidence support can be narrower because some admitted actions lack usable labels or recorded successors. A materialized row, an admissible action and a supported learning target are different predicates.

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Actor Information

core planning

Aliases actor-visible information actor inputs

Information permitted to influence action selection under a specified observation protocol.

Observation and target-source profiles specify the admitted historical evidence, earlier selected observations, and target descriptors. The oracle uses reference geometry to evaluate outcomes; exposing that geometry to a privileged control actor does not make it sensor-observed.

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Bootstrap Target

bootstrap target core supervision

Symbols
\(y_t^{(h,e)}\)rl.fitted_target \(B_t^{(h,e)}\)rl.continuation

Fitted training target combining measured immediate reward with estimated continuation value.

The continuation depends on the declared horizon, action support and successor evidence. An unavailable successor does not establish zero future reward. An exact measured continuation control and a learned backup provide different references.

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Candidate Table

candidate table core planning

Aliases candidate shell proposed candidate set

Finite collection of proposed camera poses and their aligned row data at one decision.

A candidate shell need not lie on a sphere. The admissible action set contains only the row indices retained by the validity mask.

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Composite Support Mask

composite support mask core representation

Voxelwise indicator that at least one of the specified source-support conditions is satisfied.

The implemented volume combines root feature-projection and occupancy inputs with semidense and selected-depth votes. A true entry alone does not establish measured surface or free space.

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Continuation Policy

continuation policy core planning

Aliases continuation rule

Rule for choosing later actions after a specified first acquisition.

Its information access and action choices determine which expected return a candidate value describes; the collection policy need not be the continuation being learned.

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Descriptor

descriptor core representation

Quantity or collection of quantities describing relevant properties of a scene, target, history or candidate.

Descriptors may summarize geometry, semantics or acquired support. A descriptor inventory does not imply that every field is available or used; an encoding maps selected descriptors into a model representation.

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Implemented Oracle

implemented oracle core planning

Symbols
\(\pi^{\mathrm{oracle}}\)rl.oracle_policy

Concrete privileged evaluator and collection or search procedure used to generate labels and trajectories.

It may evaluate many immediate candidates while retaining one or several continuations. Its policy, proposal support, search depth and computational budget determine what it explores; privilege alone does not make it optimal.

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Label Availability

label availability core supervision

Aliases label support

Presence of a usable measured training label for a candidate at a decision state.

An admissible action may lack a label. A one-step label does not establish that its successor or full continuation was recorded.

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Learned Encoding

learned encoding core representation

Aliases learned embedding

Model-produced representation of selected inputs.

Its numerical features depend on learned parameters. It is distinct from the descriptor inventory and from a deterministic coordinate transformation.

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Observation Modality

observation modality core representation

Aliases sensor modality

Type of acquired measurement, such as an image or a depth map.

Poses and calibration locate measurements; learned features and support summaries are derived descriptors. Availability, source and actor access must be stated separately.

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Optimal Oracle Value

optimal oracle value core planning

Symbols
\(Q_{h,e}^{*,\mathrm{oracle},\Xi}\)rl.ideal_oracle_q

The highest expected finite-horizon return achievable by a continuation policy admitted to privileged oracle information under the declared decision protocol.

The candidate-generation and execution rules still constrain actions. This privileged optimum differs from an actor-information optimum and is not established by a bounded search or one recorded trajectory.

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Policy-Relative Endpoint-Error Reduction

relative endpoint-error reduction core metrics

Aliases relative endpoint-error reduction

Reduction in endpoint reconstruction error relative to a named comparison policy.

Both policies use the same target task, acquisition budget, reference geometry and reconstruction preparation. Divide the reference-policy error minus the evaluated-policy error by the reference-policy error; the ratio is undefined at zero reference error and unstable near zero.

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Prediction Horizon

prediction horizon core planning

Aliases requested horizon query horizon

Number of future acquisition rewards included in a value query.

It includes the candidate acquired first and is bounded by the remaining acquisition budget; recorded trajectory length is a separate limit.

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Project Aria

core dataset.project_aria

Aliases Aria Project Aria ecosystem

Egocentric research-device and tooling ecosystem for calibrated, time-aligned multimodal sensing.

ARIA-NBV treats Project Aria and its MPS-style products as the actor-visible sensing contract, while ASE meshes remain offline supervision and evaluation assets.

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Recording Cutoff

recording cutoff core planning

Aliases data-collection cutoff

End of data recording before the underlying acquisition task has necessarily ended.

Later rewards are unobserved, not known to be zero. A completed prediction horizon and genuine task termination have different meanings.

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Representation Aliasing

representation aliasing core representation

Symbols
\(z_t^{\sigma}\)rl.representation

Mapping acquired histories with different action consequences to the same scorer representation.

This discards information already acquired. Partial observability also concerns scene information never acquired; the two limitations can coexist.

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Rollout Root

core planning

Aliases initial rollout state

Initial decision state from which a rollout and its comparison budget begin.

It contains the historical observations available up to the reference pose. The root reconstruction error fixes the normalization for root-gain rewards; the current camera pose subsequently changes while the root remains fixed.

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Root-Normalized Endpoint Gain

root-normalized endpoint gain core metrics

Aliases fractional initial-error reduction

Reduction from initial to endpoint target error, divided by the initial error plus a stabilizer.

For complete, consistently measured chains it equals the undiscounted sum of root-normalized rewards. Relative endpoint-error reduction against another policy uses a different denominator.

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Sampled Return

sampled return core planning

Symbols
\(G_{t,e}^{(h,\mathrm{oracle})}\)rl.sampled_oracle_return

Realized sum of acquisition rewards along one trajectory over a stated horizon.

It is one outcome under the named continuation policy, not that policy’s expected value or the best achievable value. Shared-prefix branches are dependent, and retaining only the largest observed returns changes their sampling interpretation.

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Successor Availability

successor availability core supervision

Aliases stored-successor support

Presence of a recorded successor linked to a selected acquisition.

It supports learning from that transition; longer-horizon targets also require the observations and labels needed by their continuation rule.

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Target Reconstruction Error

core metrics

Aliases target point-mesh error

Discrepancy between prepared reconstructed geometry and the fixed reference target mesh.

The implemented point-mesh error sums squared point-to-mesh accuracy and equal-face mesh-to-point completeness terms, in square metres. Equal-face weighting depends on mesh tessellation. Error reduction measures reconstruction improvement.

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Value Calibration

value calibration core model

Symbols
\(\widehat{Q}_{\theta,h}^{\sigma,\Xi}\)rl.learned_q

Agreement of numerical return predictions with the expected return specified by a declared continuation policy and reference population.

It requires suitable independent outcome evidence. Candidate ranking or useful policy selection can succeed without accurate numerical values; a privileged search reference need not equal the actor-achievable expectation.

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Volumetric Fusion

volumetric fusion core representation

Aliases voxel-grid fusion

Integration of spatially aligned information from several observations or sources in a common voxel grid.

The admitted sources and update rule determine its meaning. Combining acquired measurements and learned features does not make every grid cell a measured surface.

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Dataset

Aria Digital Twin

ADT background dataset.aria

Aliases ADT

Project Aria dataset with real-world captures and digital-twin scene annotations.

ADT is adjacent to ARIA-NBV’s sim-to-real context; the current experiments focus on ASE and EFM3D/ATEK exports, while ADT remains a relevant transfer surface.

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Aria Everyday Objects

AEO background dataset.aria

Aliases AEO

Small-scale real-world Project Aria object dataset used by EFM3D for egocentric 3D perception evaluation.

AEO is relevant as a possible sim-to-real check for ARIA-NBV ideas that are first developed on ASE mesh-supervised snippets.

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Virtual Reality Standard

VRS background dataset.file_format

Aliases VRS file Project Aria VRS

File format used by Project Aria tooling to store multi-modal sensor recordings efficiently.

VRS is part of the upstream Project Aria ecosystem, while ARIA-NBV primarily consumes ASE/ATEK-derived tensorized snippets for current experiments.

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Central Pupil Frame

CPF background dataset.frames

Aliases central pupil coordinate frame

Coordinate frame placed at the midpoint between the left and right eye boxes of Project Aria glasses.

CPF is used by Project Aria for gaze-related quantities and should remain distinct from rig, camera, world, and PyTorch3D frames in ARIA-NBV docs.

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Machine Perception Services

MPS background dataset.project_aria

Aliases Project Aria MPS

Project Aria services that derive poses, mapping, and other perception outputs from recordings.

MPS-style poses and semidense points describe available sensing products. They should not be confused with the ASE-depth reconstruction used by the current oracle evaluation.

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SceneScript Language

SSL background dataset.scene_representation

Aliases Structure Scene Language SceneScript structured language

Structured language representation for indoor scene layout using primitives such as walls, doors, windows, and objects.

SceneScript is relevant to ARIA-NBV as a possible semantic/global planning layer and as one source of ASE scene-structure context.

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Motion Trajectory Data

MTD background dataset.stream

Aliases trajectory data pose stream

Device poses over time, usually represented as a sequence of 6-DoF transformations.

MTD supplies the logged egocentric trajectory used to define snippet state, current reconstruction context, and candidate-view reference poses.

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Multi-Semi-Dense Point Data

MSDPD background dataset.stream

Aliases multi-frame semi-dense points semi-dense point stream

Semidense point observations associated with a trajectory or temporal window.

These provide observed geometry for actor features and legacy diagnostics. They are distinct from the rendered-depth clouds used by the current ASE oracle.

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Aria Synthetic Environments

ASE support dataset.synthetic

Aliases Aria Synthetic Environment ASE dataset

Synthetic indoor dataset with simulated Aria observations, trajectories, and scene annotations.

The thesis uses ASE reference meshes and rendered depth to measure target reconstruction improvement. Semidense actor evidence is a separate input, not the default oracle reconstruction source.

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Geometry

Frustum

frustum support geometry.camera

Aliases viewing frustum camera frustum

Camera viewing volume bounded by the field of view and near and far depth limits.

For the pinhole camera model it is a truncated pyramid. Inclusion permits projection into the image but does not imply visibility: other surfaces can occlude a point.

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Left-Up-Forward

LUF support geometry.frames

Aliases LUF frame left up forward

Camera coordinate convention whose x axis points left, y axis points up, and z axis points forward.

LUF is one of the coordinate-frame conventions that must stay explicit when moving between Project Aria cameras, PyTorch3D cameras, and ARIA-NBV candidate poses.

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Degrees of Freedom

DoF background geometry.pose

Aliases DoF

Number of independent parameters describing a pose or permitted motion.

A rigid camera pose has six degrees of freedom: three translation and three rotation. Candidate generation with fixed roll uses a five-degree-of-freedom parameterization while still producing rigid poses in SE(3).

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Six Degrees of Freedom

6DoF background geometry.pose

Aliases 6-DoF 6 degrees of freedom

Pose parameterization with three translational and three rotational degrees of freedom.

Project Aria poses, candidate cameras, and world-to-device transforms are usually represented as 6-DoF rigid-body transforms.

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Metrics

Coverage Ratio

CR support metrics.coverage

Aliases surface coverage ratio

Fraction of a specified target surface or region treated as observed under a stated visibility or distance rule.

Coverage is a diagnostic here. The primary reconstruction objective uses root-normalized error reduction, whose value also depends on the accuracy of reconstructed geometry.

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Area Under Curve

AUC support metrics.evaluation

Aliases AUC

Aggregate score computed by integrating a metric curve over an acquisition, threshold, or ranking axis.

AUC can summarize how quickly reconstruction quality, coverage, or ranking quality improves as views are acquired or candidate thresholds change.

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Ground Truth

GT support metrics.reference

Aliases reference annotation oracle reference

Reference geometry or annotations used to define supervision and evaluation.

In this thesis, ASE meshes and object annotations provide this reference. Their reference role does not make them actor-visible, and the resulting measurements still depend on rendering, sampling, and reconstruction-error conventions.

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Model

Egocentric Foundation Model 3D

EFM3D support model.backbone

Aliases EFM egocentric foundation model

Egocentric 3D perception framework used to extract spatial evidence from observations.

Its EVL architecture supplies frozen features and geometric predictions to the candidate-value model; the perception backbone and the learned planning head serve different roles.

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Egocentric Voxel Lifting

EVL support model.backbone

Aliases voxel lifting EVL backbone

Architecture that lifts synchronized egocentric image evidence into a gravity-aligned voxel feature volume.

EVL belongs to the EFM3D framework. Its features and prediction heads provide observed spatial evidence; they do not by themselves supply observations from unvisited candidate poses.

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View Introspection Network

VIN support model.scoring

Aliases VIN scorer VIN-NBV model Aria-VIN-NBV

Learned model that estimates the utility of a proposed view before acquiring its observation.

The one-step baseline predicts reconstruction improvement from available evidence; the finite-horizon extension predicts return after selecting the candidate and continuing for the requested horizon.

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CORAL Q-Value Decoder

Q-CORAL support model.value.decoder

Aliases CORAL value head ordinal Q decoder finite-horizon CORAL

Symbols
\(\widehat{Q}_{\theta,h}^{\sigma,\Xi}(z_t^{\sigma},e,q_{t,i})\)rl.conditional_q \(e_k^Q\)rl.coral_q_edge \(u_k^Q\)rl.coral_q_value \(c_n^Q\)rl.coral_q_label
Equations
\(\begin{gathered}c_n^Q=\sum_{k=0}^{K-2}\mathbb{1}[y_n>e_k^Q],\quad l_{n,k}=\mathbb{1}[c_n^Q>k];\\ \mathcal{L}_Q^{\mathrm{CORAL}}=-\sum_n\sum_{k=0}^{K-2}\left(l_{n,k}\log p_{n,k}+(1-l_{n,k})\log(1-p_{n,k})\right),\quad p_{n,k}=\sigma(o_{n,k});\\ \pi_{n,k}^{\mathrm{raw}}=p_{n,k-1}-p_{n,k},\quad \widetilde{\pi}_{n,k}=\frac{\max(\pi_{n,k}^{\mathrm{raw}},0)}{\sum_j\max(\pi_{n,j}^{\mathrm{raw}},0)+\varepsilon_{\mathrm{num}}},\quad \widehat Q_n^{\mathrm{cond}}=\sum_{k=0}^{K-1}\widetilde{\pi}_{n,k}u_k^Q\end{gathered}\)rl.qh_coral_interface

Ordinal ablation over the same continuous fitted-Q target as direct regression.

CORAL converts a K-class ordinal label into K-1 cumulative binary targets. The locally archived VIN-NBV method discretizes Oracle RRI into 15 ordered classes and uses CORAL to preserve their order. In the ARIA Q_H ablation, a provenance-bound support maps continuous fitted-Q targets to labels; cumulative threshold logits are decoded through fixed, increasing return representatives to produce the public scalar conditional Q. The support artifact, representative values, non-monotone class-mass repair, and saturation diagnostics are ARIA decoder rules, not properties attributed to CORAL. The ablation never assigns hard-invalid or unsupported rows to the lowest ordinal class.

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Planning

Five Degrees of Freedom

5DoF background planning.action_space

Aliases 5-DoF 5 degrees of freedom

Reduced camera-action parameterization commonly used when roll is fixed or otherwise constrained.

ARIA-NBV uses 5-DoF language for candidate and planning abstractions where position and viewing direction matter while roll is not an independently optimized control dimension.

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Operational Feasibility Teacher

operational teacher support planning.constraints

Aliases recorded operational mask teacher feasibility teacher labels

Symbols
\(z_{t,i}^{F}\)rl.feasibility_teacher \(\ell_{t,i}^{\mathrm{feas}}\)rl.feasibility_logits \(m_{t,i}^{\mathrm{act}}\)rl.action_mask \(m_{t,i}^{\mathrm{cand}}\)rl.candidate_row_mask
Equations
\(\mathcal{I}_t^F=\{i:m_{t,i}^{\mathrm{cand}}=1\},\quad\mathcal{T}_F=\{t:\mathrm{step}_t=1,|\mathcal{I}_t^F|>0\},\quad z_{t,i}^F=m_{t,i}^{\mathrm{act}},\quad\mathcal{L}_F=\frac{1}{|\mathcal{T}_F|}\sum_{t\in\mathcal{T}_F}\frac{1}{|\mathcal{I}_t^F|}\sum_{i\in\mathcal{I}_t^F}\operatorname{BCEWithLogits}(\ell_{t,i}^{\mathrm{feas}},z_{t,i}^F)\)rl.qh_operational_feasibility_bce

Recorded action-mask labels used to supervise auxiliary feasibility prediction.

The teacher reflects the operational validity decisions recorded by the pipeline on materialized candidate rows; it does not certify complete geometric safety. Teacher support is distinct from value-label and successor support.

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Reconstruction

Track

track background reconstruction.features

Aliases feature track 2D track SLAM track

Temporal sequence of corresponding image-feature detections across frames, usually carrying per-frame image coordinates, timestamps, and camera IDs.

Tracks can be triangulated or optimized into 3D points, making them a bridge between image evidence and the semi-dense point clouds used by ARIA-NBV.

\[ \mathcal{T}=\{(u_k,v_k,\mathrm{cam}_k,t_k)\}_{k=0}^{N} \]

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Multi-view Stereo

MVS background reconstruction.geometry

Aliases multiview stereo

Reconstruction of scene geometry from multiple calibrated images.

It is background context for view planning. The current oracle uses ASE rendered depth and reference meshes rather than evaluating a multi-view stereo reconstruction pipeline.

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Visual-Inertial Odometry

VIO background reconstruction.pose

Aliases visual inertial odometry inertial visual odometry

Pose-estimation method that combines visual measurements from cameras with inertial measurements from IMUs.

Project Aria pose and mapping products build on visual-inertial estimation, and ARIA-NBV depends on those pose streams for snippet state and candidate frame contracts.

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Simultaneous Localization and Mapping

SLAM support reconstruction.state

Aliases simultaneous mapping and localization

Joint estimation of sensor motion and a map from observations.

Logged poses and semidense mapping products provide actor-side evidence in this thesis. The default oracle reconstruction measurement instead uses ASE rendered depth and reference meshes.

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Representation

3D Gaussian Splatting

3DGS background representation.radiance_field

Aliases 3D Gaussian Splatting 3DGS Gaussian splatting

Explicit radiance-field representation using optimized 3D Gaussian primitives for real-time novel-view synthesis.

ARIA-NBV treats active 3DGS work as proposal, uncertainty, and simulator-bridge literature, not as a replacement for ASE mesh-supervised RRI.

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Occupancy Grid

support representation.spatial

Aliases occupancy volume

Spatial grid used to represent evidence about occupied and free space.

Unknown space has not been sufficiently observed and is distinct from observed free space. A low occupancy prediction alone does not establish free-space evidence; interpretation depends on the measurement and representation model.

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References

[1]; [2]; [3]; [4]; [5]; [6]; [7]; [8]; [9]; [10]; [11]; [12]; [13]

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References

[1]
W. Cao, V. Mirjalili, and S. Raschka, “Rank consistent ordinal regression for neural networks with application to age estimation.” 2019. Available: https://arxiv.org/abs/1901.07884
[2]
V. Mnih et al., “Playing atari with deep reinforcement learning,” CoRR, vol. abs/1312.5602, 2013, Available: http://arxiv.org/abs/1312.5602
[3]
H. van Hasselt, A. Guez, and D. Silver, “Deep reinforcement learning with double q-learning.” 2015. Available: https://arxiv.org/abs/1509.06461
[4]
J. Straub, D. DeTone, T. Shen, N. Yang, C. Sweeney, and R. Newcombe, “EFM3D: A benchmark for measuring progress towards 3D egocentric foundation models.” 2024. Available: https://arxiv.org/abs/2406.10224
[5]
Meta Platforms Inc., “Egocentric voxel lifting (EVL) documentation.” [Online]. Available: https://facebookresearch.github.io/projectaria_tools/docs/open_models/evl
[6]
Wikipedia contributors, “Frustum.” [Online]. Available: https://en.wikipedia.org/wiki/Frustum
[7]
B. Kerbl, G. Kopanas, T. Leimkuehler, and G. Drettakis, “3D gaussian splatting for real-time radiance field rendering,” ACM Transactions on Graphics, vol. 42, no. 4, 2023, doi: 10.1145/3592433.
[8]
X. Chen, Q. Li, T. Wang, T. Xue, and J. Pang, “GenNBV: Generalizable next-best-view policy for active 3D reconstruction,” in Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, 2024, pp. 16436–16445. Available: https://openaccess.thecvf.com/content/CVPR2024/html/Chen_GenNBV_Generalizable_Next-Best-View_Policy_for_Active_3D_Reconstruction_CVPR_2024_paper.html
[9]
I. Kostrikov, A. Nair, and S. Levine, “Offline reinforcement learning with implicit q-learning.” 2021. Available: https://arxiv.org/abs/2110.06169
[10]
Meta Platforms Inc., “Aria synthetic environments dataset.” [Online]. Available: https://facebookresearch.github.io/projectaria_tools/docs/open_datasets/aria_synthetic_environments_dataset
[11]
A. Avetisyan et al., “SceneScript: Reconstructing scenes with an autoregressive structured language model.” 2024. Available: https://arxiv.org/abs/2403.13064
[12]
N. Frahm et al., “VIN-NBV: A view introspection network for next-best-view selection.” 2025. Available: https://arxiv.org/abs/2505.06219
[13]
J. Engel et al., “Project aria: A new tool for egocentric multi-modal AI research.” 2023. Available: https://arxiv.org/abs/2308.13561