Joint Angle-Based Refinement (JAR)

• JAR is an angle-centric refinement paradigm that transforms noisy observations into stable angular representations for improved accuracy.
• It applies consistent angular corrections across domains such as deblurring, human pose estimation, robotics, and communications to enforce kinematic and physical constraints.
• Its multi-stage optimization framework leverages coarse initialization followed by progressive angular correction to enhance performance in diverse applications.

Joint Angle-Based Refinement (JAR) denotes a family of refinement procedures in which angular variables are treated as primary state variables, conditioning signals, or physically meaningful latent parameters rather than as incidental outputs. Across the cited literature, the term is not used as a single standardized label: it is explicit in marker-free human pose estimation, while several other works can be read as natural JAR instantiations because they refine trajectories, reconstructions, or dynamical models by diagnosing, estimating, or constraining angle-dependent structure (Peng et al., 15 Jul 2025, Lai et al., 30 Nov 2025, Fabisch, 2019, Kasani et al., 2024, Gao et al., 11 May 2026, Xi et al., 28 Nov 2025). This suggests that JAR is best understood as an angle-centric refinement paradigm rather than a single algorithm.

1. Terminological scope and conceptual core

The cited works use or motivate JAR in materially different domains. In rotational deblurring, CAR-Net jointly corrects blur angle information and progressively refines a deblurred image under semi-blind angle uncertainty (Lai et al., 30 Nov 2025). In robot skill learning, joint-space policy search refines demonstrated skills directly in joint coordinates, with comparison against Cartesian-space refinement mediated by inverse kinematics (Fabisch, 2019). In ergonomic posture analysis, joint angles are predicted from partially occluded 2D observations and can then be used as constraints for downstream pose correction (Kasani et al., 2024). In marker-free human pose estimation, JAR is a post-processing pipeline that converts HRNet keypoints to joint angles, regularizes them temporally, and reconstructs refined coordinates (Peng et al., 15 Jul 2025). In articulated-object simulation, JAR corresponds to gradient-based refinement of joint dynamics parameterized over joint angle (Gao et al., 11 May 2026). In near-field XL-MIMO, angle estimates obtained gridlessly are used to bootstrap joint angle-range nonlinear refinement under the exact spherical model (Xi et al., 28 Nov 2025).

Domain	Angle variable	Refinement target
Rotational deblurring	Blur angle $\theta$	Deblurred image
Robot skill refinement	Joint angles $q(t)$	Demonstrated policy
Ergonomic pose analysis	Body-part joint angles	Pose interpretation or refinement
Marker-free HPE	12 joint angles from 13 keypoints	Spatiotemporal keypoint trajectories
Articulated-object dynamics	Normalized joint coordinate $s$	Joint-level dynamics field
Near-field XL-MIMO	AoA $\theta$ and range $r$	Channel and user localization

A common conceptual thread is the replacement of a poorly conditioned or noisy observation space by an angle-structured intermediate representation. This suggests a recurring design pattern: an initial estimate is formed from noisy observations, angular variables are inferred or corrected, and refinement then proceeds under kinematic, physical, or geometric consistency constraints.

2. Mathematical role of angle parameterization

In the deblurring setting, the underlying motivation is model simplification. Rotational blur is spatially variant in Cartesian coordinates,

$B = I \otimes H(\theta, c) + n,$

but after mapping to the Polar Coordinate System (PCS) it becomes a 1D circular convolution along the angular axis,

$g_p = f_p * K_p(\theta_{GT}, c) + n_p.$

Angle uncertainty is modeled as $\theta_{\text{initial}} = \theta_{GT} + \epsilon$ with $\epsilon \sim N(0,\sigma^2)$, and mismatch in $K_p(\theta)$ directly causes ringing and residual blur in inversion (Lai et al., 30 Nov 2025).

In human pose estimation, the angle parameterization is kinematic rather than optical. The ergonomic prediction work derives target angles from body-part triplets using

$q(t)$0

and organizes the image as a structured relation tensor over OpenPose joints and connections, so that missing joints can be handled through masking and learned inter-joint structure (Kasani et al., 2024). The HRNet post-processing work instead forms 12 joint angles from 13 keypoints using an atan2-based construction on parent–joint–child vectors, treating angle trajectories as the stable representation to be denoised and regularized over time (Peng et al., 15 Jul 2025).

In articulated-object dynamics, angle parameterization becomes the state variable of the dynamics itself. JODA normalizes the joint coordinate to

$q(t)$1

and defines a three-channel field over $q(t)$2: conservative force/torque $q(t)$3, dry friction magnitude $q(t)$4, and damping coefficient $q(t)$5. The internal torque is decomposed as

$q(t)$6

with $q(t)$7 (Gao et al., 11 May 2026).

In near-field XL-MIMO, the angle variable appears jointly with range. Under a second-order approximation of the spherical-wave steering vector, the $q(t)$8th element is represented as

$q(t)$9

where $s$0 and $s$1. This separates a far-field complex exponential from a chirp-like modulation, enabling gridless angle recovery before joint angle-range refinement (Xi et al., 28 Nov 2025).

These formulations indicate that angle parameterization serves at least three mathematically distinct roles: reducing model complexity, encoding kinematic invariants, and exposing low-dimensional physical structure.

3. Refinement mechanisms and optimization patterns

A defining property of JAR systems is that refinement is not a single pass. In CAR-Net, deblurring begins with a numerically stabilized inverse filter in PCS,

$s$2

followed by a cascade of residual stages

$s$3

for $s$4, with the original blurred observation $s$5 concatenated at every stage. The paper reports $s$6 as optimal, with a fourth stage slightly degrading PSNR from $s$7 dB to $s$8 dB (Lai et al., 30 Nov 2025).

The same paper couples refinement to angle correction through an Angle Detection Module. A first inversion using $s$9 yields a deliberately coarse $\theta$0; the module regresses $\theta$1 from $\theta$2 and $\theta$3; a second inversion using $\theta$4 produces $\theta$5 for refinement. Training uses

$\theta$6

with $\theta$7, $\theta$8, $\theta$9, and $r$0 in CAR-Net-AD (Lai et al., 30 Nov 2025).

In the HRNet post-processing pipeline, refinement is temporal. Joint-angle trajectories are modeled by an 8th-order Fourier series,

$r$1

with $r$2, and a two-layer BiGRU-Attention network refines noisy angle windows of length 100 frames using MSE in angle space. Long videos are handled by overlapping windows and distance-weighted aggregation,

$r$3

with $r$4 (Peng et al., 15 Jul 2025).

Optimization strategies differ by domain but preserve the same angle-centric logic. Robot skill refinement uses CMA-ES over DMP weights, with joint-space initial step size empirically set to be 2–3 times larger than Cartesian-space $r$5 to induce similar end-effector variability (Fabisch, 2019). JODA uses Adam for differentiable refinement through MJX rollouts, starting from a VLM-generated initialization of angle-dependent dynamical primitives (Gao et al., 11 May 2026). Near-field XL-MIMO first solves a convex regularized atomic norm problem to extract angles gridlessly, then refines angles and ranges jointly under exact spherical geometry using alternating gradient descent with Armijo backtracking (Xi et al., 28 Nov 2025).

A recurring implication is that JAR methods separate initialization from refinement rather than attempting to solve the full problem in one stage.

4. Imaging and vision instantiations

In rotational motion deblurring, CAR-Net is an explicit example of joint use of angle information and progressive refinement. The architecture operates entirely in PCS apart from non-trainable CPT/PCT transforms, uses Adam with initial learning rate $r$6, ReduceLROnPlateau, 200 epochs, batch size 4, $r$7, and $r$8 for the re-blur physics loss (Lai et al., 30 Nov 2025). Under angle noise, the practical role of angle correction is visible in the reported robustness: CAR-Net-Base changes from $r$9 at $B = I \otimes H(\theta, c) + n,$0 to $B = I \otimes H(\theta, c) + n,$1 at $B = I \otimes H(\theta, c) + n,$2, whereas CAR-Net-AD remains at $B = I \otimes H(\theta, c) + n,$3 for both $B = I \otimes H(\theta, c) + n,$4 and $B = I \otimes H(\theta, c) + n,$5. Module ablations at $B = I \otimes H(\theta, c) + n,$6 further show inversion-only at $B = I \otimes H(\theta, c) + n,$7 dB / $B = I \otimes H(\theta, c) + n,$8, AD alone at $B = I \otimes H(\theta, c) + n,$9 dB / $g_p = f_p * K_p(\theta_{GT}, c) + n_p.$0, refinement alone at $g_p = f_p * K_p(\theta_{GT}, c) + n_p.$1 dB / $g_p = f_p * K_p(\theta_{GT}, c) + n_p.$2, and AD + refinement at $g_p = f_p * K_p(\theta_{GT}, c) + n_p.$3 dB / $g_p = f_p * K_p(\theta_{GT}, c) + n_p.$4 (Lai et al., 30 Nov 2025).

The same results also delimit the method’s scope. The semi-blind formulation assumes $g_p = f_p * K_p(\theta_{GT}, c) + n_p.$5 is reasonably close to $g_p = f_p * K_p(\theta_{GT}, c) + n_p.$6 and within the training range of $g_p = f_p * K_p(\theta_{GT}, c) + n_p.$7–$g_p = f_p * K_p(\theta_{GT}, c) + n_p.$8; the rotation center $g_p = f_p * K_p(\theta_{GT}, c) + n_p.$9 is fixed and known; evaluation is restricted to the central circular ROI because PCT corners can be undefined; and 3D effects such as deocclusions and lens distortions are not modeled in the 2D blur synthesis (Lai et al., 30 Nov 2025). The physics prior is likewise domain-dependent: on simple patterns, $\theta_{\text{initial}} = \theta_{GT} + \epsilon$0 caused training collapse at $\theta_{\text{initial}} = \theta_{GT} + \epsilon$1 dB, while $\theta_{\text{initial}} = \theta_{GT} + \epsilon$2 improved performance to $\theta_{\text{initial}} = \theta_{GT} + \epsilon$3 dB; on real-world images, $\theta_{\text{initial}} = \theta_{GT} + \epsilon$4 was best at $\theta_{\text{initial}} = \theta_{GT} + \epsilon$5 dB and $\theta_{\text{initial}} = \theta_{GT} + \epsilon$6 slightly degraded to $\theta_{\text{initial}} = \theta_{GT} + \epsilon$7 dB (Lai et al., 30 Nov 2025). This directly contradicts any assumption that stronger physical regularization is uniformly preferable.

In static human posture analysis for ergonomics, the cited method does not itself perform explicit keypoint refinement, but predicts joint angles robustly under partial visibility and can be integrated into a refinement stage. OpenPose keypoints are normalized by a scale factor of $\theta_{\text{initial}} = \theta_{GT} + \epsilon$8, recentered at joint 8, and converted into a $\theta_{\text{initial}} = \theta_{GT} + \epsilon$9 relational tensor whose channels are displacement, distance, and confidence-derived features. The final model is a set of 16 CNN regressors, trained with Adam, learning rate $\epsilon \sim N(0,\sigma^2)$0, batch size 128, and RMSE loss (Kasani et al., 2024). Reported test performance is RMSE $\epsilon \sim N(0,\sigma^2)$1 and MAE $\epsilon \sim N(0,\sigma^2)$2 on the test dataset, with per-angle errors ranging from $\epsilon \sim N(0,\sigma^2)$3 for NBL to $\epsilon \sim N(0,\sigma^2)$4 for SR2 (Kasani et al., 2024).

The marker-free HPE JAR pipeline makes the refinement step explicit. HRNet keypoints are converted to angles, the nose trajectory is smoothed by a Savitzky–Golay quadratic fit with window $\epsilon \sim N(0,\sigma^2)$5, limb lengths are stabilized by a trust-region optimization that enforces inter-limb ratios and frame-to-frame constancy, and refined angles are decoded back to coordinates via forward kinematics (Peng et al., 15 Jul 2025). In challenging athletic motion, the paper reports outlier correction rates of $\epsilon \sim N(0,\sigma^2)$6 versus $\epsilon \sim N(0,\sigma^2)$7 for standing triple jump, $\epsilon \sim N(0,\sigma^2)$8 versus $\epsilon \sim N(0,\sigma^2)$9 for sprint, and an overall rate of $K_p(\theta)$0, “nearly 2× SmoothNet” (Peng et al., 15 Jul 2025). The comparison highlights a characteristic JAR advantage in vision: refinement in angle space can correct left-right confusions and suppress temporal jitter without retraining the base detector.

5. Robotics, articulated dynamics, and control

In robot skill refinement, JAR corresponds to policy search in joint space. The policy outputs joint-angle trajectories directly through DMPs, with 50 weights per dimension and fixed metaparameters, and rewards are computed from end-effector behavior plus joint-velocity and joint-acceleration penalties (Fabisch, 2019). For the viapoint task,

$K_p(\theta)$1

while obstacle avoidance and pouring use distinct non-separable reward structures (Fabisch, 2019).

The empirical comparison is not uniformly favorable to JAR. In the viapoint and obstacle-avoidance tasks, Cartesian-space refinement with the proposed approximate IK is more sample-efficient than JAR, and exact pseudoinverse-based IK is worse because infeasible Cartesian targets generate rough reward surfaces (Fabisch, 2019). In the pouring task, by contrast, JAR and Cartesian refinement perform nearly identically, while exact IK again performs worse. A central conclusion of that work is therefore conditional rather than absolute: Cartesian refinement is advantageous when objectives are defined in Cartesian space and rewards are nearly separable, whereas JAR is competitive when the reward landscape is highly nonlinear and non-smooth or when IK instability would distort optimization (Fabisch, 2019).

In articulated-object simulation, JAR operates over the dynamics rather than the pose. JODA represents each joint’s behavior as composable PCHIP-based profiles over normalized angle $K_p(\theta)$2, allowing detents, bistability, magnetic return, spring return, dry friction, and damping to be specified as local components that sum or form envelopes across three channels (Gao et al., 11 May 2026). A VLM first proposes effect templates with intervals and qualitative strengths; these are compiled into numeric PCHIP fields; differentiable MJX simulation then supports gradient-based refinement against observed trajectories. In the reported “natural release” cabinet-door experiment, trajectory MSE is reduced from $K_p(\theta)$3 to $K_p(\theta)$4 after 9 Adam steps (Gao et al., 11 May 2026).

The method’s limitations are explicit. JODA is restricted to single-DOF, three-channel fields, does not model hidden-state or explicit hysteresis, omits multi-DOF couplings, and smooths dry friction for differentiability (Gao et al., 11 May 2026). The refinement remains interpretable because conservative force, dry friction magnitude, and damping coefficient are separately parameterized, but identifiability is not guaranteed: multiple field configurations can explain similar trajectories.

6. Communications interpretation and cross-domain assessment

Near-field XL-MIMO provides a distinctly different JAR formulation. Stage I solves a gridless super-resolution problem by lifting the near-field channel into a matrix with atomic norm structure. The unknown chirp waveforms lie in a common DCR subspace with dimension $K_p(\theta)$5, reducing effective degrees of freedom and enabling a semidefinite formulation of regularized atomic norm minimization (Xi et al., 28 Nov 2025). Continuous angle estimates are obtained from a Vandermonde decomposition of the Toeplitz moment matrix, converted by

$K_p(\theta)$6

and combined with a closed-form coarse range estimate derived from the chirp ratio (Xi et al., 28 Nov 2025).

Stage II is the JAR step proper: the exact spherical steering model

$K_p(\theta)$7

is used in a nonlinear least-squares refinement over both $K_p(\theta)$8 and $K_p(\theta)$9, initialized by the Stage-I angles and coarse ranges. The reduced objective is

$q(t)$00

and the paper uses alternating gradient descent with Armijo backtracking to refine angle and range jointly (Xi et al., 28 Nov 2025). Simulations with $q(t)$01, $q(t)$02 GHz, $q(t)$03, $q(t)$04, $q(t)$05, and $q(t)$06 show that ANM(SI+SII) outperforms Stage I alone and the listed on-grid and off-grid baselines in moderate- to high-SNR regimes, with especially clear gains for SNR $q(t)$07 dB (Xi et al., 28 Nov 2025).

Across the six cited domains, several cross-cutting features recur. First, JAR almost always relies on a strong initializer: CAR-Net assumes a usable $q(t)$08; the HRNet post-processor assumes reasonable keypoints overall; JODA benefits from VLM priors and trajectory data; the XL-MIMO refinement stage depends on accurate gridless Stage-I angles (Lai et al., 30 Nov 2025, Peng et al., 15 Jul 2025, Gao et al., 11 May 2026, Xi et al., 28 Nov 2025). Second, JAR methods usually impose structure that is easier to express in angle space than in raw observation space: kinematic limits, limb-length constancy, Fourier smoothness, physical re-blur consistency, or exact spherical geometry. Third, superiority is not universal. The robotics comparison shows that angle- or joint-space refinement can lose to Cartesian refinement when the task objective is nearly separable in Cartesian coordinates and IK is well behaved (Fabisch, 2019).

These patterns suggest that JAR is most effective when angular variables concentrate the dominant invariants of the problem and when refinement can exploit explicit physics or geometry that would be difficult to impose directly in the original signal space.