MRReP: Innovations in Robotics, Radiomics, QC

• MRReP is a multidisciplinary term representing innovative research in robotics mixed reality interfaces, MRI radiomics for glioma, and quality control process monitoring.
• In robotics, MRReP employs a HoloLens-based hand-drawn path interface with real-time ROS integration, achieving significant improvements in path accuracy and usability.
• For quality control, MRReP utilizes a ratio–product exponential estimator to reduce the average run length for mean shifts, while MRI radiomics applies fractal features for rapid early progression prediction.

MRReP refers to three distinct but technically rigorous research contributions in robotics, medical image analysis, and industrial quality control, each delineated by its specific domain context and mathematical underpinnings. The term has appeared as: (1) Mixed Reality-based Hand-drawn Reference Path Editing Interface for mobile robot navigation (Taki et al., 31 Mar 2026), (2) MRI Radiomics for Rapid Early Progression (REP) prediction in glioma patients (Farzana et al., 2023), and (3) the Mrep (MRReP) repetitive sampling control chart in industrial process monitoring (Rafique et al., 6 Oct 2025). Each of these MRReP technologies employs domain-specific innovations with explicit mathematical formulations and evaluation protocols.

1. Mixed Reality-based Hand-drawn Reference Path Editing for Mobile Robots

MRReP, as introduced by Cook et al., designates a mixed reality (MR) interface that enables explicit, gesture-driven path specification for autonomous mobile robots in human-shared environments (Taki et al., 31 Mar 2026). The system operationalizes human spatial intention by allowing a user to hand-draw a reference path (HRP) directly onto the physical floor via HoloLens 2, with real-time robotic stack integration through ROS 2.

Key interface elements include:

• Optical see-through MR head-mounted display (HoloLens 2)
• Unity 3D running an application employing the Vuforia Engine for AprilTag/QR localization
• Multi-stage coordinate frame alignment between Unity (U), ROS 2 map (M), and robot base (R), using $T_{M \leftarrow U} \in SE(3)$

Hand gestures are interpreted with MRTK/HoloLens APIs. The “pinch” gesture, sampled at ~30 Hz with 0.2 m waypoint threshold, constructs a path segment. Upon pinch release, the HRP is finalized and transmitted through ROS-TCP-Connector to the /hrp_points topic.

The corresponding planner architecture avoids any smoothing, global re-planning, or cost-map optimization; the HRP sequence is directly mapped into the $nav\_msgs/Path$ message, and a custom Nav2 GlobalPlanner plugin simply returns this path for downstream Regulated Pure Pursuit control. Orientation for each path pose is determined by the tangent between consecutive HRP points: $$\theta_i = \mathrm{atan2}(y_{i+1} - y_i,\; x_{i+1} - x_i)$$; the quaternion is $q_i = [0, 0, \sin(\theta_i/2), \cos(\theta_i/2)]^T$.

Quantitative evaluation via a within-subjects study (n=16) against a 2D map-drawing baseline revealed statistically significant improvements in path accuracy and human factors metrics (SUS, NASA-TLX), with the MRReP interface achieving 100% median HRP-in-ground-truth for complex paths (p=0.00121), F1-scores of 88.1% (stage A) and 83.4% (stage B), and a SUS of 75.0 vs 51.3 for the 2D baseline. Task completion time was higher for MRReP, attributable to users' ability to perceive and finely adjust path deviations in situ.

Limitations identified include arm fatigue, gesture recognition errors, and field-of-view constraints intrinsic to HoloLens 2. The system pipeline, including messaging, transforms, and plugin logic, is specified for reproducibility (Taki et al., 31 Mar 2026).

2. MRI Radiomics for Rapid Early Progression (REP) in Glioma

In neuro-oncology, MRReP refers to a computational framework for predicting rapid early progression (REP) and stratifying survival risk in grade 4 glioma using MRI radiomics (Farzana et al., 2023). The pipeline extracts, selects, and fuses conventional first-order, shape, texture (GLCM, NGTDM, GLZSM), and multi-resolution fractal features (PTPSA, mBm, GmBm) from skull-stripped, denoised, and intensity-matched T1C MR images (1mm³ resampled voxels, affine registration via FSL-FLIRT).

Fractal descriptors are derived as follows:

• Piecewise Triangular Prism Surface Area (PTPSA), with fractal dimension $D = 2 - \lim_{s \to 0} [\log A(s) / \log s]$
• Multi-resolution Brownian motion (mBm), with local structure function $S_2(s) \sim C \cdot s^{2H}$
• Generalized multifractal modeling (GmBm) via Hölder exponents $\alpha(x)$

Feature selection is a two-step process using repeated random sub-sampling and 5-fold CV, accepting features with mean $F_1 \geq 0.6$ and $p < 0.05$. CatBoost ensemble classifiers are trained and evaluated with 1000x5-fold CV. For REP prediction, fractal features yield an AUC of $0.793 \pm 0.082$ vs $nav\_msgs/Path$0 for conventional features, and a PPV of $nav\_msgs/Path$1 vs $nav\_msgs/Path$2.

Survival analysis employs copula-graphic estimation under dependent censoring, using a semiparametric Cox model extended via a Clayton copula: $nav\_msgs/Path$3, with survival times modeled as $nav\_msgs/Path$4. Prognostic indices are constructed as $nav\_msgs/Path$5, defining risk groups; fractal features achieve superior group separation (D=0.157, p=0.014) and capture 84.62% of REP cases in the bad prognostic group.

Binary survival outcomes, modeled with top copula-selected features, show further fractal advantage in AUC ($nav\_msgs/Path$6) and PPV ($nav\_msgs/Path$7). The addition of IDH molecular marker marginally improves PPV but not AUC; MGMT methylation lacks significance (p=0.965). These results indicate multi-resolution fractal texture features substantially enhance REP and survival discrimination over standard radiomics.

3. Repetitive Sampling Control Chart (Mrep) for Process Monitoring

MRReP (“Mrep”), as formalized in quality control, is a Shewhart-type chart using a ratio–product exponential-type estimator for the process mean, implemented under repetitive sampling with a single auxiliary variable $nav\_msgs/Path$8 (Rafique et al., 6 Oct 2025). This method is designed to improve sensitivity to shifts in the process mean when strong correlation exists between the measured characteristic $nav\_msgs/Path$9 and $$\theta_i = \mathrm{atan2}(y_{i+1} - y_i,\; x_{i+1} - x_i)$$0.

The RP-exponential estimator for the population mean $$\theta_i = \mathrm{atan2}(y_{i+1} - y_i,\; x_{i+1} - x_i)$$1 is: $$\theta_i = \mathrm{atan2}(y_{i+1} - y_i,\; x_{i+1} - x_i)$$2 where $$\theta_i = \mathrm{atan2}(y_{i+1} - y_i,\; x_{i+1} - x_i)$$3 are subgroup means, $$\theta_i = \mathrm{atan2}(y_{i+1} - y_i,\; x_{i+1} - x_i)$$4 is the known auxiliary mean, and $$\theta_i = \mathrm{atan2}(y_{i+1} - y_i,\; x_{i+1} - x_i)$$5 is optimized as: $$\theta_i = \mathrm{atan2}(y_{i+1} - y_i,\; x_{i+1} - x_i)$$6 The control charting statistic is set as $$\theta_i = \mathrm{atan2}(y_{i+1} - y_i,\; x_{i+1} - x_i)$$7. Under in-control conditions, $$\theta_i = \mathrm{atan2}(y_{i+1} - y_i,\; x_{i+1} - x_i)$$8 is approximately Gaussian: $$\theta_i = \mathrm{atan2}(y_{i+1} - y_i,\; x_{i+1} - x_i)$$9 for subgroup size $q_i = [0, 0, \sin(\theta_i/2), \cos(\theta_i/2)]^T$0. Classical $q_i = [0, 0, \sin(\theta_i/2), \cos(\theta_i/2)]^T$1 limits are applied. Average Run Length (ARL) under in-control ($q_i = [0, 0, \sin(\theta_i/2), \cos(\theta_i/2)]^T$2) and shifted conditions ($q_i = [0, 0, \sin(\theta_i/2), \cos(\theta_i/2)]^T$3) are computed with closed-form expressions; for $q_i = [0, 0, \sin(\theta_i/2), \cos(\theta_i/2)]^T$4-size mean shifts: $q_i = [0, 0, \sin(\theta_i/2), \cos(\theta_i/2)]^T$5

Monte Carlo studies show that for strong auxiliary correlation ($q_i = [0, 0, \sin(\theta_i/2), \cos(\theta_i/2)]^T$6), the Mrep chart reduces $q_i = [0, 0, \sin(\theta_i/2), \cos(\theta_i/2)]^T$7 by up to 30% compared with the regression-based $q_i = [0, 0, \sin(\theta_i/2), \cos(\theta_i/2)]^T$8 chart for $q_i = [0, 0, \sin(\theta_i/2), \cos(\theta_i/2)]^T$9 and moderate shifts ($D = 2 - \lim_{s \to 0} [\log A(s) / \log s]$0–2). Performance improvement is most marked for detection of modest mean shifts, endorsing the method for settings with reliable auxiliary variables.

4. Core Mathematical and Algorithmic Frameworks

Each MRReP context leverages rigorous mathematical models suited to the target application:

• Robotics: Rigid-body transformations in $D = 2 - \lim_{s \to 0} [\log A(s) / \log s]$1, tangent-based orientation assignment, and direct $D = 2 - \lim_{s \to 0} [\log A(s) / \log s]$2 construction with quaternion orientation; no global optimization or smoothing applied (Taki et al., 31 Mar 2026).
• Radiomics: Multi-stream feature extraction (GLCM, PTPSA, mBm), CatBoost ensemble modeling, significance filtering, and copula-graphic survival estimation with semiparametric Cox modeling and Clayton copula for dependent censoring (Farzana et al., 2023).
• Quality Control: Ratio–product exponential-type estimator, optimization of estimator weights by coefficients of variation and correlation, analytical ARL calculations under Normal approximation, and repetitive sampling protocol (Rafique et al., 6 Oct 2025).

5. Comparative Evaluation and Empirical Results

A common thread across MRReP implementations is the explicit empirical benchmark against conventional baselines, using domain-standard accuracy and usability metrics:

• In robot navigation, MRReP demonstrates increased path accuracy (e.g., Stage B F1-score 83.4% vs. 56.5% for 2D) and usability (SUS 75.0 vs. 51.3; NASA-TLX 47.7 vs. 61.5), at the expense of increased completion time (Taki et al., 31 Mar 2026).
• In radiomics, fractal-based MRReP outperforms conventional features in REP classification (AUC +0.120), survival precision (PPV +0.009), and prognostic group separation (D=0.157 vs. 0.128), with significance by ANOVA and Wald test (Farzana et al., 2023).
• For quality charts, simulation demonstrates Mrep's ARL reduction (up to 30%) for moderate shifts over traditional regression-based charts, particularly where auxiliary correlation is strong (Rafique et al., 6 Oct 2025).

6. Limitations and Domain-Specific Challenges

Each version of MRReP is constrained by context-specific technical or user limitations:

• Robotics MRReP: Physical fatigue, MR gesture recognition failures, and limited HoloLens field of view are documented constraints, as well as the lack of path smoothing or global replanning (Taki et al., 31 Mar 2026).
• Radiomics MRReP: Reliant on high-quality, preprocessed 3D MRI data and the statistical significance of fractal features; limited further gain from molecular markers such as MGMT (Farzana et al., 2023).
• Mrep chart: Maximum benefit is observed only with high $D = 2 - \lim_{s \to 0} [\log A(s) / \log s]$3-$D = 2 - \lim_{s \to 0} [\log A(s) / \log s]$4 correlation and moderate sample sizes; increased sampling rounds may incur cost or time penalties in practice (Rafique et al., 6 Oct 2025).

7. Application Scope and Reproducibility

MRReP technology in these domains is algorithmically well-specified and experimentally validated, supporting direct replication:

• Source code and experimental materials for the MR-based path editing are available as specified in (Taki et al., 31 Mar 2026).
• Radiomics feature extraction, selection, and modeling are described with sufficiently detailed steps for implementation from standard radiomics/machine-learning tools (Farzana et al., 2023).
• The Mrep quality chart provides all necessary formulas for limit setting and ARL calculation; implementation involves standard computational statistics and repetitive sampling procedures (Rafique et al., 6 Oct 2025).