An Automated Thickness Evaluation Procedure Using an Integrated Structured Light 3D Camera in a Robotic Bioprinting Framework

I. INTRODUCTION

• Existing robotic bioprinting studies largely lacked quantitative BPC geometry assessment; reported evaluations instead measured platform motion accuracy or compared images with commanded trajectories.The paper says alignment and uniformity influence cell growth and maturation,, motivating fast, reliable geometric measurements.Source: §I · pp. 1–2
• Earlier thickness methods required manual sample selection or relied on geometric assumptions that excluded straight-line-only or single-valued curve representations,,.The paper notes these assumptions fail for geometries that curve back onto themselves, such as spirals or loops.Source: §I · p. 2
• The method combines RGB-based Canny contour delineation with point-cloud scans and robot end-effector path data to measure BPC thickness automatically.The approach requires no user input and is described as computationally efficient, enabling future real-time optimization of printing parameters.Source: §I · p. 2
• Robotic bioprinting experiments demonstrated the method on printed constructs, complementing simulation validation.The authors report using their algorithms on a robotic bioprinting system; prior to this, the introduction describes the method as validated in simulation and experimental studies.Source: §I · p. 2

II. PROBLEM FORMULATION

• Thickness is the filament dimension parallel to the surface and perpendicular to the printing direction, distinct from height perpendicular to the surface.The defined width is used later for thickness calculation.Source: §II · p. 2
• The segmentation problem divides image pixels into bio-printed material B and background G, then seeks the minimum number of contours satisfying the formulation.The passage identifies pixels in B as material and pixels in G as background.Source: §II · p. 2
• The thickness problem uses an RGB-aligned 3D point cloud and the deposition needle path to determine material thickness along the path.Each RGB pixel corresponds to a possibly noisy 3D point in the point cloud.Source: §II · p. 2

III. APPROACH

• The approach addresses RGB segmentation before thickness calculation, with each distinct material region represented by a contour.Precise delineation matters for subsequent width calculation and should preserve jumps and discontinuities without excessive smoothing.Source: §III · p. 2, A. Delineation and Segmentation · pp. 2–3

A. Delineation and Segmentation

• Canny-based segmentation extracts raw contours, generates rough contours, and fuses them into precise final contours.The pipeline has three stages: raw-contour extraction, rough-contour generation, and contour fusion.Source: A. Delineation and Segmentation · p. 3

1) Raw Contours:

• Raw contours lie on actual boundaries and preserve pixel ordering, but may self-trace, fail to enclose a region, or include reflection boundaries.Multiple raw contours can correspond to one material region.Source: 1) Raw Contours · p. 3

2) Rough Contours:

• Rough contours are generated by filling raw contours, dilating the filled regions to close gaps, then detecting contours; they cover regions but may include background pixels.The rough contours prioritize full region coverage over boundary precision.Source: 2) Rough Contours · p. 3

3) Fusion of Raw and Rough Contours:

• Fusion assigns raw contours mostly inside each rough region, selects nearby raw vertices as anchors, and uses raw-vertex ordering to restore missed boundary segments.Raw contours provide precise boundary locations and ordering, while rough contours separate regions reliably; when anchor points fall on different raw contours, the final contour connects them directly.Source: 3) Fusion of Raw and Rough Contours · p. 3

B. Thickness Calculation

• Thickness at each needle-path point is the distance between the two segmented-boundary intersections in a plane orthogonal to the local path direction.The contours are represented in 3D from the camera point cloud; the method assumes printing occurs on a flat deposition plane.Source: B. Thickness Calculation · p. 3
• The contours are fitted to a plane by minimizing mean squared point-to-plane distance, with the fitted normal obtained from the smallest-eigenvalue eigenvector of P⊤P.The fitted plane supports subsequent contour and path-point projection.Source: B. Thickness Calculation · p. 4
• After projecting contours and path points onto the fitted plane, ray casting identifies the polygon containing each point; points outside all polygons receive zero thickness.The local tangent and contour intersections define left and right side points, and repeating the calculation along the path produces a thickness profile.Source: B. Thickness Calculation · p. 4

IV. EVALUATION STUDIES & RESULTS

• The evaluation uses eight 2D simulation cases with available ground truth for qualitative and quantitative assessment.The studies also assess computational efficiency.Source: §IV · p. 4
• The real-data evaluation applies the algorithm to four cases collected using the robotic setup and 3D camera.These cases are used to demonstrate applicability to real-world scenarios.Source: §IV · p. 4
• All studies use a Jump Threshold of 10, with Canny detection, contour finding, and dilation implemented using Python OpenCV.Source: §IV · p. 4

A. Simulation Data

• The simulation section uses Archimedean and Fermat curves as its two complex spiral-curve families.Source: A. Simulation Data · p. 4
• An Archimedean spiral is parameterized by r = aϕ, or (x, y) = (aϕ cos ϕ, aϕ sin ϕ) in Cartesian coordinates.Source: 2) Fermat spiral · p. 4
• A Fermat spiral has polar form r = ±a√ϕ for ϕ ≥ 0, with the two branches expressed as opposite Cartesian coordinates.The branches are (a√ϕ cos ϕ, a√ϕ sin ϕ) and (−a√ϕ cos ϕ, −a√ϕ sin ϕ).Source: 2) Fermat spiral · p. 4

2) Fermat spiral:

• Fermat spirals use a = 90 and maximum angle ϕ ≤ 2π for both branches; Archimedean spirals use a = 12 and π ≤ ϕ ≤ 6π.Source: 3) Simulation parameters · p. 4, Figure 3 · p. 5

3) Simulation parameters:

• Each simulated robot path has 1,000 points sampled uniformly by arc length to match constant-speed deposition and a fixed sampling rate.The default image is 512 × 512 pixels, with each pixel representing 0.1 mm × 0.1 mm.Source: 3) Simulation parameters · pp. 4–5

4) Thickness simulation:

• Synthetic ground-truth thickness is generated by moving half the specified thickness to either side of each path point along rotated tangent directions.Zero-thickness segments form disconnected polygons, and polygon vertices are discretized to the image resolution.Source: 4) Thickness simulation · p. 5

5) Test cases:

• The test cases cover 2 mm and 4 mm uniform thickness, thickness varying linearly from 1 mm to 4 mm, and interrupted spirals with 10 random gaps.Each gap is about 2% of curve length and may overlap; resolution and thickness are also varied in the performance tests.Source: 5) Test cases · pp. 5–6, Figure 4 · p. 6
• Resolution and thickness tests averaged time or accuracy across 10 curves with 10 random gaps each, measuring runtime and normalized MAE for resolution, and runtime and accuracy for thickness.Thickness used 10 equally spaced samples from 0.4 mm to 4 mm; gap starts were uniform and gap lengths were about 2% of curve length.Source: 5) Test cases · p. 6, Figure 4 · p. 6

• The setup combined a 7-DoF KUKA manipulator, custom extruder-based bioprinter, and structured-light 3D camera with approximately 0.2 mm point-cloud resolution.Source: B. Experimental Studies · p. 6
• Four printed geometries were a straight line, Fermat spiral, Archimedean spiral, and Archimedean spiral with discontinuities.The straight line used injection only over the first half; the spiral prints used constant injection rates.Source: B. Experimental Studies · p. 6
• For each print, the robot path, RGB image, and point cloud were recorded, then RGB segmentation and contour processing supported thickness estimation.The contour was mapped to the point cloud; side points were found for path points, and their distance defined thickness.Source: B. Experimental Studies · p. 6, Figure 6 · p. 7

V. DISCUSSION

• Across resolutions, computation time increased roughly linearly with the number of pixels, while accuracy degraded rapidly as resolution decreased; thickness-calculation MAE and segmentation, thickness-estimation, and overall-pipeline times were averaged over 10 runs.Source: §V · p. 7
• Across thicknesses from 0.5 mm to 4.0 mm, accuracy remained largely independent of thickness and total processing time rose from approximately 70 ms to 90 ms.Source: §V · p. 7
• Hardware experiments lacked ground-truth thickness, so results report mean, standard deviation, and quartiles rather than minimum and maximum.Quartiles were used because calculated thickness may contain linearization noise.Source: §V · p. 7
• The Fermat and Archimedean spirals had an average thickness standard deviation of 0.34 mm, while the half-injected line had a 1.280 mm standard deviation as thickness decayed after injection stopped.Source: §V · p. 8
• Mean absolute thickness errors ranged from 0.025 mm to 0.057 mm across simulated shapes and profiles at 0.1 mm × 0.1 mm spatial resolution.Across the simulation cases, the maximum absolute error was approximately 0.15 mm, about one pixel, with discretization identified as the main error source.Source: §V · p. 7, §VI · p. 8

VI. CONCLUSION

• The proposed framework combines RGB-based BPC segmentation with geometry-driven thickness measurement from point-cloud scans.The conclusion describes validation through simulation and experimental studies.Source: §VI · p. 8
• Future work will integrate the framework into closed-loop printing for on-demand feedback to modulate deposition rate and robot velocity, including multilayer, multimaterial tasks.Source: §VI · p. 8