Synthetic Deformable Tubular Benchmark: A mechanically annotated dataset for evaluating deformable 3D reconstruction
Organizations: Universidad de Zaragoza · Universidad de Zaragoza, Pedro Cerbuna 12, 50009 Zaragoza, Spain
Abstract
Evaluating deformable 3D reconstruction requires ground truth linking camera motion, surface deformation, material correspondence and image appearance. We introduce the Synthetic Deformable Tubular Benchmark, generated with LumenMorph, an open-source toolkit for creating, annotating and evaluating tubular scenes. The release contains 5,580 RGB images. Its baseline crosses three surface-motion conditions with moving and stationary cameras in six scene families; matched appearance variants cover only moving-camera finite-element actions in four families. Documented public and evaluation interfaces expose camera poses, geometry, depth, deformation fields, persistent material correspondences and discrete finite-element records. Persistent triangle identities and material weights let users track the same surface location across frames and query its three-dimensional trajectory. Separately implemented geometric and mechanical checks assess annotation consistency with the generating models. Structure-from-motion, optical-flow and supplied-geometry displacement-interpolation studies demonstrate how the resource distinguishes registration coverage from geometric accuracy, exposes camera- and surface-motion effects, and tests the benefits and mismatch of mechanical priors. Public readers, evaluation contracts and the configurable generator support reuse and extension. Data integrity, fixed-environment repeatability and retained-prediction score replay have distinct verification scopes. The benchmark provides a controlled synthetic reference without claiming anatomical or clinical realism.
Figures & tables
| Resource | Established capability | Relevant distinction |
|---|---|---|
| SimCol3D; RealSynCol | Synthetic colon depth/pose; broader anatomy or appearance | Rich geometric annotations precede this resource. |
| C3VD; C3VDv2 | Real imaging of phantoms; dense registered static labels | C3VDv2 deformation videos lack dense per-step labels. |
| DynamicColon | Deforming geometry with per-step point clouds and depth | Cage-based motion; three reported scenes. |
| C3VD-DEFCOL | Parameterized dynamic geometry and depth-conditioned appearance | Geometric motion; reported biomechanical and appearance-alignment limits. |
| VR-Caps; SimIntestine | Capsule simulation with varied acquisition or peristalsis | Different acquisition setting; complete mechanical export schemas not verified here. |
| SimuScope | Surgical simulation with deformable tissues and instruments | Adjacent anatomy/task; mechanics is established simulation practice. |
| Family | Centerline | Motion scale | Static / FE / non-FE | Original role | Appearance |
|---|---|---|---|---|---|
| f01 | Straight | v1 / v2 / v3 | Development | Yes | |
| f02 | Right turn, | v4 / v5 / v6 | Development | No | |
| f03 | Upward turn, | v7 / v8 / v9 | Development | No | |
| f04 | Left , down | v10 / v11 / v12 | Validation | Yes | |
| f05 | Right turn, | v13 / v14 / v15 | Recovery test | Yes | |
| f06 | Up , left | v16 / v17 / v18 | Recovery test | Yes |
| Record | Content | Information boundary |
|---|---|---|
| public/ | RGB, intrinsics, timestamps, acquisition metadata, shared reference links | Sensor/acquisition inputs |
| evaluation/<stream>/states.npz | Vertices, displacements, camera transforms, time | Evaluator-only prescribed geometry |
| evaluation/<stream>/dense/*.npz | Depth, face ID, material barycentrics, normals, valid mask | Evaluator-only dense truth |
| evaluation/<stream>/flow_forward/*.npz | Pixel flow and visibility categories | Evaluator-only correspondence truth |
| evaluation/family/ | FE nodes, elements, parameters, stiffness and response bases | Generating-model state, not inferred tissue |
| reconstruction/ ; bundles_moving/ | Estimated reference/action globals and local models; image/window mapping | Independently estimated additional inputs |
| Annotation | Baseline bank | Appearance extension |
|---|---|---|
| RGB, calibration, timestamps | Stored | Stored for five matched conditions |
| Camera poses, deformed vertices, topology | Stored | Stored; shared by appearance conditions |
| Depth, validity, triangle ID, material weights | Stored dense maps | Stored fresh tracer labels |
| World positions, face normals | Positions derived; normals stored | Derived by appearance reader |
| Material trajectories and displacement | Derived from identity and states | Derived from identity and metre-valued states |
| Next-frame flow and visibility categories | Stored; arbitrary stored-time pairs derivable | Material projection derivable; no equivalent occlusion classification |
| Task | Required prediction | Evaluation contract |
|---|---|---|
| Per-frame geometry | Camera-z depth or oriented world normals at source pixels | Absolute depth / angular normal error and coverage |
| Image correspondence | Next-frame pixel displacement | Flow endpoint error and coverage on fixed visible support; separate visibility strata |
| Material motion | for the material point visible at source | 3D endpoint error against , with source-valid denominator |
| Complete deformable reconstruction | Estimated cameras and a time-indexed surface with predicted cross-time material associations | Camera errors, bidirectional geometry/support and material-motion error, each with coverage and declared gauge |
| Supplied-geometry interpolation | Displacement field from sparse observations, supplied geometry/identities and declared mechanical records | Displacement error under that privileged-input contract; not image-only reconstruction |
| Family | |||
|---|---|---|---|
| f01 | 0.00994 | 0.04022 | 0.99076 |
| f02 | 0.01087 | 0.03571 | 0.99193 |
| f03 | 0.02047 | 0.14501 | 0.98030 |
| f04 | 0.00876 | 0.04245 | 0.99109 |
| f05 | 0.01168 | 0.07836 | 0.98845 |
| f06 | 0.01912 | 0.08372 | 0.98323 |
| Motion | Noise | Zero | RBF | FE | FE |
|---|---|---|---|---|---|
| Static | 0.000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |
| Static | 0.001 | 0.000000 | 0.001090 | 0.000888 | 0.000886 |
| Static | 0.010 | 0.000000 | 0.010896 | 0.008879 | 0.008858 |
| FE | 0.000 | 0.032708 | 0.000278 | 0.000207 | 0.000208 |
| FE | 0.001 | 0.032708 | 0.001224 | 0.000984 | 0.000983 |
| FE | 0.010 | 0.032708 | 0.011442 | 0.009276 | 0.009255 |
| Acquisition | Min. sequence median / | Max. sequence median / |
|---|---|---|
| Rigid reference | 0.001006 | 0.002230 |
| Static action | 0.000608 | 0.001263 |
| FE action | 0.016414 | 0.050363 |
| Non-FE action | 0.019402 | 0.035162 |
| Family | Model | A coverage | A ATE (mm) | B coverage | B ATE (mm) | (mm) |
|---|---|---|---|---|---|---|
| f01 | global | 90/90 | 0.3154 | 90/90 | 0.3156 | 0.0001997 |
| f01 | local | 15/15 | 0.003651 | 15/15 | 0.003418 | -0.0002324 |
| f04 | global | 90/90 | 0.4944 | 90/90 | 0.4947 | 0.0002967 |
| f04 | local | 15/15 | 0.006227 | 15/15 | 0.004536 | -0.001691 |
| f05 | global | 90/90 | 0.4789 | 90/90 | 0.48 | 0.001186 |
| f05 | local | 15/15 | 0.00434 | 15/15 | 0.003798 | -0.0005421 |
| Case | Pipeline | Models | Max. coverage | ATE (mm) | Abs. rot. ( ∘ ) |
|---|---|---|---|---|---|
| trans 0–60 | A | 1 | 2/61 | — | — |
| trans 0–60 | B | 1 | 2/61 | — | — |
| desc 0–29 | A | 1 | 30/30 | 0.08297 | 28.72 |
| desc 0–29 | B | 1 | 30/30 | 0.08298 | 27.16 |
| desc 30–59 | A | 1 | 30/30 | 0.02939 | 10.55 |
| desc 30–59 | B | 1 | 30/30 | 0.02926 | 10.16 |
| Family | Condition | A points | B points | A RMSE | B RMSE | A support | B support |
|---|---|---|---|---|---|---|---|
| f01 | D | 6039 | 5600 | 1.306 | 1.462 | 0.4641 | 0.4754 |
| f01 | C | 3554 | 3337 | 1.352 | 1.806 | 0.7033 | 0.7303 |
| f01 | As | 5973 | 5450 | 1.158 | 0.7982 | 0.4684 | 0.4853 |
| f01 | 0.5E | 3569 | 3378 | 0.8694 | 0.5672 | 0.7187 | 0.7367 |
| f01 | 2E | 9319 | 8544 | 2.657 | 0.8892 | 0.3543 | 0.3648 |
| f04 | D | 5726 | 5328 | 3.71 | 3.412 | 0.4774 | 0.4922 |
| Motion | Camera | Zero | Farnebäck | DIS | RAFT |
|---|---|---|---|---|---|
| static | moving | 9.378 | 0.3954 | 0.2082 | 0.1878 |
| static | stationary | 1.126e-05 | 0.01962 | 0.0208 | 0.008854 |
| fem | moving | 9.385 | 0.3936 | 0.2084 | 0.1883 |
| fem | stationary | 0.6793 | 0.05887 | 0.0375 | 0.04739 |
| nonfem | moving | 9.261 | 0.3928 | 0.2086 | 0.1893 |
| nonfem | stationary | 0.8128 | 0.0637 | 0.04083 | 0.04416 |
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.