Synthetic Deformable Tubular Benchmark: A mechanically annotated dataset for evaluating deformable 3D reconstruction

Íñigo Cirauqui-Viloria

Figure 1: Six controlled scene families: one straight tube (f01), single bends to the right or upward (f02, f03, f05), and two successive bends (f04, f06). Geometry views share a common scale; the right column shows each family’s reference image with its seeded wall texture. f03 and f06 use twice the displacement-basis amplitudes of the other families. Table 2 specifies bend angles and paired acquisitions.

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.

Table 1: Comparison based on primary publications and author release descriptions. It is not an independent numerical validation of competing archives. C3VD-DEFCOL’s release repository lists the dataset as forthcoming ( Durr Lab, n.d. ) ; reported capability and downloadable availability are distinct. An unverified export is not evidence that it does not exist. The distinction claimed here is an explicit, accessible and checked connection between annotations, not priority for depth, displacement or FE simulation individually. The six engineered families do not establish clinical realism.

Figure 2: Information flow through LumenMorph and the usage studies. Generation produces both public image inputs and evaluator-only truth. Image-based methods receive the upper route; their predictions are compared with the lower route during scoring. Independently implemented validation also checks truth against the generating geometry and mechanics. Registration, accuracy and surface support are reported separately, so a missing or incomplete output cannot masquerade as a low error. Below, one baseline f01 FEM moving-camera frame (52) links RGB, camera-z depth, persistent material position, displacement from rest, next-frame flow (52 to 53) and deformed surface geometry. The material colour is rest longitudinal position, not a new material label; triangle IDs and barycentrics carry the actual identity. Depth and displacement are normalized by the reference radius

R

. Flow colour encodes direction and magnitude in pixels; its key gives the display scale. Background is grey in truth maps. The surface view cuts away the near wall for display; all annotations use the complete surface. Codex (version not recorded) assisted the diagram and plotting code.

Family	Centerline	Motion scale	Static / FE / non-FE	Original role	Appearance
f01	Straight	$1\times$	v1 / v2 / v3	Development	Yes
f02	Right turn, $30^{\circ}$	$1\times$	v4 / v5 / v6	Development	No
f03	Upward turn, $35^{\circ}$	$2\times$	v7 / v8 / v9	Development	No
f04	Left $27^{\circ}$ , down $20^{\circ}$	$1\times$	v10 / v11 / v12	Validation	Yes
f05	Right turn, $38^{\circ}$	$1\times$	v13 / v14 / v15	Recovery test	Yes
f06	Up $25^{\circ}$ , left $25^{\circ}$	$2\times$	v16 / v17 / v18	Recovery test	Yes

Table 2: Complete family/package map. Turns describe the configured centerline; seeded wall perturbations, texture, camera offset and angular load locations also vary by family. The motion multiplier scales all three spatial bases within each motion class (Section 2.2 ); it is not the peak composed displacement. Every row supplies seven baseline streams: one rigid reference and three motion conditions observed by two camera modes, or 630 images per family. Each “Yes” adds five 90-frame appearance streams of the moving FE action, or 450 images, without adding a new anatomy. Roles are original design assignments: all six families have been inspected for dataset generation/reconstruction quality checks and are not unseen reconstruction tests.

Figure 3: Stored f01 weights for the three displacement bases. (a) The complete action alternates rest, two rises and two plateaux before returning to rest. The phase strip identifies the six 15-frame intervals, and the orange box locates the enlarged region. (b) The first rise and low plateau expose the weight of 0.02 and the three different transition profiles. A weight multiplies a vector-valued spatial basis; it is not displacement divided by radius. FE and non-FE actions use this schedule, whereas static actions apply zero displacement. Frames are action-local.

Figure 4: From the mechanical wall to the rendering surface. The intact and cutaway views show the stored f01 mesh; the cutaway hides its upper half for viewing only. Element topology and interpolation are schematics. The modeled wall has no longitudinal opening. Codex (version not recorded) assisted the topology and interpolation code.

Figure 5: Stored f01 motion at frame 52. The upper row shows the three-dimensional surface at its true deformation scale, coloured by displacement magnitude divided by reference radius

R

; colours average vertex magnitudes per face. Grey lines project the rest wireframe. Below, the retained RGB and image-space material maps use the same stationary camera; each foreground pixel measures its material point’s displacement from rest. Both colour scales span

0

–

0.08R

, without motion magnification. Grey in the image maps denotes background; black denotes zero displacement. FE and non-FE fields have different prescribed amplitudes.

Figure 6: Matched appearance at f01/frame 67. Each column shows one retained RGB image and enlarges the same cyan-marked

240\times 240

-pixel wall region (rows 120–359, columns 80–319, zero-based). To reveal the darker wall, both RGB rows use the identical display mapping

I_{\mathrm{display}}=\sqrt{I/255}

on every saved encoded channel

I\in[0,255]

. This is a viewing adjustment, not regenerated illumination; there is no per-image normalization. The bottom row makes changes relative to diffuse symmetric visible: each pixel is the mean absolute difference of its three original encoded RGB channels after division by 255, before display brightening. A common square-root color scale resolves subtle lighting changes without saturating any displayed value; these are image differences, not physical radiance or reconstruction errors. Geometry, camera and texture coordinates are identical across columns. Lighting redistributes left/right power, coating changes reflectance, and exposure applies a 0.5 or 2 gain to the baseline linear radiance before encoding.

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

Table 3: Records in a baseline condition package benchmark/vN and their inference/evaluation roles. Paths are relative to that package; <stream> denotes moving or stationary, and relative links provide the shared family/reference assets. The collection contains 24 global and 162 local reconstructions in total, not in each package. Public images, calibration and clocks are separated from privileged geometry, correspondence and mechanics. Dense and forward-flow records describe the baseline bank; the appearance add-on provides fresh tracer labels and cross-time projection, but not baseline-equivalent occlusion-aware flow. Reconstructed models are estimated outputs, not substitutes for ground truth. Lossy MP4 previews are illustrative; PNGs are the canonical images.

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

Table 4: Annotation availability, separate from access permissions. “Derived” means computed from released records, not estimated from RGB. Non-FE actions have prescribed kinematics without applied FE equilibrium; static/reference fields are zero. Appearance coordinates use the declared render-world metre scale and do not calibrate FE forces or tissue properties. The baseline CLI scorer is not an automatic adapter for the appearance schema.

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	$\widehat{\Delta X}_{s,t}(p)$ for the material point visible at source $s$	3D endpoint error against $X_{t}(m_{p})-X_{s}(m_{p})$ , 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

Table 5: Tasks enabled by the linked annotations. The dense CLI implements the first three task rows for the baseline schema; surface and camera scoring use the separate study tools. Complete deformable reconstruction is a defined evaluation target, not a claim that the present studies solve it or that one CLI command scores an arbitrary dynamic representation.

Figure 7: Spatial interpretation of the reconstruction experiment. (a) The ground-truth moving-camera trajectory and the local frames 60–74 inside the f01 appearance wall at frame 67, which is constant over this plateau. The near half of the wall is omitted for display; the complete mesh is used for scoring. Camera glyphs indicate recorded positions/orientations, not calibrated fields of view. (b,c) Retained A-SIFT1 and B-ORDER1 local reconstructions for the diffuse-symmetric condition, repeat 1. Points and cameras use each model’s recorded center-fitted Sim(3), expressed in the same render-world basis; there is no additional surface fit or absolute-scale recovery claim. Each pipeline has one view retaining every point, including outliers, with identical A/B bounds and scale. Scale bars use the assigned millimeter render-world scale. (d,e) Schematic cross-sections distinguish point-to-surface error from the distance of fixed visible-surface samples to reconstructed points; they contain no experimental measurements. Codex (version not recorded) assisted the schematic code in (d,e).

Family	$\max\|\epsilon_{ij}\|$	$\max_{t}\rho_{t}$	$\min\det F$
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

Table 6: Minimum and maximum diagnostics over each retained 90-state FE audit.

\epsilon

is the infinitesimal strain tensor,

F=I+\nabla u

, and

E_{G}=\tfrac{1}{2}(F^{T}F-I)

. Here

\rho_{t}=\|E_{G}-\epsilon\|_{F}/\max(\|\epsilon\|_{F},10^{-30})

, with each norm taken over all elements, Gauss points and tensor components at that time; the table reports

\max_{t}\rho_{t}

, not a maximum pointwise ratio. The diagnostics characterize the declared small-strain model.

Motion	Noise	Zero	RBF	FE $10^{-4}$	FE $10^{-2}$
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

Table 7: Mean heldout material displacement endpoint error divided by

R

, with equal family weighting over f01–f04. Noise is the observation component standard deviation divided by

R

. Each FE/non-FE cell includes 36 requested cases (four families, three times, three seeds); each static cell includes 12. Zero-noise repetitions share identical observations. All methods have full finite coverage on 5,224 heldout vertices per case.

Acquisition	Min. sequence median / $R$	Max. sequence median / $R$
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

Table 8: Ranges of per-sequence global median camera-position errors across six families, after separate proper Sim(3) evaluation fits. Errors are divided by each family’s median reference radius

R

; each column is the minimum or maximum of six sequence medians, not a pooled point/camera percentile or an uncertainty interval. Every global model registers 90/90 frames. The rigid reference and static moving action are separate acquisitions.

Figure 8: Complete registration does not imply accurate cameras. Each marker is one global reconstruction’s median camera-center error after its own proper similarity fit, expressed as a percentage of the family’s reference radius

R

(logarithmic axis). Connected markers share a family across four acquisitions; right-hand labels identify each line. All 24 models register 90/90 frames. The deformation conditions have larger errors, but differing motion amplitudes and fields prevent a single-factor causal interpretation. Table 8 gives the ranges in unscaled fractions of

R

.

Family	Model	A coverage	A ATE (mm)	B coverage	B ATE (mm)	$B-A$ (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

Table 9: Diffuse-symmetric synthetic baseline. A and B denote A-SIFT1 and the B-ORDER1 mapper with its declared inherited matching inputs. ATE is camera-center RMSE in millimeters after each model’s own proper similarity fit. Global uses moving-action frames 0–89; local uses the consecutive frames 60–74, independently reconstructed as defined in Section 2.8 . Global spans changing wall states; local observes a constant deformed state. Their temporal supports and separate similarity fits differ, so the global/local errors do not isolate the benefit of local reconstruction. The final column fits both models on the same requested frames. Entries summarize three computational repetitions, whose values coincide exactly; they are not independent scenes or uncertainty intervals.

Figure 9: Camera-center ATE RMSE under each model’s own evaluation similarity fit, in millimeters. D: diffuse symmetric; C: coated symmetric; As: diffuse asymmetric; 0.5E and 2E: half and double exposure of the diffuse-symmetric condition. Global and local denote independently reconstructed 90-frame and 15-consecutive-frame trajectories, respectively (Section 2.8 ); indices are action-local. Each family has its own vertical limits with a zero origin. Markers summarize three computational repetitions; their min–max ranges are zero. Every model registers its complete requested trajectory.

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

Table 10: Complete source-calibrated static-phantom controls. The public color images and published calibration are remapped as described in Section 2.12 . Coverage is the largest registered requested-frame count in any returned fragment; every returned fragment is counted in Models. ATE is center RMSE in millimeters, and Abs. rot. is mean absolute angular error in degrees, after the proper similarity fit to camera centers without an extra camera-axis offset. A dash denotes an unidentifiable gauge. Full registration of the descending subsets coexists with mean orientation errors of 10.2–28.7 degrees; registration and small fitted center errors do not establish accurate camera orientations. Each row summarizes three exactly agreeing computational repetitions.

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

Table 11: Complete local appearance comparison. Condition codes follow Figure 9 . Point counts retain all reconstructed points. RMSE is point-to-surface distance; Support is the median distance from the fixed visible-wall support to its nearest reconstructed point. Both distances are in millimeters and lower is better. Each value is the median of three exactly agreeing computational repetitions, not an uncertainty estimate. All 15 requested local frames register in every case.

Figure 10: Local point counts, geometric error and support answer different questions. Distance panels show millimeters on a logarithmic scale above 0.001 mm, with a linear region below it; counts use a linear scale from zero. Vertical limits vary by family. Condition codes follow Figure 9 ; three-repeat min–max ranges are zero. Table 11 gives every numerical value; the accompanying metric records additionally retain medians and outlier tails.

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

Table 12: Visible-pixel mean endpoint error (pixels) on the corrected matched 144-pair development cohort. Eight source pairs are averaged within each family, followed by equal weighting of the three families. Three computational repetitions are summarized by their median; their predictions and score rows are exactly equal. Every visible eligible vector has a finite prediction.

Synthetic Deformable Tubular Benchmark: A mechanically annotated dataset for evaluating deformable 3D reconstruction

Abstract

Figures & tables

Appendix

3D Reconstruction Benchmarks

Future Rendering $\neq$ Future Surface: A Benchmark and Dataset for Dynamic Surface Reconstruction Beyond the Observed Window

Deform360: A Massive Multi-view Visuotactile Dataset for Deformable World Models

TrackDeform3D: Markerless and Autonomous 3D Keypoint Tracking and Dataset Collection for Deformable Objects

Abstract

3D Reconstruction Benchmarks

Explore similar work

Future Rendering ≠\neq= Future Surface: A Benchmark and Dataset for Dynamic Surface Reconstruction Beyond the Observed Window

Deform360: A Massive Multi-view Visuotactile Dataset for Deformable World Models

TrackDeform3D: Markerless and Autonomous 3D Keypoint Tracking and Dataset Collection for Deformable Objects

Future Rendering $\neq$ Future Surface: A Benchmark and Dataset for Dynamic Surface Reconstruction Beyond the Observed Window