MonoPCA: Rethinking Geometric Depth in Monocular 3D Object Detection

Depth error of GeoDepth vs PCDepth, and the geometric origin of the bias — **(a)** Even with *ground-truth* f, H, and h_2D, the classic GeoDepth formula incurs a depth error that grows with object size. PCDepth removes most of it. **(b)** Under perspective projection, the 2D box height encodes the visible front surface, not the object center.

TL;DR

The ubiquitous geometric depth z = f·H / h_2D measures the depth of an object's front surface, not its center. We derive a closed-form, parameter-free correction (PCDepth) and pair it with a distillation framework (GeoAlign) that sharpens the size and yaw predictions the correction relies on.

+1.44

AP_3D Mod. on the
KITTI leaderboard

+2.80

AP on
Omni3D_OUT

+2.32

AP_3D Mod. on
nuScenes val

−13%

GFLOPs vs. MonoCoP
(71.8 → 62.5)

Key Insight

For an object with thickness, the tight 2D box height h_2D is set by the box corner nearest to the camera. Plugging it into f·H / h_2D therefore returns that corner's depth, z − Δ, where Δ is the box's half-extent along the optical axis. Drag the controls to see how the bias depends on size and yaw.

GeoDepth: front surface PCDepth: object center

Yaw γ30° Length L3.9 m Width W1.6 m Center depth z20 m

GeoDepth—

True center—

Underestimation—

Idealized geometry (pinhole camera, upright box, tight 2D box), as in Eq. (PCDepth) of the paper. Sizes for the presets are typical values, not dataset statistics.

Abstract

Monocular 3D detection (Mono3D) hinges on recovering depth from a single image, for which the geometric formulation z ≈ f·H / h_2D is widely adopted due to its simplicity and direct grounding in projective geometry. We show that this formulation harbors a systematic, projection-induced bias: substituting the 2D bounding-box height h_2D recovers the depth of an object's visible front surface rather than its center, causing size-dependent underestimation that persists even under ground-truth inputs. We address this front-surface bias with MonoPCA, a unified framework built on a projection-consistent reformulation. At its core, PCDepth retains the measurable h_2D and closes the gap to center depth through an orientation- and size-aware correction derived from perspective geometry, eliminating the bias without introducing ill-posed regression targets. Because PCDepth couples depth to predicted object size and orientation, attribute perception becomes essential. We therefore introduce GeoAlign, a teacher–student framework that transfers geometric representations from Vision Foundation Models into a lightweight student, strengthening attribute perception at no inference cost. Across four challenging benchmarks, MonoPCA achieves state-of-the-art performance, including a +1.44% AP_3D gain on the KITTI leaderboard and +2.80% on Omni3D_OUT.

Method

Overview of the MonoPCA framework — **Overview of MonoPCA.** PCDepth corrects the projection bias analytically, making depth an explicit function of the predicted 3D size and yaw. GeoAlign strengthens those attributes by distilling a Mixture-of-Backbone (MoB) teacher into a ResNet student via Hierarchical Feature Alignment (HFA). The teacher is discarded after training.

PCDepth

parameter-free

Regressing the center-aligned height h′_2D is ill-posed: it depends on the very depth we want. Instead, PCDepth keeps the observable h_2D and adds back the optical-axis half-extent of the box footprint in closed form:

Δ reduces to W/2 at γ = 0° and L/2 at γ = 90°. Because depth is now computed from predicted attributes, the dedicated depth encoder and depth-guided decoder are no longer needed.

GeoAlign

no inference cost

PCDepth ties depth accuracy to size and yaw. GeoAlign builds a high-capacity teacher with a Mixture-of-Backbone that fuses a ResNet pyramid with a Vision Foundation Model (EVA-CLIP) through scale-wise matching and attention, then distills it into a standard ResNet-50 student.

Cosine alignment is invariant to the magnitude gap between a VFM-enriched teacher and a ResNet student, and spans all four pyramid scales.

**Geometric basis of PCDepth.** (a) Source of the front-surface bias. (b) h′_2D is depth-dependent, so regressing it is ill-posed. (c) Recovering center depth via an optical-axis correction.

Mixture-of-Backbone details — **Mixture-of-Backbone.** MoB adaptively fuses a convolutional pyramid with a single-scale VFM branch at every scale.

Results

To our knowledge, MonoPCA is the first monocular detector to reach state of the art on both the KITTI leaderboard and Omni3D_OUT.

KITTI leaderboard (test) and val, Car, IoU_3D ≥ 0.7. Bold: best among methods without extra data; underline: second best.

Method	Extra data	Test AP_3D			Test AP_BEV			Val AP_3D			Val AP_BEV
Method	Extra data	Easy	Mod.	Hard	Easy	Mod.	Hard	Easy	Mod.	Hard	Easy	Mod.	Hard
OccupancyM3D	LiDAR	25.55	17.02	14.79	35.38	24.18	21.37	26.87	19.96	17.15	35.72	26.60	23.68
OPA-3D	Depth	24.68	17.17	14.14	32.50	23.14	20.30	24.97	19.40	16.59	33.80	25.51	22.13
MonoTAKD	LiDAR	27.91	19.43	16.51	38.75	27.76	24.14	34.36	22.61	19.88	42.86	29.41	26.47
MonoCon	—	22.50	16.46	13.95	31.12	22.10	19.00	26.33	19.01	15.98	—	—	—
MonoDETR	—	25.00	16.47	13.58	33.60	22.11	18.60	28.84	20.61	16.38	37.86	26.95	22.80
MonoUNI	—	24.75	16.73	13.49	—	—	—	24.51	17.18	14.01	—	—	—
FD3D	—	25.38	17.12	14.50	34.20	23.72	20.76	28.22	20.23	17.04	36.98	26.77	23.16
MonoMAE	—	25.60	18.84	16.78	34.15	24.93	21.76	30.29	20.90	17.61	40.26	27.08	23.14
MonoCD	—	25.53	16.59	14.53	33.41	22.81	19.57	26.45	19.37	16.38	34.60	24.96	21.51
MonoDGP	—	26.35	18.72	15.97	35.24	25.23	22.02	30.76	22.34	19.02	39.40	28.20	24.42
MonoCoP	—	27.54	19.11	16.33	36.77	25.57	22.62	32.06	23.98	20.64	41.92	30.75	27.06
MonoPCA (ours)	—	30.34	20.55	17.84	38.65	26.63	24.43	35.86	26.22	23.58	46.29	33.89	30.05
Δ vs. second best		+2.80	+1.44	+1.06	+1.88	+1.06	+1.81	+3.80	+2.24	+2.94	+4.37	+3.14	+2.99

nuScenes val (front camera), Car. Bold: best; underline: second best.

Method	IoU_3D ≥ 0.7				IoU_3D ≥ 0.5
	AP_3D		AP_BEV		AP_3D		AP_BEV
	Easy	Mod.	Easy	Mod.	Easy	Mod.	Easy	Mod.
GUP Net	8.50	7.40	14.21	12.81	29.03	26.16	33.42	30.23
DEVIANT	9.69	8.33	16.28	14.36	31.47	28.22	35.61	31.93
MonoDETR	9.53	8.19	16.39	14.41	31.81	28.35	35.70	31.96
MonoDGP	10.04	8.78	16.55	14.53	29.56	26.17	32.67	29.44
MonoCoP	10.85	9.71	17.83	15.86	33.70	29.91	37.44	34.01
MonoPCA (ours)	13.75	12.03	20.97	18.49	38.50	34.11	42.03	38.49
Δ vs. second best	+2.90	+2.32	+3.14	+2.63	+4.80	+4.20	+4.59	+4.48

Omni3D (AP averaged over IoU_3D thresholds 0.05–0.50) alongside the KITTI leaderboard AP_3D.

Method	Omni3D_OUT						KITTI leaderboard
Method	AP^kit	AP^nus	AP^out	AP^large	AP^small	AP^car	Easy	Mod.	Hard
MonoDGP	—	—	—	—	—	—	26.35	18.72	15.97
MonoCoP	—	—	—	—	—	—	27.54	19.11	16.33
ImVoxelNet	23.5	23.4	21.5	—	—	—	17.15	10.97	9.15
SMOKE	25.9	20.4	20.0	—	—	—	14.03	9.76	7.84
Cube R-CNN	36.0	32.7	31.9	37.6	21.8	72.9	23.59	15.01	12.56
DetAny3D	35.8	33.9	32.2	—	—	—	26.89	18.67	15.48
MonoPCA (ours)	38.1	37.0	35.0	38.8	25.4	77.0	30.34	20.55	17.84
Δ vs. second best	+2.1	+3.1	+2.8	+1.2	+3.6	+4.1	+2.80	+1.44	+1.51

KITTI leaderboard AP_3D Mod. vs. model cost. PCDepth is parameter-free and the GeoAlign teacher is discarded after training.

MonoDGP18.7238.9M · 69.0 GFLOPs

MonoCoP19.1142.5M · 71.8 GFLOPs

MonoPCA20.5542.0M · 62.5 GFLOPs

Radar chart comparing MonoPCA with previous state of the art — **Across the board.** MonoPCA vs. the previous best on each benchmark.

PCDepth improves MonoDETR, MonoDGP and MonoCoP — **Plug-and-play.** Swapping only the depth head for PCDepth improves MonoDETR, MonoDGP, and MonoCoP by +1.54, +1.37, and +1.09 AP_3D on KITTI val.

Which depth formulation?

KITTI val, AP_3D Mod. (IoU_3D ≥ 0.7), full MonoPCA with only the depth formulation changed.

Direct regression23.82

GeoDepth with h′_2D24.18

GeoDepth with h_2D24.73

PCDepth (ours)26.22

Regressing the unobservable h′_2D hurts; keeping the observable h_2D and correcting it analytically gives +1.49 over GeoDepth.

Per-distance size, orientation and depth errors — **GeoAlign lowers the errors PCDepth depends on.** Per-distance size, orientation, and depth errors on KITTI val. Better attributes propagate directly into better depth.

Qualitative Results

Qualitative comparison with DetAny3D on Omni3D

Top: DetAny3D. Bottom: MonoPCA. Image-plane predictions (left) and bird's-eye view with a 1 m grid (right). MonoPCA is more accurate on distant and small objects such as pedestrians.

MonoPCA predictions on KITTI, with bird's-eye views. Click to enlarge.

MonoPCA predictions on nuScenes, with bird's-eye views. Click to enlarge.

BibTeX

@inproceedings{zhang2026rethinking,
  title     = {Rethinking Geometric Depth in Monocular 3D Object Detection:
               A Projection-Consistent Reformulation},
  author    = {Zhang, Zhihao and Kumar, Abhinav and Qu, Huaizhi and
               Chen, Tianlong and Liu, Xiaoming},
  booktitle = {Advances in Neural Information Processing Systems (NeurIPS)},
  year      = {2026}
}