Near-light Photometric Stereo with Symmetric Lights

Lilika Makabe; Heng Guo; Hiroaki Santo; Fumio Okura; Yasuyuki Matsushita

cs.CVMar 17, 2026

Near-light Photometric Stereo with Symmetric Lights

Authors: Lilika Makabe, Heng Guo, Hiroaki Santo, Fumio Okura, Yasuyuki Matsushita

Organizations: Graduate School of Information Science and Technology, Osaka University, Japan.

Abstract

This paper describes a linear solution method for near-light photometric stereo by exploiting symmetric light source arrangements. Unlike conventional non-convex optimization approaches, by arranging multiple sets of symmetric nearby light source pairs, our method derives a closed-form solution for surface normal and depth without requiring initialization. In addition, our method works as long as the light sources are symmetrically distributed about an arbitrary point even when the entire spatial offset is uncalibrated. Experiments showcase the accuracy of shape recovery accuracy of our method, achieving comparable results to the state-of-the-art calibrated near-light photometric stereo method while significantly reducing requirements of careful depth initialization and light calibration.

Figures & tables

Fig. 1 : Examples of light source arrangement for our method. At least three pairs of symmetric point light sources are arranged to the image plane with a shared center. Our near-light photometric stereo achieves global minima in shape recovery using the proposed symmetric near-light configuration.

Light model	Method	Light calibration	Light arrangement	Optimization	Additional requirements
Distant	[ 1 ]	Calibrated	N.A	Convex	N.A
	[ 2 ]	Partially calibrated	Axis-aligned symmetric	Convex	Constant albedo
	[ 3 ] , [ 4 , 5 ]	Partially calibrated	Ring	Convex	Integrability
	[ 6 ]	Uncalibrated	N.A.	Convex	Integrability, diffuse maxima detection
Near	[ 7 ] , [ 8 , 9 , 10 ]	Calibrated	N.A	Non-convex	Depth initialization
	[ 11 ]	Calibrated	Ring	Non-convex	Depth initialization

TABLE I : Comparison of photometric stereo methods under Lambertian reflectance. Our method assumes a more practical light model, requires less light calibration effort, and provides convex and linear optimization to achieve the global optima of surface normal and depth.

Fig. 2 : Overview of the proposed method. We consider the differences and summations of observations under the symmetric light pairs and construct a linear optimization system to estimate light-to-surface (scaled) distance $e_{*}$ . From the scaled distance $e_{*}$ , we compute the surface position (up to scale if radii are unknown) and normal.

Fig. 4 : Relative vector relation.

Fig. 5 : Examples of valid/invalid light arrangements.

Fig. 6 : Light arrangements used in the synthetic experiments. In every case, we set the inner and outer radii as

1

and

2

Panel of Figure 8 — Fig. 7 : Estimation results of our method and comparison methods, with the global offset along $z$ -axis $\mathbf{s}_{o}=\left[0.0,0.0,0.5\right]$ added to the center of the symmetric light pairs. The left-hand side and right-hand side columns show the estimations from $n_{\mathrm{pairs}}=3$ and $n_{\mathrm{pairs}}=4$ cases, respectively. We show the normal maps and depth maps along with the corresponding error maps, as well as a mean angular (for normal)/relative absolute errors (for depth) at the bottom of each error map.

Panel of Figure 9 — Fig. 8 : Estimation results of our method and comparison methods, with the global offset along all the $xyz$ -axis $\mathbf{s}_{o}=\left[0.3,0.4,0.5\right]$ added to the center of the symmetric light pairs.

Panel of Figure 10 — Fig. 9 : Depth estimation results with $n_{\mathrm{pairs}}=2$ case. We add the global offset along the $z$ -axis as $\mathbf{s}_{o}=\left[0.0,0.0,0.5\right]$ . We show a mean relative absolute error at the bottom of each error map.

Panel of Figure 11 — Fig. 10 : Estimation results with varying light-to-surface distances. We show the estimated surface normal with angular error maps, where the distance from the light to the object is set to $2$ , $3$ , $4$ , $5$ , and $6$ under the setting of $r=1$ .

Fig. 11 : (Left) Axis-aligned symmetric light arrangement used in this experiment. (Right) Estimated normal maps from the proposed method (Ours) and axis-aligned symmetric light method [ 2 ] .

Fig. 12 : Our capturing setup. We put the object approximately $60\text{\,}\mathrm{cm}$ away from the camera. Inner and outer radii are $12.5\text{\,}\mathrm{cm}$ and $$27.5\text{\,}\mathrm{cm}$,$ respectively. We use the images taken under each of the lights shown in the figure. — Fig. 12 : Our capturing setup. We put the object approximately $60\text{\,}\mathrm{cm}$ away from the camera. Inner and outer radii are $12.5\text{\,}\mathrm{cm}$ and $$27.5\text{,}\mathrm{cm} $,$ respectively. We use the images taken under each of the lights shown in the figure.

Panel of Figure 14 — Fig. 13 : Estimated normal maps for our real-world dataset. For each scene, we show one of the input images and estimate normal maps by the proposed method (Ours) and the comparison methods.

Panel of Figure 15 — Fig. 14 : Estimation results of our method and comparison methods on our synthetic scenes, which are rendered under the realistic image setting described in Sec. V-E . We show a mean angular (for normal)/relative absolute errors (for depth) at the bottom of each error map. The two values separated by “/” indicate the errors without and with masking the pixels where our depth estimation errors are larger than $0.01$ .

Surface Normal Estimation

Surface Normal Estimation recovers the orientation of visible 3D surfaces from images and other sensor data for shape understanding and reconstruction.

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PIE-PS: Photometric Stereo from Physical Irradiance Event Streams

Xiangze Meng, Guangyu Li, Jing Li, Di Mei+3

Jilin University, China · Guangdong Institute of Intelligence Science and Technology, China · Beijing Institute of Technology, China+1

Event-Based Vision Surface Normal Estimation

Open paper AskPDF arXiv

Event cameras record asynchronous log-image-irradiance changes with microsecond latency and high dynamic range. These properties are useful for photometric stereo under moving illumination, but raw events are sparse and depend on an unknown contrast threshold. We start from the event trigger model and derive a physical relation between adjacent events, light motion, and surface normals. This relation gives a direct physics-only solver, but the solver needs the threshold, enough events at each pixel, and independent per-pixel optimization. To address these limits, we introduce PIE-PS, a learning-based framework for dense surface normal reconstruction from raw event streams and known lighting. We form Physical Irradiance Events (PIEs) by pairing two adjacent events at the same pixel with their corresponding light directions. Each PIE provides a Physical Irradiance Event Feature (PIEF), defined as the signed event rate. PIEF does not require the unknown contrast threshold. To share spatial and temporal context across nearby PIEs, we introduce PIE-GNN, which treats each PIE as a graph node and encodes it with its light-pair geometry. Since the reliability of PIE observations can vary with local appearance, illumination geometry, and sensor noise, Reliability-Grading Attention (RGA) predicts reliability weights to down-weight unreliable PIEs. Pixel aggregation then produces dense normals. Experiments on synthetic and real data show that PIE-PS outperforms prior event-based photometric stereo methods and the direct solver baseline.

Abstract

Surface Normal Estimation

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