Supplementary Materials for“Symmetric-light Photometric Stereo”
Kazuma Minami

Hiroaki Santo Fumio Okura
Osaka UniversityYasuyuki Matsushita{kazuma.minami,santo.hiroaki,okura,yasumat}@ist.osaka-u.ac.jp

Mean angular error [deg.]

To further assess the proposed method, in this supplementary material,
A. we show estimation accuracies with varying elevation
angles of the light directions,B. we evaluate the proposed method under a near-lightsetting,
C. we evaluate the proposed method with non-Lambertianscenes,
D. we show the estimation results on the DiLiGenT
dataset using different sets of light directions.

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A. Synthetic experiments with varying the elevation angles of light directions
In Sec. 5.1 in the main paper, we only show the comparison for the scenes rendered under the fixed light directions. Figure S.1 shows the estimation results for a sphere
scene with varying the elevation angles of the light directions from 55 to 80 [deg.]. The sphere has the Lambertiansurface and is rendered without the global-illumination effects. The smaller elevation angles naturally bring the larger
estimation errors in both the proposed method and the comparison method, Calibrated, due to the effect of shadows.
The overall results demonstrate that the proposed method isindependent of the elevation angles of the light directions.

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0.5 [deg. ]0.0 [deg. ]Figure S.1: Estimation results of the sphere scene with varying elevation angles of the light directions. The plots of themean angular errors in degrees are shown on the top of the
input images, estimated normal maps, and corresponding
error maps.

B. Effect of near-light settings
The proposed method assumes distant-light settings,
which means point light sources are placed infinitely far
away from a scene. However, in realty, there are many
setups that are a near-light setting. We thus evaluate theproposed method under a near-light setting. For the evaluation, we render a Lambertian sphere with varying the distance between the target object to light sources. The radiusof the sphere is 1 [m] and is placed 5 [m] away from thecamera. Figure S.2 shows the estimation results and theplots of the mean angular errors. When the light sources
are placed farther than about 8 [m], the proposed and comparison methods show almost the same accuracy with thedistant-light setting. As the distance between the target andlight sources becomes smaller, the proposed method is affected by the near-light effect. Since the proposed method
uses a pixel pair for surface normal estimation, when allpixels have systematic errors affected by the near-light, theproposed method starts to exhibit larger errors compared tomethods that works in a per-pixel manner.
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30 [deg. ]0.0 [deg. ]Figure S.3: Estimation results of the sphere scene with varying roughness. The plots of the mean angular errors in degrees are shown on the top of the input images, estimatednormal maps, and corresponding error maps.

C. Effect of non-Lambertian reflectance
We evaluate the proposed method with non-Lambertian
scenes. We use a sphere scene with a non-Lambertian diffuse reflectance model, the Oren-Nayar model [2]. The light
directions are the same as Sec. 5.1 in the main paper. Figure S.3 shows the estimation results with varying the roughness. Since the proposed and comparison methods assume
the Lambertian surface, the estimation errors increase forboth methods as the effect of roughness becomes stronger.
As discussed in Sec. B, since the deviation of the Lambertian assumption by the non-Lambertian surface uniformly
affects all pixels, the proposed method exhibits larger errors
than the comparison method.

D. Results for DiLiGenT dataset
From the 96 light directions in the DiLiGenT dataset, we
use one set of four light directions for the symmetric-light
photometric stereo in Sec. 5.2 in the main paper. Here, weshow the estimation results using different sets of approximately symmetric lights.
Figure S.4 shows the three sets of four light directions,

all lights
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L-B
L-C (in main paper)

Figure S.4: Visualization of the light directions in the DiLiGenT dataset. We choose three sets of light directions thatare roughly symmetric. L-C is used in the main paper.

L-A, L-B, and L-C, where L-C corresponds to the set usedin the main paper (illustrated in Sec. 5.2 in the main paper).
Figure S.5 shows the estimation results under L-A and LB. The proposed method shows consistent results to ones
shown in Fig. 4 in the main paper. For the BEAR scene
under L-A, both methods exhibit significantly larger errors
compared to L-B and L-C. This is due to the fact that oneof the four images in the BEAR scene contains error as discussed in [1].

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Figure S.5: Estimation results for the DiLiGenT dataset under the two sets of light directions, L-A and L-B. For each row, weshow one of the input images, results of albedo and surface normal clustering, the ground-truth and estimated normal maps
for each method, and corresponding error maps. For each error map, we show the mean angular errors in degrees. Note thatthe BEAR scene under L-A contains error, resulting in significant estimation errors for both methods.

References[1] Satoshi Ikehata. CNN-PS: CNN-based photometric stereo forgeneral non-convex surfaces. In Proceedings of European
Conference on Computer Vision (ECCV), pages 3–18, 2018.
[2] Michael Oren and Shree K. Nayar. Generalization of Lam-bert’s reflectance model. In Proceedings of SIGGRAPH, pages
239–246, 1994.