Single-shot Acquisition of Cylindrical Mesostructure Normals using

Diffuse Illumination

Inseung Hwang, Daniel S. Jeon and Min H. Kim

KAIST School of Computing, South Korea

Keywords:

Cylindrical Mesostructure, Surface Normals, Diffuse Illumination.

Abstract:

Capturing high-quality surface normals is critical to acquire the surface geometry of mesostructures, such as

hair and metal wires with high resolution. Existing image-based acquisition methods have assumed a speciﬁc

type of surface reﬂectance. The shape-from-shading approach, a.k.a. photometric stereo, makes use of the

shading information by a point light, assuming that surfaces are perfectly diffuse. The shape-from-specularity

approach captures specular reﬂection densely, assuming that surfaces are overly smooth. These existing meth-

ods often fail, however, due to the difference between the presumed and the actual reﬂectance of real-world

objects. Also, these existing methods require multiple images with different light vectors. In this work, we

present a single-shot normal acquisition method, designed especially for cylindrical mesostructures on a near-

ﬂat geometry. We leverage diffuse illumination to eliminate the reﬂectance assumption. We then propose a

local shape-from-intensity approach combined with local orientation detection. We conducted several experi-

ments with synthetic and real objects. Quantitative and qualitative results validate that our method can capture

surface normals of cylindrical mesostructures with high accuracy.

1 INTRODUCTION

Capturing the surface geometry of mesoscale objects,

such as textiles, brush hair, and metal wires, is de-

manding, and is often limited by the optical resolving

power of 3D scanning systems; i.e., the spatial res-

olution of many 3D scanning systems is limited by

the spatial resolution of the active illumination mod-

ule. To overcome the limitation of 3D scanning res-

olution, a hybrid approach that combines the low-

resolution geometry and the high-resolution surface

normals has been proposed and commonly used (Ne-

hab et al., 2005). For instance, we can obtain high-

frequency geometric details as surface normals us-

ing a high-resolution camera. These normals are then

transferred into low-frequency 3D geometry through

the backprojection of the normals, yielding a high-

resolution 3D model.

To this end, capturing high-quality surface nor-

mals is critical to achieving high-resolution 3D scan-

ning. Existing image-based acquisition methods rely

on some assumptions. More speciﬁcally, they assume

that the target object has a speciﬁc type of surface re-

ﬂectance. For instance, the shape-from-shading ap-

proach, a.k.a. photometric stereo imaging (Wood-

ham, 1980), estimates surface normals by means of

the shading information. It captures multiple images

with a point light of known positions and decomposes

shading to light vectors and surface normals by as-

suming that the surface reﬂectance is perfectly dif-

fuse. Another popular approach is the shape-from-

specularity approach that captures specular reﬂections

very densely (Sanderson et al., 1988; Oren and Nayar,

1997). The surface normals are then estimated by de-

composing the specular reﬂections into the half-way

vectors and surface normals, assuming that surfaces

are overly smooth. However, these existing methods

to capture surface normals often fail due to the dif-

ference between the presumed and the actual surface

reﬂectance of real-world objects.

In this work, we present a single-shot normal ac-

quisition method that can capture high-quality surface

geometry of mesostructures. In particular, we target

cylindrical mesostructures on a ﬂat geometry, such as

threads, brush hair, wires, etc. We ﬁrst built an ex-

perimental setup for diffuse illumination, where 156

lights illuminate the target object. The diffuse illu-

mination setup removes the long-employed assump-

tion on the type of surface reﬂectance in our method.

We then propose a novel, local shape-from-intensity

method, combined with local orientation detection to

enhance robustness against noise. We derive the re-

Hwang, I., Jeon, D. and Kim, M.

Single-shot Acquisition of Cylindrical Mesostructure Normals using Diffuse Illumination.

DOI: 10.5220/0009181205610568

In Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2020) - Volume 4: VISAPP, pages

561-568

ISBN: 978-989-758-402-2; ISSN: 2184-4321

561

lation between the unit variance of the input image

and the local height under diffuse illumination by for-

mulating a cylindrical model for orientation cues. Fi-

nally, we calculate normals from the orientation cues

through the local orientations of cylindrical shapes.

Our method does not assume any speciﬁc surface

reﬂectance and can robustly capture surface normals

of any diffuse and specular surfaces of various ob-

jects. The input of our method is a single-shot image

under diffuse illumination. This allows us to capture

normals efﬁciently.

2 RELATED WORK

Photometric Stereo. The shading information con-

tains incident light direction and surface normals. It

has been used to estimate surface normals by formu-

lating a linear equation of the cosine law, so-called

photometric stereo (Woodham, 1980). However, this

method is valid only with perfect diffuse reﬂectance.

Specular reﬂection often breaks the cosine law.

Several advanced photometric stereo methods

have been proposed to overcome the limitation by

specular reﬂection. Barsky and Petrou use four

images to perform photometric stereo (Barsky and

Petrou, 2003). Mallick et al. extract the pure dif-

fuse component in the color space, which is perpen-

dicular to incident light color (Mallick et al., 2005).

Ma et al. separate diffuse and specular reﬂection us-

ing the different polarization properties of both re-

ﬂections (Ma et al., 2007). However, their method

has limitations as perfect diffuse specular separation

is impossible.

Shape from Specularity. Instead of relying on

shading information, many shape-from-specularity

methods have been proposed to capture surface nor-

mals. Chen et al. exploit specular highlights from

densely captured images in different illumination

(Chen et al., 2006). In their method, if a pixel is

a specular highlight, then the surface normal of the

point is calculated from light and view vectors. How-

ever, this method requires a set of many input images

with a condition that the entire surfaces should show

specular highlights more than one time. Specular re-

ﬂection is supposed to be observed in a narrower an-

gle range than diffuse reﬂection; therefore, the meth-

ods that exploit specular reﬂection require many input

images.

Shape Acquisition from a Single Image. There

have been several attempts to obtain shape from a sin-

gle image using strong assumptions. Langer et al. pro-

posed the so-called dark-means-deep model (Langer

and B

ulthoff, 2000). Dong et al. obtain spatial varying

reﬂectance properties and a normal map from a sin-

gle image using user interaction (Dong et al., 2011).

Barron et al. calculate shape, reﬂectance, and illumi-

nation from a single image (Barron and Malik, 2015).

However, the shape calculation of these methods as-

sumes that speciﬁc reﬂection cases to solve a severely

ill-posed problem. Recently, the methods to calcu-

late SVBRDF from a single image have been devel-

oped (Aittala et al., 2016; Li et al., 2017; Deschaintre

et al., 2018; Li et al., 2018). They exploit deep learn-

ing techniques. Existing single-shot normal acquisi-

tion methods require strong prior information, such as

user interaction, diffuse surface, or training data. In

contrast, our method requires only a single shot un-

der uniform illumination, measuring surface normals

directly without any prior or inference.

3 CAPTURING CYLINDRICAL

MESOSTRUCTURES

Overview. Our method employs a single image

taken under diffuse illumination as input. We then

standardize the input image with local mean and vari-

ance to make the input illumination-invariant. Next,

we detect the radius of the cylindrical shapes of

mesostructures using the scale-invariant Laplacian

detector. Futhermore, we detect the per-pixel orien-

tation of local geometry in the screen space. Lastly,

we compute surface normals using the cross product

after projecting image gradients to the local orienta-

tion. Figure 1 provides an overview.

Input

image

Intensity

standard.

Radius

detection

Normal

estimation

Orientation

detection

Output

normals

Figure 1: Normal estimation pipeline of our algorithm. We

calculate normal orientation using the Gabor ﬁlter and a

unit-variance intensity map from intensity statistics. The

ﬁnal normal output comes from combining orientation and

a unit-variance intensity map.

3.1 Cylindric Image Formation

The target objects of our method are a set of cylin-

drical mesostructures that spread on a nearly ﬂat

plane. In our research scope, we ignore the property

of surface colors, assuming that the surface albedo

is monochromatic. Our main objective is to cap-

ture high-frequency surface normals of cylindrical

mesostructures from an intensity image taken under

diffuse illumination.

VISAPP 2020 - 15th International Conference on Computer Vision Theory and Applications

562

Figure 2: The light-stage system that we built to capture

the input image. The light stage consists of uniformly dis-

tributed 156 LED lights.

Input. Our method takes a single intensity image

as input. The image is taken under diffuse illumina-

tion, implemented by building a light stage. The light

stage includes 156 LED lights, which are uniformly

distributed over the sphere. Figure 2 presents our cap-

ture system. We then take a monochromatic intensity

image as input.

Image Formation Model. We ﬁrst begin with the

traditional formulation of a cylinder shape (Glencross

et al., 2008). Suppose a cylinder of radius R exists

along the vertical y-axis. The height of the cylinder

comes out along the z-axis on the right-hand basis,

assuming an orthographic camera model. It can be

parameterized by the x-coordinates as follows:

h(x) =



−x



. (1)

The basic image formulation of our method fol-

lows the existing methods of the shape-from-intensity

approaches (Glencross et al., 2008; Beeler et al.,

2010). They assume that the locally lower points,

such as pores or wrinkles, are darker, and higher

points are lighter on the human face. Local heights

correspond to the high-pass ﬁltered image in their

method. However, the high-pass ﬁltered values are

intensity-variant; i.e., the heights estimated in the

bright region will be elongated relative to those es-

timated in the dark region. To achieve intensity-

invariant estimation, we propose a local adaptation

method of image intensity.

Under diffuse illumination, the image intensity

can be determined by the local height of the point.

Since a cylinder is symmetric, the points on the half

side of the cylinder have their correspondences in the

opposite side. Also, any points on the same latitude

level are assumed to have the same level of illumi-

nation. For half of the cylinder, the height increases

monotonically for each level of pixel positions. The

relation of the set of points that have the same inten-

sity to the height level is a bijective function. Now the

domain of the intensity function can change from the

position to the height:

I (x) = f (h (x)) , (2)

where I is the intensity of the position x, h is the height

of the position x, and f (·) is the unknown mapping

function from height to intensity (see Section 4.2 for

validation).

Since we use the linear camera signals without ap-

plying gamma correction, we assume that the above

mapping function f is linear as follows:

I (x) = c

·h(x) + c

, (3)

where c

and c

are unknown constants. The con-

stants c

and c

include all information of image for-

mation, such as surface albedo, incident light inten-

sity, camera exposure, linear camera response func-

tion, etc. To eliminate the constants c

and c

, we

standardize the image intensity as unit variance, a.k.a.

the z-score value, using a function z(·):

z(I (x)) =

·h(x) + c

) −(c

·µ + c

)

·σ

h(x) −µ

(4)

where µ is the mean of height h and σ is the stan-

dard deviation of height h. With the assumption of

cylindrical shapes of objects, the height function is

symmetric and thus the mean and variance can be cal-

culated for only a half period as follows:

µ =

h(x)dx =

R. (5)

This integral can be solved as an area of a quarter of

a circle. The variance is

h(x)

dx −µ

−

. (6)

Finally, the height function of the z-score of image

and the cylinder radius can be written as follows:

h(x) =

−

Rz(I (x)) +

R. (7)

3.2 Estimating Mesostructures

Intensity Standardization. As mentioned earlier,

z-score maps can be converted to height maps using

Equation (7). However, the simple and global for-

mulation does not hold in a real scene; for instance,

the real-world object might not be a perfect plane and

might not be perfectly parallel to the sensor space due

to its shape geometry. In addition, even our experi-

mental setup is not perfect diffuse illumination due to

the sparsity of the lights.

Single-shot Acquisition of Cylindrical Mesostructure Normals using Diffuse Illumination

563

To mitigate these issues, we use the local z-score

map. First, the mean calculation in Equation (4) is

replaced with the Gaussian-weighted local mean µ

(x, y) = (G

∗I) (x, y) , (8)

where G is the Gaussian kernel, σ is the standard devi-

ation of the Gaussian kernel, and ∗ is the convolution

operator. Similarly, the local standard deviation σ

(x, y) =

∗I

)(x, y) −((G

∗I) (x, y))

. (9)

The local unit-variance value can then be expressed

I (x, y) =

I (x, y) −µ

(x, y)

. (10)

The local unit-variance value is invariant to low-

frequency change of local intensity and irregular light

conditions. The smaller sigma makes the local unit-

variance more independent of local illumination dif-

ference, but an overly small value can lose local statis-

tics. We select a sigma level that has a larger value

than the diameters of the cylindric objects in the im-

age.

Radius Detection. The radius of the cylinder is re-

quired to calculate the height map from the local

unit-variance map. Assuming that the same cylindric

shapes exist in the scene, only a radius value in the

screen coordinates is required to calculate the surface

normal. We obtain the radius of the cylinder from

the blob size using the Laplacian of Gaussian (LoG)

blob detection (Lindeberg, 1998) based on the hills

and valleys model of (Langer and B

ulthoff, 2000). A

hill means a high area in the cylinder, which is a bright

area in the image. Valleys are the opposite of hills.

The LoG blob detection algorithm detects both areas,

and thus we use both blob scale results.

In detail, we apply the LoG blob detection ﬁrst to

the local unit-variance map. Owing to the maximum

response of the LoG operation, the blob size is multi-

plied by

√

2. The detected position and blob size can-

not be used directly as the numbers of blobs in hills

and valley are different. A blob is identiﬁed as either

a hill or a valley by the z-score of the blob position

in the local unit-variance map. If the z-score is larger

than a threshold, the blob is in the hill. Otherwise, the

blob is in the valley.

Orientation Detection. In our cylinder model, the

gradient of the image is perpendicular to the cylinder

orientation (the height axis of the cylinder). However,

the gradient is not perfectly perpendicular to the ori-

entation in the real scene. The derivation operation

to calculate gradients is sensitive to noise in nature.

Since we are targeting small-scale objects of a small

radius, our method is very sensitive to noise in gradi-

ents. To mitigate the noise problem, we exploit direc-

tional derivatives using the cylinder orientation from

the larger-scale operation.

We ﬁrst employ the Gabor ﬁlter to ﬁnd the orienta-

tion of the cylinders. The Gabor ﬁlter has been com-

monly used in the orientation estimation of objects

with a small cylindrical geometry, such as hair (Paris

et al., 2004; Jakob et al., 2009; Nam et al., 2019). We

estimate the orientations of cylinders by detecting the

maximum amplitude of the Gabor ﬁlter.

∗

(x, y) = argmax

∗I) (x, y)

, (11)

where F

is the Gabor ﬁlter that is tilted at the θ angle

from the x-axis and θ

∗

is the calculated orientation

map.

We compute the orientation map by convolving

the input image with predeﬁned angle candidates in a

certain angle resolution. We apply the Gabor ﬁlters of

different angles in 5-degree intervals. We then apply a

median ﬁlter of 3×3 to suppress noise. However, the

angle values have a period; the median ﬁlter cannot

be used directly. Therefore, we ﬁrst apply the median

ﬁlters to three different angle ranges as follows:

(x, y) = mod



median

(s,t)∈S

(θ

∗

(s, t)), π



, (12)

where m

is the median ﬁlter result where the range

shifted

nπ

radians, n is 0, 1 or 2, S

is a 3×3 window

of the median ﬁlter, and the shifted angle values as

∗

(x, y) = mod



∗

(x, y) −

nπ

, π



nπ

. (13)

We obtain the cosine value of the angle difference

to derive the angle pair with high conﬁdence that has

the smallest difference:

i j

(x, y) = cos (m

(x, y) −m

(x, y)). (14)

where i 6= j.

We choose the pair that has the largest absolute

cosine value, not the signed cosine value, as the di-

rection, and the opposite direction is the same for the

cylinder orientation:

∗

(x, y), j

∗

(x, y)) = argmax

i. j



i j

(x, y)



s.t. i 6= j.

(15)

We use the mean angle of the pair of the median

value. When the mean angle is calculated, the direc-

tion and the opposite direction yield different values.

We compute the mean angle that has a smaller differ-

ence with the median value.

i j

(x, y) =

(

(x,y)+m

(x,y)

if C

i j

(x, y) ≥ 0

(x,y)+m

(x,y)+π

otherwise

(16)

VISAPP 2020 - 15th International Conference on Computer Vision Theory and Applications

564

Orientation

 

h d



Figure 3: The image gradients are projected to the direction

perpendicular to the cylinder orientation, suppressing noise

in the calculated gradients.

Finally, the median angle estimated by the Gabor ﬁlter

is given as follows:

med

(x, y) = θ

∗

(x,y), j

∗

(x,y)

(x, y). (17)

Normal Estimation. The ﬁnal step is to calculate

normals from the unit-variance intensity map and the

orientation map. First, we obtain the local height map

from the local z-score map.

h(x, y) =

−

I (x, y) (18)

The coefﬁcients of the local z-score values are inher-

ited from Equation (7). The constant term in Equa-

tion (7) is not necessary as we use the derivation of

the local height map to compute the normal map.

Next, we obtain the directional derivatives that are

perpendicular to the cylinder orientations. We calcu-

late partial derivatives of the x - and y-axis using the

Sobel ﬁlter:

(x, y) =

∂h(x, y)

∂x

, h

(x, y) =

∂h(x, y)

∂y

. (19)

The gradients are then projected to the lines that are

perpendicular to the cylinder orientations by the dot

product:

(x, y) =



(x, y)



d(x, y), (20)

where

d(x, y) =



sinθ

∗

(x, y) −cos θ

∗

(x, y)



is the

direction that is perpendicular to the cylinder orienta-

tion, and θ

∗

is the angle of the cylinder orientation

from the x-axis. The projection mechanism is de-

picted in Figure 3.

Finally, we obtain the surface normals from the

cylinder directions and the derivatives. The tangent

vector

t of the normal vector is

t(x, y) =

t(x, y)

, (21)

where

t(x, y) =



sinθ

∗

(x, y) −cos θ

∗

(x, y) h

(x, y)



(22)

And its bitangent vector

b is

b(x, y) =



cosθ

∗

(x, y) sin θ

∗

(x, y) 0



. (23)

The bitangent vector is the orientation that makes the

normal orientation to the camera placement. Finally,

the normal map

n can be calculated as follows:

n(x, y) =

t(x, y) ×

b(x, y). (24)

4 RESULTS

In this section, we validate our normal estimation

algorithm by providing quantitative and qualitative

analyses of experiment results with synthetic ground

truth and real data. We implemented our algorithm in

MATLAB without code optimization and computed

in Intel i7-7700K CPU and 32GB memory. For an

image with a resolution of 256×256, our algorithm

took approximately 0.63 seconds in total.

4.1 Evaluation on Real Data

Experimental Details. For real scene experiments,

we built a light stage with 156 LED lights uniformly

distributed over the sphere to capture an object. The

LED lights (CXA1512-0000-000N00N20E1) have a

ﬂux of 1650lm, a power 12.6W, and a correlated color

temperature of 6500K. The lights are located at the

edge and vertex of the subdivision of an icosahedron.

The diameter of a sphere is 2.6m. We use a machine-

vision camera (GS3-U3-123S6C-C) with a resolution

of 4096×3000 and a pixel pitch size of 3.45µm. To

achieve the orthographic camera assumption of our

image formation, we employ a lens with a focal length

of 35mm and crop the 256×256 center region of the

captured image, of which the ﬁeld of view is 1.45

◦

Qualitative Comparison. We compared our re-

sults with four existing methods: photometric stereo,

mesostructure from specularity (Chen et al., 2006),

and two deep learning-based single image normal ac-

quisition methods (Ye et al., 2018; Deschaintre et al.,

2018). For photometric stereo and mesostructure

from specularity, we captured 60 images with differ-

ent light positions and calibrated them using a mirror

sphere. As Deschaintre’s method requires a captured

image under a ﬂashlight, we captured an image with

a single light. We experimented with various surfaces

for our model. They include diffuse surfaces (ﬂower

Single-shot Acquisition of Cylindrical Mesostructure Normals using Diffuse Illumination

565

Input Photometric stereo Chen et al. Ye et al. Deschaintre et al. Ours

Paint brush

Flower wire

Bamboo mat

Skein

Figure 4: We compare the results of our normal estimation method with other existing methods. Other methods fail to estimate

thin cylindrical structures of surfaces.

wire, bamboo mat), thin speucular structures (brush),

and complex structures (skein).

Figure 4 shows the captured images and recon-

structed normal maps. Photometric stereo measures

the overall normal map well but fails in capturing

high-frequency surface orientation. Deep learning-

based methods show low-quality normal map results

for thin cylindrical structures. These methods re-

quire a single input image with specular reﬂection

under a point light. For transparent surfaces and

thin cylindrical shapes, these methods fail to capture

high-frequency details because specular reﬂection oc-

curs in arbitrary directions by refraction and occlu-

sion. This phenomenon reduces the surface orienta-

tion cues of the light direction. Compared with other

existing methods, our method shows the best quality,

achieving ﬁne-level details of surface orientations of

mesostructures.

4.2 Quantitative Evaluation with

Simulation

Here we validate our cylinder model by comparing

the ground truth normals and reconstructed normals

from synthetic images. We rendered an array of cylin-

ders in a uniform illumination using the Mitsuba ren-

derer. The GGX microfacet distribution (Walter et al.,

2007) was used for a specular reﬂectance model. All

cylinders have the same radius and reﬂection param-

eters, including albedo and specular roughness, by

changing α parameter of the GGX model. We eval-

uate our algorithm with various roughness to validate

the performance of our algorithm.

Figures 5(a) and (b) present rendered synthetic in-

put images and the ground truth normal maps of the

same geometry. Figures 5(c) and (d) show the nor-

mal maps yielded by our method and the angle differ-

ence between our results and the ground-truth normal

maps. Almost every position over the mesostructures

presents smaller differences than 20 degrees. How-

ever, we found that there are large angle differences

in the deepest points in the valley. These points are

not differentiable and thus the ﬁnite differences lead

to suboptimal results.

Figure 5(e) shows the relation between the

ground-truth height and the unit variance intensity

values. It shows that the height and the unit-variance

intensity have a linear relation for a wide range of

roughness. When the surface is a mirror, the sur-

face makes only two values that are the high inten-

sity from the specular reﬂection and the low intensity

VISAPP 2020 - 15th International Conference on Computer Vision Theory and Applications

566

(a) Input

(d) Angle difference map (e) Height-intensity relation

(b) Ground-truth normal map

0 0.5 1

Height

-4

-3

-2

-1

Unit-variance intensity

Synthetic image

Our model

0°

10°

20°

30°

40°

50°

0 0.5 1

-4

-3

-2

-1

Height

Unit-variance intensity

Synthetic image

Our model

0 0.5 1

-4

-3

-2

-1

Height

Unit-variance intensity

Synthetic image

Our model

4.0=α

6.0=α

8.0=α

0°

10°

20°

30°

40°

50°

0°

10°

20°

30°

40°

50°

Figure 5: Quantitative evaluation with the synthetic ground-truth dataset. (a) Input image of cylinders (without gaps) rendered

with the Mitsuba renderer. (b) Ground-truth normals of the same geometry (c) Estimated normals. (d) The angle difference

between our results and the ground truth. (e) The comparison between the intensities and the estimated height levels.

from the occlusion around cylinders. If the surface

becomes rougher, the relation of the height and the

unit-variance intensity become closer to the linear re-

lation. However, the intensity of the top of the cylin-

der is weaker than near points where the surface is dif-

fuse because the top of the cylinder does not have in-

terreﬂection. Table 1 shows the average angle differ-

ence in each image. The average angle difference is

smaller than 15 degrees in the tested roughness range.

The average differences decrease when the roughness

becomes larger, but they increase again when the sur-

face is highly diffuse. Figure 6 includes the results

for different alignment of cylinders, such as varying

on the inter-cylinder distance and crossing. All cylin-

ders have the ﬁxed roughness (α=0.4). The intervals

among cylinders are set to half of a cylinder and a

cylinder. The background shown in the intervals is

(a) Input (d) Angle difference(b) GT normal (c) Estimated normal

0°

10°

20°

30°

40°

50°

Interval: RInterval: 2RCrossing

0°

10°

20°

30°

40°

50°

0°

10°

20°

30°

40°

50°

Figure 6: Quantitative evaluation with the synthetic ground-

truth dataset which have inter-cylinder distance and cross-

ing. The intervals among cylinders are set to half of a cylin-

der and a cylinder. (a) Input image. (b) Ground-truth nor-

mals. (c) Estimated normals. (d) The angle difference be-

tween our results and the ground truth.

set to the inﬁnite distance, yielding no value of ren-

dering. Therefore, we exclude the values at the inﬁ-

nite distance from the calculation. The results of the

inter-cylinder gap and crossing also show small dif-

ferences, compared with the ground truth.

Table 1: Average angle errors of our method with different

surface roughness parameters.

Roughness (α)

0.4 0.5 0.6 0.7 0.8

Mean error (deg)

10.64 9.49 8.57 8.26 8.91

Std. dev (deg)

8.49 8.23 7.88 7.51 7.15

5 LIMITATIONS

Our method is not free from limitations. First, our

method presents a suboptimal performance in captur-

ing normals for highly specular objects such as a mir-

ror or highly diffuse objects. As shown in our syn-

thetic experiments, the perfect mirror surfaces present

only two intensity levels: light existing and light oc-

cluded. For perfect diffuse surfaces, the interreﬂec-

tion becomes larger where the height is smaller, while

our relation conversion is valid on the top of cylin-

ders. This breaks our assumption. These surfaces of

extreme reﬂectances require a roughness estimation

or interreﬂection calculation. Second, the processing

of string crossing areas of our method could be devel-

oped further. If the texture has many cross-sections,

the ambiguity in detecting surface orientations might

become severely ill-posed when applying for the Ga-

bor ﬁlter. Third, diffuse illumination is hard to ac-

quire. We used a large light stage to obtain diffuse

illumination. Single-shot acquisition of cylindrical

Single-shot Acquisition of Cylindrical Mesostructure Normals using Diffuse Illumination

567

mesostructure normals with a point light or without

any light condition are possible areas of future work.

6 CONCLUSIONS

We have presented a normal map acquisition method

primarily designed for mesoscale cylindric objects us-

ing a single input image. We have discovered that

mesoscale geometry can provide local intensity statis-

tics to solve practical issues in the existing shape-

from-intensity approach. We showed that the rela-

tion of the local height and unit-variance intensity un-

der diffuse illumination of the light stage. We cal-

culated the normal maps from the local unit-variance

values and the detected cylindric orientations from

a single image. We validated that our method con-

sistently outperforms existing methods for capturing

high-frequency details of the surface orientation of

both specular and diffuse objects in the real world.

ACKNOWLEDGEMENTS

Min H. Kim acknowledges Korea NRF grants

(2019R1A2C3007229, 2013M3A6A6073718) and

Cross-Ministry Giga KOREA Project (GK17P0200).

REFERENCES

Aittala, M., Aila, T., and Lehtinen, J. (2016). Reﬂectance

modeling by neural texture synthesis. ACM Trans.

Graph., 35(4):65.

Barron, J. T. and Malik, J. (2015). Shape, illumination, and

reﬂectance from shading. IEEE TPAMI, 37(8):1670–

1687.

Barsky, S. and Petrou, M. (2003). The 4-source photometric

stereo technique for three-dimensional surfaces in the

presence of highlights and shadows. IEEE TPAMI,

25(10):1239–1252.

Beeler, T., Bickel, B., Beardsley, P., Sumner, B., and Gross,

M. (2010). High-quality single-shot capture of facial

geometry. In ACM Trans. Graph., volume 29, page 40.

Chen, T., Goesele, M., and Seidel, H.-P. (2006). Mesostruc-

ture from specularity. In Proc. IEEE CVPR 2006, vol-

ume 2, pages 1825–1832.

Deschaintre, V., Aittala, M., Durand, F., Drettakis, G., and

Bousseau, A. (2018). Single-image svbrdf capture

with a rendering-aware deep network. ACM Trans.

Graph., 37(4):128.

Dong, Y., Tong, X., Pellacini, F., and Guo, B. (2011). App-

gen: interactive material modeling from a single im-

age. In ACM Trans. Graph., volume 30, page 146.

Glencross, M., Ward, G. J., Melendez, F., Jay, C., Liu, J.,

and Hubbold, R. (2008). A perceptually validated

model for surface depth hallucination. In ACM Trans.

Graph., volume 27, page 59.

Jakob, W., Moon, J. T., and Marschner, S. (2009). Capturing

hair assemblies ﬁber by ﬁber. In ACM Transactions on

Graphics (TOG), volume 28, page 164. ACM.

Langer, M. S. and B

ulthoff, H. H. (2000). Depth discrimina-

tion from shading under diffuse lighting. Perception,

29(6):649–660.

Li, X., Dong, Y., Peers, P., and Tong, X. (2017). Model-

ing surface appearance from a single photograph using

self-augmented convolutional neural networks. ACM

Trans. Graph., 36(4):45.

Li, Z., Xu, Z., Ramamoorthi, R., Sunkavalli, K., and Chan-

draker, M. (2018). Learning to reconstruct shape

and spatially-varying reﬂectance from a single image.

ACM Trans. Graph., page 269.

Lindeberg, T. (1998). Feature detection with automatic

scale selection. IJCV, 30(2):79–116.

Ma, W.-C., Hawkins, T., Peers, P., Chabert, C.-F., Weiss,

M., and Debevec, P. (2007). Rapid acquisition of spec-

ular and diffuse normal maps from polarized spherical

gradient illumination. In Eurographics, page 183.

Mallick, S. P., Zickler, T. E., Kriegman, D. J., and Bel-

humeur, P. N. (2005). Beyond lambert: Reconstruct-

ing specular surfaces using color. In Proc. IEEE

CVPR 2005, volume 2, pages 619–626. Ieee.

Nam, G., Wu, C., Kim, M. H., and Sheikh, Y. (2019).

Strand-accurate multi-view hair capture. In Proc.

IEEE CVPR 2019, pages 155–164.

Nehab, D., Rusinkiewicz, S., Davis, J., and Ramamoorthi,

R. (2005). Efﬁciently combining positions and nor-

mals for precise 3d geometry. ACM Trans. Graph.,

24(3):536–543.

Oren, M. and Nayar, S. K. (1997). A theory of specular

surface geometry. IJCV, 24(2):105–124.

Paris, S., Brice

no, H. M., and Sillion, F. X. (2004). Cap-

ture of hair geometry from multiple images. In ACM

Trans. Graph., volume 23, pages 712–719. ACM.

Sanderson, A. C., Weiss, L. E., and Nayar, S. K. (1988).

Structured highlight inspection of specular surfaces.

IEEE TPAMI, 10(1):44–55.

Walter, B., Marschner, S. R., Li, H., and Torrance, K. E.

(2007). Microfacet models for refraction through

rough surfaces. In Eurographics, pages 195–206.

Woodham, R. J. (1980). Photometric method for determin-

ing surface orientation from multiple images. Optical

engineering, 19(1):191139.

Ye, W., Li, X., Dong, Y., Peers, P., and Tong, X. (2018).

Single image surface appearance modeling with self-

augmented cnns and inexact supervision. In Computer

Graphics Forum, volume 37, pages 201–211.

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