Application of reflectance transformation imaging for the
display of handwriting traces
Wei Wei (魏 巍)
1,2
, Lihua Huang (黄立华)
1,
*, Xinran Zhu (朱信冉)
1,2
,
Liqing Ling (凌丽青)
1
,KaiGuo(郭 凯)
1
, and Huijie Huang (黄惠杰)
1
1
Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China
2
Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences,
Beijing 100049, China
*Corresponding author: hlh@siom.ac.cn
Received April 17, 2019; accepted June 20, 2019; posted online September 4, 2019
In our Letter, two kinds of handwriting traces, colored and colorless, are studied by means of reflectance
transformation imaging. The illumination direction and rendering mode can be changed alternatively to obtain
two-dimensional and three-dimensional details of the traces that are not recognized easily by naked eyes.
Furthermore, an objective evaluation method without reference is applied to evaluate the reconstructed images,
which provides a basis for setting the illumination direction and rendering mode. Therefore, the handwriting
trace information including the written content, the writing features, and the stroke order features can be
obtained objectively and accurately.
OCIS codes: 110.3010, 120.6650, 330.1715.
doi: 10.3788/COL201917.111101.
The term “reflectance transformation imaging” (RTI) was
first developed by Tom Malzbender at Hewlett Packard
Laboratories, who invented the image processing methods
known as polynomial texture mapping
[1]
. Cultural Herit-
age Imaging developed the technique in the field of
cultural heritage
[2,3]
. The exact capture and processing
pipeline have been used to survey surface information
and reveal the clues that are not easily visible to the naked
eye
[4–6]
.
Handwriting is a special kind of trace and a carrier of
various information
[7]
. The commonly used methods for
the display of dielectric surface traces include the method
of lateral light observation under a microscope, side light
infrared imaging, static voltage trace development, and
the method of laser confocal scanning microscopy
[8]
. These
methods have their own shortcomings in showing the
detailed features of handwriting traces.
In our work, the application of RTI for the display of
handwriting traces is studied. First, a laboratory device
is set up to obtain a series of images of handwriting traces
on the object. After image reconstruction of these series of
images, the light direction and rendering mode can be ap-
plied interactively to obtain the detailed features of the
handwriting traces. Not only can the information such
as the writing content and writing order of the colored
handwriting traces be obtained, but also the three-
dimensional texture features of the colorless handwriting
indentation. From the experim ental results, the detailed
features of the handwriting traces are closely related to
the incident light angle and the rendering mode, especially
for the colorless handwriting. Therefore, it is necessary to
find an evaluation method to determin e the incident light
direction and rendering mode to obtain the detailed fea-
tures as much as possible. An objective evaluation method
without reference is proposed that can provide a basis for
selecting the incident light direction and rendering mode.
Furthermore, detailed features can be obtained from the
images of handwriting traces.
RTI uses a set of digital photographs of a stationary
object. A mathematical model describing the luminance
information for each pixel in an image in terms of a func-
tion representing the direction of incident illumination
was presented by Malzbender et al.
[9]
. The x and y coordi-
nates of the projection of the normalized light vector onto
the image plan e are given by the light direction (l
u
, l
v
).
The luminance function for each pixel is approximated
by a biquadratic polynomial in l
u
and l
v
:
Lðu; v; l
u
; l
v
Þ¼a
0
ðu; vÞl
u
2
þ a
1
ðu; vÞl
v
2
þ a
2
ðu; vÞl
u
l
v
þ a
3
ðu; vÞl
u
þ a
4
ðu; vÞl
v
þ a
5
ðu; vÞ: (1)
The six coefficients a
0
–a
5
are stored with the unscaled
RGB (red/green/blue) values of the pixel. By making a
series of images with the camera and specimen in fixed po-
sitions, and with varying directions of incoming light, the
coefficients of the luminance polynomial for each pixel can
be computed by a least-squares method (regression) using
singular value decomposition. The normal vector per pixel
can be estimated by computing the brightest incident
illumination
[10]
.
The whole set of normal vectors provides the “descrip-
tion” of the topography of the object accurately and
completely. So, reproducing pixel by pixel the surface
texture as well as its color and reflective properties to
create a digital map is possible. The properties including
surface interreflection, subsurface scattering, and self-
shadowing can be recorded in the per pixel information.
COL 17(11), 111101(2019) CHINESE OPTICS LETTERS November 2019
1671-7694/2019/111101(6) 111101-1 © 2019 Chinese Optics Letters