1 Introduction

The current global trend toward high resolution color imaging calls for a versatile, compact, user-friendly, and robust scanning system that can be operated in different outdoor and indoor environments even without electricity, such as remote mural painting sites, yet capable of acquiring images with enough details to allow the viewer to fully appreciate the imaged subjects.

Digital imaging is generally performed by either an area image sensor or a linear image sensor. The area image sensors are composed of two-dimensional array of imaging sensor elements, and the linear sensors are composed of one-dimensional array of imaging sensor elements. Area image sensors are better known because they are widely used in commercial DSLR (digital single-lens reflex) cameras. However, they can only acquire limited small to medium-sized images. On the other hand, linear sensors, in theory, have no size limit since there are no inherent limitations on the length of their travel along the scanning direction. Therefore, the linear sensors can capture very high-resolution images. But it is difficult to apply them to some environments, because they have many practical limitations, for example, the issue of vibrations accompanied by motion [2–4].

A simple scanning system should be composed of a readily available area image sensor camera yet capable of capturing very high-resolution images. Here, the authors propose a scanning system stitching images acquired by area imaging sensor. It was not easy to stitch these images (in this paper, stitching means to combine multiple image tile into one panoramic image), because deformation happens after stitching, we calculated the value of deformation and introduced the scanning condition at which the deformation does not happen.

2 Modeling

In order to introduce the scanning condition at which the deformation does not happen, we introduce the camera coordinate system as shown in Fig. 1 and considered perspective projection. The relationship of the real space coordinate and image space coordinate is depicted as

Fig. 1.
figure 1

The camera coordinate system: A point P on an object with coordinates (X, Y, Z) will be imaged at some point p = (x, y) in the image plane. A point C is called optical center and the origin of the real space coordinates. The length of the image plane and optical center f is called the focal length [1].

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$$ \begin{aligned} {\text{x}} = {\text{f}}\frac{\text{X}}{\text{Z}} , \hfill \\ {\text{y}} = {\text{f}}\frac{\text{Y}}{\text{Z}} . \hfill \\ \end{aligned} $$
(1)

When a camera is moved by the distance C on X axis, Eq. 1 is depicted as

$$ \begin{aligned} {\text{x}} - {\text{fC}} = {\text{f}}\frac{{{\text{X}} - {\text{C}}}}{\text{Z}} , \hfill \\ {\text{y}} = {\text{f}}\frac{\text{Y}}{\text{Z}} . \hfill \\ \end{aligned} $$
(2)

The deformation is caused by the difference of the distance on X axis of any two points calculated by Eqs. 1 and 2. Each distances \( \varDelta x_{1} \) and \( \varDelta x_{2} \) are depicted as

$$ \begin{aligned} \varDelta {\text x}_{1} = {\text f}\frac{{\text{X}_{2} }}{{Z_{2} }} - {\text f}\frac{{{\text X}_{1} }}{{{\text Z}_{1} }}, \hfill \\ \varDelta {\text x}_{2} = {\text f}\frac{{{\text X}_{2} -\, {\text C}}}{{{\text Z}_{2} }} - {\text f}\frac{{{\text X}_{1} - \,{\text C}}}{{{\text Z}_{1} }}, \hfill \\ \end{aligned} $$
(3)

and the difference \( {\text{e}}_{\text{x}} \) is depicted as

$$ \begin{aligned} {\text e_{x}} & = \left| {\varDelta {\text x_{1}} - \varDelta {\text x_{2}} } \right|, \\ & = {\text f}\frac{{\text C\left| {{\text Z}_{1} - {\text Z}_{2} } \right|}}{{{\text Z}_{1} {\text Z}_{2} }} \\ \end{aligned} $$
(4)

When two points (P1 and P2) is on an object, \( {\text{Z}}_{1} \) and \( {\text{Z}}_{2} \) are described as

$$ \begin{aligned} {\text{Z}}_{1} = {\text{Z}}_{0} +\updelta_{1} , \hfill \\ {\text{Z}}_{2} = {\text{Z}}_{0} +\updelta_{2} , \hfill \\ \end{aligned} $$
(5)

where \( {\text{Z}}_{0} \) is the position of a center of an object and \( \updelta_{1} \) and \( \updelta_{2} \) are the distance of each points and \( {\text{Z}}_{0} \). If \( {\text{Z}}_{0} \) is much bigger than \( \updelta_{1} \) and \( \updelta_{2} \), \( \updelta_{1}\updelta_{2} \) can be neglected, Eq. 4 is depicted as

$$ {\text{e}}_{\text{x}} = {\text{f}}\frac{{{\text{C}}\left| {\updelta_{1} -\updelta_{2} } \right|}}{{{\text{Z}}_{0}^{2} + {\text{Z}}_{0} (\updelta_{1} +\updelta_{2} )}} . $$
(6)

When \( {\text{e}}_{\text{x}} \) is maximum, Eq. 6 is depicted as

$$ {\text{e}}_{\text{M}} = {\text{f}}\frac{\text{CL}}{{{\text{Z}}_{0}^{2} }}, $$
(7)

where L is the depth of an object.

Since the resolution (Dpi) is in direct proportion to \( \text{f/}{\text{Z}}_{0} \), Eq. 7 is depicted as

$$ {\text{e}}_{\text{M}} =\upalpha\frac{\text{CL}}{{{\text{Z}}_{0} }}({\text{DPI}}), $$
(8)

where (DPI) is the resolution of an image and \( \upalpha \) is a constant depending on an area sensor’s structure.

Equation 8 indicates this system is useful for imaging objects which have very small L, for example wall paintings, because when \( {\text{L}} \cong 0,\,{\text{e}}_{\text{M}} \) is very small.

When \( {\text{L}} \ne 0 \), the deformations occur. Difference \( {\text{e}}_{\text{M}} \) is in direct proportion to (a) the movement distance of the camera “C”, (b) the depth of the object “L”, and (c) the resolution of an image “(DPI)”, and inversely proportion to the distance between optical center and the object “Z0”.

3 A Scanning Device

Equation 8 shows that difference \( {\text{e}}_{\text{x}} \) is in direct proportion to the movement distance of the camera C and the depth of the object “L”. We should construct a scanning device to reduce these parameters.

When an area image sensor camera moves slowly at constant speed (condition (a)) with programmed constant and continuous shooting function, the moving distance of the camera C decreases and the deformation is reduced. The slower the speed of the camera, the less image blurring occurs.

Moreover, when this system is applied for paintings, the camera direction should be as parallel to object as possible (condition (b)).

3.1 Components of the Device

The scanning system based on the proposed method is shown as Fig. 2. The conditions required mentioned above could be satisfied by this system. The constructed scanning device is composed of only four parts: (1) the area image sensor camera, (2) the camera stage, (3) two friction dampers, and (4) the rack and rail guide module. These four parts can be used together to built a high-resolution scanning system without the need for electricity supply and a PC. The brief introductions for each part are as follow:

Fig. 2.
figure 2

Scanning device: This device is a simple scanning system depending on gravity force instead of electricity. This device does not need a PC and a motor to control the position of the camera. This is composed of only four parts: (1) an area image sensor camera, (2) a camera stage, (3) two friction dampers, and (4) a rack and rail guide module. Friction dampers keep the drop speed of the camera constant and slow.

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Area image sensor camera:

The area image sensor camera should be able to take consecutive pictures and be set at high ISO speed. The system proposed use a canon EOS 5D Mark III camera. We use a remote switch to operate the camera.

Camera Stage:

The camera stage is composed of some aluminum frames, two linear guides, and a plate. It can be designed for a camera based on its size and shape, as well as its application environment and so on.

Friction Dampers:

Condition (a) is satisfied through the use of friction dampers shown in the photograph. It contains several gear with special feature that the faster rotating speed, the more torque is produced. The magnitude of torque can be controlled. The drop speed can be controlled by changing the magnitude of torque. The dampers enable to control the position of the camera without electricity supply and a PC.

Rack and Rail Guide Module:

Condition (b) is satisfied trough the use of the rack and rail module. A rack and rail guide module is composed of some aluminum frames, a stopper, two racks, and a rail guide. It also can be designed for specific application environments, the size of an object, and so on.

4 Experiments

This system is useful for imaging wall paintings, because they have very small depth. In order to show how this system can be used for wall paintings, an oil painting on the wall was taken as scanning object. Figure 3 shows scanning work. This system reacquires only pulling a stage up by hand and releasing it then gravity takes over.

Fig. 3.
figure 3

Scanning procedure: This system reacquires only repeating pulling the stage up on the rail and releasing it while the camera is in a continuous shooting mode.

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Figure 4 shows an image acquired by this system and Table 1 shows the experiment condition including the parameter setting of the area sensor camera, dimension information of the wall painting and other detailed information. A high-resolution image is composed of several pictures taken by an area image sensor camera. The stitched image is composed about 1650 pictures (Approximately, 50 pictures in vertical direction × 33 pictures in horizontal direction). Although the painting was relatively large, this system can acquire high-resolution images without PC and electricity supply. (In this experiment, we used electricity for light source. If this system is used in an environment without electricity, a battery can be used to power the light source.) The image which is acquired without electricity supply is about 700 dpi and has very small deformation. This experiment proved that this system is useful for wall paintings.

Fig. 4.
figure 4

The image acquired by the system: Even if an object is very large, this system can acquire a high-resolution image. This image is about 700 dpi and 12.5 GB. Moreover, it was acquired without PCs and electricity supply. (Note: In this experiment, we used electricity for light source but this could also be supplied by a battery) The details of the image could be observed after zooming in.

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Table 1. The condition of wall painting experiments
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5 Application

The simplicity of the system enables many applications. One of applications is 3D reconstruction. It becomes more difficult when this system is applied to imaging objects which have three-dimensional contours, because the depth of the object “L” causes deformations. The images cannot be stitched correctly unless it is further improved for 3D scanning. As shown in Fig. 5, we developed the device that is composed of two or more cameras. This device can acquire many high resolution images for stereo vision. Moreover, arranging several cameras in a line at same time enables to acquire wide range of an object at once and reduce scanning time. This system can be applied to various situations.

Fig. 5.
figure 5

Application for stereo vision: This system can be applied to many kinds of demand. For example, this system can be applied to stereo vision. This system cannot digitize objects which have three-dimensional contours, but it can acquire images which can be used for 3D reconstruct.

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6 Discussion

In the oil painting experiment mentioned in the previous section, it was demonstrated that our system is very simple and works without PC and electricity supply. It can acquire a high-resolution image with small deformation anywhere. We assumed that the blurring was caused by the movement of camera stage module, but there was negligible blurring on some part of the image being caused by the movement of camera stage module. This experiment demonstrated that we can scan big wall paintings without PC and electricity supply. When scanning in remote locations without electricity, this will be a serious problem. We used 12 V power supply for light source. A 12 V mobile battery should be applied for the light source of this system. Moreover the small deformations can be recognized on the image. They are caused by vibration in the normal direction of picture and stitching program Photomerge. We should improve the device and develop novel stitching algorithms. For 3D objects, images acquired by this system have deformations. For scanning of 3D objects, the hardware and software of this system still need to be improved. Although some challenges remain, we developed scanning system which can acquire high-resolution image wherever you want to scan.

7 Conclusion

We have constructed a simple and robust scanning system that takes advantage of gravity and does not depend on electricity for its scanning motion. This device is composed of very few parts without PC and motors, yet it is capable of acquiring high-resolution images regardless of the size of the subject, making it suitable for scanning of large painting in an electric-free environment.

In order to demonstrate that this system is very useful for wall paintings, we scanned the paint on the wall. Although the paint was large, this system acquired high resolution image (700 dpi) without PC and motor. We demonstrated that this system can acquire high resolution image in spite of object’s size and would be able to scan very large wall paintings.

On the other hand, when imaged objects have three-dimensional contours, we cannot develop definite way. To digitize objects which have three-dimensional contours, we should develop a 3D reconstruction method which suits for the system.

Although deformation are still a challenge, we have built an image acquisition system that is easy to use, can be applied to various environment, takes advantage of gravity instead of electric power for its scanning motion, yet capable of acquiring very high-resolution images of paintings.

This system can be used easily in remote locations without electricity or narrow-space environment. In order to scan, the user would only need to pull up the camera module along the rail, and release it while the camera is in a continuous shooting mode. This proposed system could help many researchers around world digitize the cultural heritage easily and utilize the acquired data for their field of discipline.