1. Introduction
Dual-layer flat-panel detectors (DFDs) enable single-exposure spectral imaging based on energy-selective imaging from copper filtering or beam hardening [
1,
2,
3]. This detector has a variety of applications, such as in bone and tissue separations [
1], material decomposition [
4], and bone mineral density estimation [
5]. It can also improve the contrast-to-noise ratio and detective quantum efficiency (DQE) [
6,
7,
8]. Engel
et al. [
7] showed an increased DQE from DFDs than a case of a single-layer detector having an added thickness of the scintillator layers of DFD. Kim [
8] showed that a convex combination of the upper and lower images acquired from DFD yielded the added DQE of their values and decreased the noise power spectrum (NPS) [
9]. Su
et al. [
10] obtained super-resolution images based on DFD. Dual-energy cone-beam computed tomography is a suitable field for the application of DFD [
4,
5,
6].
As shown in
Figure 1, the structure of DFD consists of two layers, where the upper and lower detector layers are attached as close as possible [
3,
8,
12]. The lower layer usually absorbs relatively high-energy x-ray photons due to the beam hardening compared to the upper layer case. The intermediate layer between the upper and lower layers can prevent mutual transmission of light photons and can contain a spectral filter for x-rays [
1,
8,
13]. The DFDs introduced in the literatures are summarized in
Table 1, where indirect conversion flat-panel detectors with CsI(Tl) scintillator layers and pixel pitches of 0.140 mm and 0.145 mm are used [
3,
5,
6,
8,
10,
11,
12].
When stacking the upper and lower detector layers to construct a DFD, the images acquired from the layers should be registered because misalignments occur between the layers. By using a physical positioning device, the rotational deviation between the layers can be controlled to be as small as possible while stacking the layers. However, physically aligning the detector-element positions of the lower thin-film transistor (TFT) layers with respect to those of the upper layer is not easy [
8,
12]. Hence, geometric translocation of the lower layer exists in both horizontal and vertical directions with respect to the upper layer.
To conduct an image registration, geometric transformations are first estimated between the upper and lower images acquired with an object and then are employed to register the images based on interpolation schemes [
14]. Various registration methods have been developed [
15,
16]. Shi
et al. [
3] registered the lower image using an affine transform accounting for translation, rotation, and scale based on an interpolation with the IsoCal phantom [
17]. Kim [
8], and Lee and Kim [
11] estimated the translation parameters based on a slant-edge phantom, which is used for measuring the modulation transfer function (MTF), and conducted transforms with those translation parameters. Wang
et al. [
5] also aligned the lower image based on an interpolation. However, the employed registrations and transforms are usually based on interpolation schemes and thus cause registration errors due to the amplitude and phase distortions of interpolation. Note that the traditional intensity-based and feature-based registration approaches [
15,
18], which use natural scenes, produce large registration errors and thus are not appropriate for the registration purpose of DFD.
When registering the upper and lower images acquired from DFD, the following two items should be considered.
The first item is concerned with the registration of the spatial horizontal and vertical translations as shown in
Figure 2(a). In DFD, image registration is a simple process of finding the misaligned spatial translations and using these to transform the lower image. Here, a subpixel registration method [
19,
20,
21,
22,
23,
24,
25,
26,
27,
28] is required to accurately find the spatial translation. Subpixel registration is not only important for obtaining aligned image pairs, but also for checking the uniform pixel alignment of the stacked detector layers [
10]. If the translation parameter of DFD is accurately estimated, then using the parameter the translation of the images acquired from the same DFD can be performed every time to acquire registered image pairs. Hence, there is no need to perform separate image registration in the application of an image processing method. The second item is concerned with a transform of the image scale change due to the x-ray projection as shown in
Figure 2(b). Because x-rays generated in the form of a point source in an x-ray tube are projected onto DFD, the x-ray image obtained from the lower layer is more magnified than the image obtained from the upper layer.
In this paper, a two-step image registration method for DFD is introduced. Conventional one-step registration methods have errors depending on objects in the x-ray images acquired from the upper and lower detector layers [
15]. The proposed method for high-precision image registration for DFD consists of two steps; the first step is conducting a spatial translation according to the Fourier shift theorem with a subpixel registration, and the second step is conducting a scale transformation using a cubic interpolation to process the x-ray projections. To conduct an accurate subpixel registration, we employed a method based on the notion of maximum amplitude, where a conventional slant-edge phantom is used as a fiducial mark [
11,
12]. This maximum-amplitude method can provide high-precision spatial translation compared to the methods that use the entire pixels of natural scenes [
19,
20,
22,
23,
24,
25,
27,
28]. The proposed two-step method can achieve more accurate image registration than the conventional one-step case, especially for the DFD applications.
This paper is organized in the following way. In
Section 2, we first describe the registration of images acquired from DFD. We then propose a two-step registration method for DFD. Theoretical analysis on the proposed method is conducted to observe the registration performance in
Section 3. To experimentally evaluate the registration accuracies, extensive experiments using x-ray images acquired from DFD are conducted in
Section 4 with discussions. The conclusion is then stated in the last section.
2. Two-Step Registration for the Dual-Layer Flat-Panel Detector
In this section, we first comparatively discuss subpixel registration methods for the images acquired from DFD. We then introduce a two-step registration method that takes into account the magnified image due to the x-ray projection.
In order to obtain an aligned image pair from DFD, the lower image acquired from the lower detector layer should be accurately aligned with respect to the upper layer. We first consider the translation of horizontal and vertical directions as shown in
Figure 2(a), where the lower detector is translated by (-2.6, 1.8) pixels as an example. We can transform the lower image by using the translation parameter based on the Fourier shift theorem or interpolation schemes, such as the linear and cubic interpolations. Here, the translation parameter can be estimated from a subpixel registration method [
19]. Conventional intensity-based subpixel registration algorithms generally use the entirety of pixels of natural scenes and thus are not suitable to find such a fine translation of subpixel resolutions for DFD.
To increase the accuracy of subpixel registration for a given small area, we should design a complicate phantom with special patterns as a fiducial mark. However, designing a phantom with such a special pattern is difficult for radiography detector applications. Instead of using such a special phantom, Kim [
8] used the conventional slant-edge phantom and maximized the DQE value to obtain a registered convex combination image. Lee and Kim [
11,
12] recently conducted a subpixel registration based on a necessary condition on maximizing an amplitude response and extended this notion to developing a high-precision measurement algorithm, where a cyclic-coordinate optimization based on the maximum amplitude is conducted. Note that this method can find local subpixel translations using a small portion of the slant edge as Positions 1, 2, and 3 in
Figure 3.
Because the x-ray generated in the form of a point source from the x-ray tube is projected onto DFD, the x-ray image acquired from the lower layer is more enlarged than the image obtained from the upper layer. As shown in
Figure 2(b), letting
denote the source-to-image distance (SID), a horizontal pixel location of
u from the aligned center pixel produces the deviation
pixels in the lower layer with respect to the upper layer. In other words, the lower image is enlarged by a scale factor of
compared to the upper image. To minimize the deviation
due to the projection, we need to minimize the distance
between the TFT layers of the upper and lower detector layers. Several examples of the distance are shown in
Table 1. We can compensate the enlarged lower image using the scale factor and an interpolation scheme to conduct a high-precision image registration considering the projection. We can also experimentally obtain the sale factor by measuring pixel deviations from the three slant-edge phantoms of
Figure 3.
By using the estimated translation and scale parameters, we can conduct an image transformation based on an interpolation [
14]. However, the employed interpolation usually deteriorates frequency responses of the transformed image. To alleviate the deterioration, we propose a two-step method based on the Fourier shift and scaling with an interpolation. The proposed method for DFD is summarized as follows.
Two-Step Registration for the Dual-Layer Flat-Panel Detector:
- 0)
Find the translation of the lower image based on a subpixel registration; calculate the scale factor for a given SID.
- 1)
Translate the lower image using the translation estimate based on the Fourier shift theorem.
- 2)
Transform the lower image using the scale factor based on a cubic interpolation.
Note that the proposed method is composed of two steps: translation based on the Fourier shift theorem and scaling based on a cubic interpolation. Instead of these two steps, we can consider a one-step translation with the translation and scale parameters based on an appropriate interpolation, such as the linear or cubic schemes. However, this single translation can reduce the MTF response and distort the phase response due to the employed interpolation scheme [
14]. On the other hand, the proposed two-step method can alleviate the degradation problem from the interpolation-based transformation approach.
4. Numerical Results
In this section, we experimentally observe the registration performance of the proposed high-precision two-step registration method for DFD, which is constructed by stacking upper and lower detector layers as shown in
Figure 1 (DRTECH Co. Ltd., South Korea,
www.drtech.com) [
8]. Each layer has a CsI(Tl)-scintillator layer with
photodiode pixels controlled by amorphous indium-gallium-zinc-oxide (a-IGZO) TFT panel. The pixel pitch is 140
m yielding a sampling frequency of
lp/mm and the resolution is 16 bits/pixel. The thicknesses of the upper and lower scintillator layers are
mm and
mm, respectively.
For Step 0), several methods are applied to estimate the translation parameters and the results are illustrated in
Figure 6. The conventional registration methods using chest images show erroneous deviations compared to the methods that use the slant-edge phantom as a fiducial mark to estimate only two translation parameters. The maximum-amplitude method yields a translation estimate of
, which will be shown as an accurate estimate in terms of the MTF and DQE in this section. In Step 1), the lower image is shifted using the translation estimate based on the Fourier shift theorem, and in the following step, Step 2), the shifted image is then transformed by using the scale factor
with an interpolation method, where
mm and
mm.
4.1. Numerical Performance Observation
In
Figure 7, numerical results on measuring directional MTF values are illustrated for the convex combination of the registered images from the proposed registration method. From "Theoretical" and "Trans. (Fourier shift)" in
Figure 7(a), we can observe that the MTF of the convex combination is very close to the theoretical value. As shown in (
3), we can observe that the theoretical MTF is between the upper and lower MTF values. If we conduct the translation based on the interpolation scheme, then the MTF is reduced as mentioned in (
7) and (
8) ("Cubic interp.+max ampl. (slant edge)" and "Linear interp.+max ampl. (slant edge)" in
Figure 7).
If the lower image is not aligned, then the MTF values of relatively high frequencies are usually lower than the theoretical ones. Hence, precisely aligning the lower image is important to ensure good MTF performance even at relatively high frequencies. In the intensity-based or feature-based subpixel registration methods, the estimate accuracy depends on the object of the x-ray image and can be degraded as shown in
Figure 6. For example in
Figure 7, the translation result from the maximum amplitude is close to the theoretical value ("Fourier shift+max ampl. (slant edge)"). However, the shift parameter estimated from an intensity-based subpixel registration method shows lower values than the theoretical case ("Fourier shift+intensity (MSE, slant edge)").
Directional NNPS measurement examples are illustrated in
Figure 8(a). Here, we compensated the NNPS values, which were inflated during the gain correction procedure, by considering the number of white images acquired under an incident exposure for the gain map design [
9,
38]. We can observe that the NNPS value of the upper layer is less or better than that of the lower layer and the NNPS value of the convex combination is less than those of both layers. Hence, to improve the noise performance, we can use the convex combination of the images from both upper and lower layers for an appropriate combination coefficient of
. In the experiments of
Figure 7 and
Figure 8(a), optimal values of
are used for the combination coefficient.
Under an x-ray beam of RQA 9, DQE experiments are illustrated in
Figure 8(b) for an optimum of
, which is equal to
. As observed in this figure, DFD showed improved DQE values closely to the theoretically achievable values, which are derived based on a parametric model [
8]. Here, the MTF and NPS curves are modeled by performing third-order polynomial fits. For the experiments of the detector, the optimal curve of
is approximately constant for all
[
8]. Hence, we can observe from
Figure 8(b) that
overall frequencies as shown in (
11). For high energy x-ray tube voltages such as in RQA 9 of
Figure 8(b), the upper detector layer showed
. The lower detector layer had a lower
than the upper layer case, because the remaining photons were utilized in the lower layer. Using DFD, we can increase the DQE value as
at the zero frequency.
4.2. Registration Example of the Chest X-Ray Images
We now observe a registration example for the chest x-ray images acquired from the upper and lower layers as in
Figure 1. To observe misalignments between the images acquired from DFD, we use the ratio of the upper and lower images and show several ratio images in
Figure 9. We can observe from
Figure 9(a) that the upper and lower images acquired from DFD is severely misaligned. In
Figure 9(b) and (c), registration examples from conventional gradient-based and feature-based methods are shown. Here, a one-step transform with the translation and scale was conducted. The bronchioles inside the lung and lines outside of the lung are observed due to misalignment.
Based on the Fourier shift theorem, we can translate the lower image without attenuating its magnitude response. Here, the translation parameter was estimated based on the maximum-amplitude subpixel registration method. The registration result is shown in
Figure 9(d). However, due to the enlarged lower image caused by the x-ray projection, the alignment error increases as the pixel positions move further outward from the image. In the proposed registration method, the translated lower image is then scaled based on a cubic interpolation as shown in
Figure 9(e). We can observe very low misalignment errors over the entire image area.