1. Data acquisition

Cine chest anteroposterior radiographs were obtained with an angiography system (Artis zee ceiling PURE®, Siemens, Munich, Germany). The matrix size was 960 × 1240 pixels, and the pixel size was 0.308 × 0.308 mm. The grey-level range was 4096. Dark areas in the images have low pixel values and stand for low X-ray permeability in this system.

The tube voltage and the tube current were automatically determined by the angiography system before the examination and then fixed not to change during the examination. The source to image distance was 0.88 m. The X-ray with a duration of 8.0 ms/pulse was exposed at a rate of 15 frames/second. A total of 198 frames were acquired in the dynamic imaging sequence.

All radiographs were obtained from a healthy volunteer, 43 years old non-smoker male, in a supine position. The ethics committee has determined that this study does not require review.

2. Imaging analysis

Our analysis schema is shown in Fig. 1. The lung field was subdivided into small blocks, and the difference of the average pixel value, Δ intensity (ΔI), was calculated in each block. Finally, the result was normalized (frequency-tuned ΔInorm) and visualized.

All of the analyses were conducted on a personal computer (MacBook Pro) with software developed by us. A Fast Fourier Transform (FFT) and Inverse FFT (IFFT) were performed using R version 3.2.1 (R Foundation for Statistical Computing).

2 − 1. Lung field subdivision

## Lung field definition

A left lung field was defined with 6 quadratic Bézier curves described by 12 control points (Fig. 2a). Then, other lung fields were calculated as described subsequently, assuming that each lung field is transformed linearly between the minimum shape and the maximum shape (Fig. 2b).

First, a y-coordinate of P5 was defined in all frames and minimum/maximum frames were determined based on its value. Then, transform rate (rt) was computed for all frames;

$${r}_{t}=\frac{{y}_{5\bullet t}-{y}_{5\bullet min}}{{y}_{5\bullet max}-{y}_{5\bullet min}}, t=1, 2, \dots .,N$$

where t is frame number and N is total number of frames. Finally, each 12 control points were defined manually in a minimum/maximum frame, and linear transform was performed on other frames by computing each control point as follows;

$${P}_{i\bullet t}=\left(\begin{array}{c}{x}_{i\bullet t}\\ {y}_{i\bullet t}\end{array}\right)=\left(\begin{array}{c}\left(1-{r}_{t}\right){x}_{i\bullet min}+{r}_{t}{x}_{i\bullet max}\\ \left(1-{r}_{t}\right){y}_{i\bullet min}+{r}_{t}{y}_{i\bullet max}\end{array}\right), i=1, 2,\dots , 12$$

We defined two curve segments as vertical axes, and one line segment as the intermediate line. Vertical axes and intermediate line were equally divided into M segments, and their points of division described M + 1 quadratic Bézier curves, which divided the lung filed into M horizontal areas (Fig. 3a).

Then, in each horizontal area, a shorter Bézier curve was divided by 4 pixels, and we denote the number of curve fragments as Nm. The top and bottom Bézier curves were equally divided into Nm segments, and their points of division described Nm+1 line segments, which subdivided the horizontal area into Nm blocks (Fig. 3b).

2–2. Detection of vital signs

The respiratory rate (RR) was computed from the movement of the diaphragm. The FFT was performed on the sequence of y coordinates. The heart rate (HR) was computed from the ΔI of the heart area. The FFT was performed on the sequence of average intensities.

2–3. Visualization of frequency-tuned normalizedΔΙ

## ΔΙ calculation

To calculate the average pixel intensity of the block approximately, the circumscribing rectangle was defined as ROI.

$${ROI}_{mnt}=\left\{\left(x,y\right) | \underset{x\in {X}_{{mnt}}}{\text{min}}x\le x\le \underset{x\in {X}_{{mnt}}}{\text{max}}x, \underset{y\in {Y}_{{mnt}}}{\text{min}}y\le y\le \underset{y\in {Y}_{{mnt}}}{\text{max}}y,x\in \mathbb{Z},y\in \mathbb{Z}\right\}$$

$${X}_{mnt}=\left\{{x}_{mnt1}, {x}_{mnt2}, {x}_{mnt3}, {x}_{mnt4}\right\}$$

$${Y}_{mnt}=\{{y}_{mnt1}, {y}_{mnt2}, {y}_{mnt3}, {y}_{mnt4}\}$$

For a given ROI in a sequence of chest images, f (x, y, t), ΔI of each block, g (m, n, t), was computed as follows.

$$g(m, n, t)=\frac{{\sum }_{x,y\in {ROI}_{mnt}}f\left(x, y,t+1\right)-f(x,y,t)}{\left|{ROI}_{mnt}\right|} t=0,\dots ,N-1$$

## FFT filtering

On each block, a FFT was performed on its ΔI.

$$h\left(m, n,k\right)=\sum _{t=0}^{N-1}g(m,n,t){e}^{-i\frac{2\pi }{N}tk} k=0,\dots , N-1$$

Subsequently, a frequency-tuned ΔI was synthesized by IFFT. The frequency range (fmin ≤ f ≤ fmax) was specified based on the RR or HR, and frequency components included in the range were selected as components of interest (COI) for IFFT:

$$COI= \left\{C | \frac{{f}_{min}}{{f}_{1}}\le C\le \frac{{f}_{max}}{{f}_{1}}, {f}_{max}\le {f}_{n}, C\in \mathbb{Z}\right\}$$

$$i\left(m,n,t\right)=\frac{2}{N}{\sum }_{k\in COI}h(m,n,k){e}^{i\frac{2\pi }{N}tk} t=0,\dots ,N-1$$

The fundamental frequency and the Nyquist frequency are denoted as f1 and fn, respectively.

## Construction of normalized images

The frequency-tuned ΔInorm were visualized by pseudo-color mapping. We defined these normalized images as respiratory-related differential projection (RDP) and blood flow-related differential projection (BDP) and the relationship between vital signs detected from the images was evaluated.