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Pelvic tilt (Benchmark Datachart at the bottom)

For citation and more details, please refer to the related publication: (author information and citation information)

  • Four observers annotated the landmarks in Figure 1 to calculate the anatomical pelvic tilt: {PT_a} (defined by the anterior pelvic plane) and mechanical pelvic tilt {PT_m} (defined by the center of femoral heads and the midpoint of sacral plate).
  • 115 lateral pelvic x-rays were recruited for the measurements.

Protocol

1. Scaling coefficient {\eta}:

{\eta_i=\frac{1}{2 N} x\left(\frac{\sum_{i=1}^N L_i}{L_i}+\frac{\sum_{i=1}^N \widehat{L_i}}{\widehat{L_i}}\right)}

where the {\eta_i} is a ratio to unify the size of image i; {L_i} and {\widehat{L_i}} are the distances between {P_{ASISs}}, {P_{Pubic  Tubercles}}, {P_{Center  of  femoral  heads}}, and {P_{Midpoint  of  sacral  plate}}, respectively; N is the total image amount.

2. For observer s, the coordinate of landmark j on the image:

{\hat{x}_{i j}^{(s)}=\eta_i\left(x_{i j}^{(s)}-\frac{\sum_{s=1}^4 x_{i j}^{(s)}}{4}\right)}
{\hat{y}_{i j}^{(s)}=\eta_i\left(y_{i j}^{(s)}-\frac{\sum_{s=1}^4 y_{i j}^{(s)}}{4}\right)}

where ({x_{i j}^{(s)}, y_{i j}^{(s)}}) and  ({\hat{x}_{i j}^{(s)}, \hat{y}_{i j}^{(s)}}) is the original and centralized coordinate of landmark j on the image i.

3. These points were projected to an axis representing the average pelvic tilt ( {\theta_{ave}}) for their density distribution at the direction of interest. The projected coordinates can be expressed as follows:

{\tilde{x}_{i j}^{(s)}=\hat{x}_{i j}^{(s)} \times \cos \left(P T_{a v e}\right)-\hat{y}_{i j}^{(s)} \times \sin \left(\theta_{a v e}\right)}
{\tilde{y}_{i j}^{(s)}=\hat{y}_{i j}^{(s)} \times \cos \left(P T_{a v e}\right)+\hat{x}_{i j}^{(s)} \times \sin \left(\theta_{ave}\right)}

4. The landmark accuracy is calculated from the maximum impact of the distance of k% data points of the two ends ({P_1} and {P_2}) on the pelvic tilt ({\theta_{\max}^k}):

{\theta_{\max }^k=2 \tan^{-1}\left(\frac{L_1^k+L_2^k}{L_{P_1 P_2}}\right)}

Benchmark Data Chart
Data pending publication

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Dataset

Chai, Yuan (2023). Sagittal Pelvic Radiographs: A Dataset for Clinical Quantification of Radiographic Annotation Accuracy. figshare. https://doi.org/10.6084/m9.figshare.23820879.v1

Chai, Yuan (2023). Data records for Clinical Quantification of Radiographic Annotation Accuracy. figshare. Dataset. https://doi.org/10.6084/m9.figshare.23831553.v1