A schematic illustration on how to compute the visual feature of a sampled 3D image patch for RF training and regression.

<p><b>Left</b>: a sub-volume is sampled from a MRI/CT volume. <b>Middle</b>: we divide the sampled image patch into <i>k</i> × <i>k</i> × <i>k</i> blocks. <b>Right</b>: for each block, we compute its mean and variance using the integral image technique.</p

Successful detection rate with various ranges of accuracy when evaluated on 23 3D MR images.

<p>In the first row, number of successfully detected VBs are given, and in the second row the successful detection rate are shown.</p

Average localization error (MLD with SD: mm) when evaluated on 10 3D CT data.

<p>Average localization error (MLD with SD: mm) when evaluated on 10 3D CT data.</p

The fine-tuning step for localization of the estimated VB centers on the same test CT image used in Fig 4.

<p>The response volume of L3, L4, and L5 are visualized in each row, with 3 randomly selected 2D sagittal slices. The fine-tuning is performed only in a reduced local region around the initial guess obtained from the first step. Thus, the associated probabilities in the response volume are concentrated to a small region.</p

Successful detection rate with various ranges of accuracy when evaluated on 10 3D CT images.

<p>In the first row, number of successfully detected VBs are given, and in the second row the successful detection rate are shown.</p

Segmentation results on one test CT image visualized in 2D sagittal slices.

<p>The automatic segmentation (the bottom row) are compared with the ground-truth segmentation (the top row).</p

Segmentation results when the present method was evaluated on 23 3D MR images with a leave-one-out experiment.

<p>The results are calculated on 2D mid-sagittal slices.</p

Initial estimation of the VB centers on one test CT image.

<p>The estimation is done in a coarse resolution. The response volume of L3, L4, and L5 are visualized in each row, with 3 randomly selected 2D sagittal slices. The diffused probability distribution is observed in the response volumes due to the repetitive pattern of the VBs.</p

Segmentation results visualized with 3D surface models.

<p>Images on the left side show the segmentation results on 2 3D MR test images and images on the right side present the segmentation results on 2 3D CT images. It is worth to note that the second CT data (bottom right image) shows osteophytes in some of the VBs but our method successfully identified and segmented all the 5 VB regions in this CT data with a Dice of 90.7%.</p

Segmentation results when the present method was evaluated on 23 3D MR images with a leave-one-out experiment.

<p>The results are calculated on 3D volumes.</p