Robust automatic segmentation of multiple implanted cylindrical gold fiducial markers in cone-beam CT projections
The five steps of the segmentation method.
Step 1: (A) Part of a CBCT projection of a prostate cancer patient with identified marker candidates shown as white blobs. (B) The same part with white arrows showing the actual markers and a black arrow indicating a structure falsely identified as a potential marker.
Step 2: Appearance of segmented blobs and dynamic template during tracing where: Pn is an unfiltered part of the CBCT projection. Bn is the blob segmented from Pn. Tdyn,n is the dynamic template updated as a running average and used for template based segmentation in Pn+1. n denotes the projection number with n = 1 being the projection in which the marker candidate was first identified and the trace was started.
Step 2: Identified trace candidates shown in x and y direction of the CBCT projections for the prostate case presented in Fig. 2. The circles show the marker candidates identified in step 1 in the projection in Fig. 2. The black arrow indicates the erroneous marker candidate from Fig. 2(B).
Step 3: Gray and black curves show the trace candidates from Fig. 4. (step 2) for the same prostate CBCT scan. The red and green curves indicate the expected location region of candidate traces if the two bold black trace candidates were representing true markers.
Step 4: (A) Division of projections into segments based on the beginnings and endings of traces from step 3. The labeled segments each contain four traces, which is the highest number, and will form the basis of the average 3D marker constellation model. (B) The four P’s in the plot represent the four traces of segment P in (A), etc. Based on 3D distance, groups of P+Q+R+S’s are combined to form a marker. (C) Resulting average 3D marker constellation model.
Step 4: (A) Projected center-of-mass position in cranio-caudal direction of two traces from step 3 for two implanted liver markers. The colors show the grouping into four subsets based on the cranio-caudal position. (B) Average 3D marker constellation model. (C) Four position-dependent 3D marker constellation sub-models based on the subsets in (A).
Examples of templates for segmentation constructed by projection of the position dependent 3D marker constellation model. (A) Prostate markers from the example in Figs. 2–6. (B) Liver markers from the example in Fig. 7. Boxes indicate the use of joint templates. Projection numbers are consistent with Figs. 4–7. The numbers in parenthesis are the kV imager angle.
Final segmentation of four prostate markers (left panel) and two liver markers (right). (A) Projected center-of-mass position in Cranio-Caudal direction of the traces from step 4, and its division into four subsets. (B) Maximum cross correlation coefficient in search area for templates based on the four position dependent 3D marker constellation sub-models. (C), (D) Final segmented x and y position of each implanted marker with color coding showing which 3D marker constellation sub-model was used.
Constants and thresholds used for marker segmentation in the five steps. The same set of values was used for prostate, liver, and external markers.
Segmentation success rates and properties of data set. The CBCT scans with external markers are a subset of the liver scans, where external markers were placed on the abdomen of the patient.
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