Simulational Evaluation of Medial Axis Detection

We evaluated the medial axis detection performance using synthesized 3-D images of lines with pill-box cross-sections. A simulated partial volume effect was incorporated when synthesizing the images. We focused on the effects of the filter scale af used in medial axis detection on the detection various widths of line structures.

Synthesized 3-D images of a line with a circular axis were generated. The diameter of the line, D, was varied between 2.0 and 11.3) voxels. The radius of the circular axis was proportional to D (we used 4 x D). Gaussian noise with 25% standard deviation in the intensity height of pill-box cross-sections was added to the images. After line and sheet enhancement filtering with

Figure 10.12: Medial axis detection from synthesized 3-D images. All units are voxels. (a) Volume-rendered images of original synthesized 3D images with Gaussian noise. Upper: D = 2.0. Lower: D = 11.3. (b) Examples of successful axis detection where the filter scale af is appropriate for the line diameter D. The detected axis points are shown as bright points. Upper: D = 2.0, af = 1.4. Lower: D = 11.3, af = 4.0. (c) Examples of undesirable axis detection. Upper: D = 2.0, af = 4.0. When diameter D is smaller than that appropriate for the filter scale a f, many true axis points are overlooked. Lower: D = 11.3, a f = 1.4.When D is larger than that appropriate for af, many false axis points are detected.

Figure 10.12: Medial axis detection from synthesized 3-D images. All units are voxels. (a) Volume-rendered images of original synthesized 3D images with Gaussian noise. Upper: D = 2.0. Lower: D = 11.3. (b) Examples of successful axis detection where the filter scale af is appropriate for the line diameter D. The detected axis points are shown as bright points. Upper: D = 2.0, af = 1.4. Lower: D = 11.3, af = 4.0. (c) Examples of undesirable axis detection. Upper: D = 2.0, af = 4.0. When diameter D is smaller than that appropriate for the filter scale a f, many true axis points are overlooked. Lower: D = 11.3, a f = 1.4.When D is larger than that appropriate for af, many false axis points are detected.

integration of scales appropriate for the line diameter [7, 11], the candidate regions were extracted by thresholding and extracting large connective components. The medial axis points were detected within these regions using the procedures described in Section 10.4.1 with two values for the filer scale af, V2

1.4) and 4.0 voxels. The same candidate regions were used for both values of a f.

Figure 10.12 shows the volume rendering of the synthesized 3-D images and typical axis detection results. The detection was successful using appropriate combinations of line diameter D and filter scale af (Fig. 10.12(b)). Many axis points are overlooked when the filter scale is larger than appropriate, while a number of false detections are made when the filter scale is smaller than appropriate (Fig. 10.12(c)).

2 2.82 4 5.66 8 11.31 Line_Diameter (voxels)

2 2.82 4 5.66 8 11.31 Line_Diameter (voxels)

2 2.82 4 5.66 8 11.31 Line_Diameter (voxels)

2.82 4 5.66 8 11.31 Line_Diameter (voxels)

10

-1-

—i-1-n-r

CD

o =1.4 —1-4

£ TO CD

8

\

of=4.0 —x-4- -

\

/

6

\

/ -

O

\V

/

LL¡

4

/ ~

CD

---

TO

2

-

C <

0

,

2.82 4 5.66 8 11.31 Line_Diameter (voxels)

2.82 4 5.66 8 11.31 Line_Diameter (voxels)

2.82 4 5.66 8 11.31 Line_Diameter (voxels)

Figure 10.13: Performance evaluation of medial axis detection. See text for the definitions of true and false detections. (a) False positive detection ratio, which is the ratio of the number of false detections to all the detections. The ratio was zero for all the line diameters at af = 4.0 voxels. (b) True positive detection ratio, which is the ratio of the number of true detections to all the analytically determined points. (c) Average position error of axis points regarded as true detections. The distance between detected points and analytically determined points was used as the error. (d) Average angle error of the directions of axis points regarded as true detections.

Figure 10.13 shows the performance evaluation results. Detected axis points were evaluated by comparing them with analytically determined axis points. We regarded a detected point as a true detection if the distance between its position and one of the analytically determined points was within two voxels; otherwise, detected points were regarded as false. The false and true positive detection ratios are shown in Figs. 10.13(a) and 10.13(b); the plots verify the observations in Fig. 10.12. The positions and directions of the detected axis points regarded as true detections were compared with analytically determined ones (Figs. 10.13(c) and 10.13(d)). These graphs clarify the effect of af on accurate and reliable axis detection.

Figure 10.14: Diameter estimation of bronchial airways from CT images. (a) Original CT images. The bronchial airway regions, which are darker than the surrounding structures, are shown by arrows. (b) Detection of medial axes at three different scales. Left: af = 1.4 voxels. Middle: af = 2.0 voxels. Right: af = 2.8 voxels. (c) Diameter estimation at the three different scales. (A color version of this figure will appear on the CD that accompanies the volume.)

Figure 10.14: Diameter estimation of bronchial airways from CT images. (a) Original CT images. The bronchial airway regions, which are darker than the surrounding structures, are shown by arrows. (b) Detection of medial axes at three different scales. Left: af = 1.4 voxels. Middle: af = 2.0 voxels. Right: af = 2.8 voxels. (c) Diameter estimation at the three different scales. (A color version of this figure will appear on the CD that accompanies the volume.)

0 0

Post a comment