Topomorphologic separation of fused isointensity objects via multiscale opening: separating arteries and veins in 3-D pulmonary CT

Abstract

A novel multiscale topomorphologic approach for opening of two isointensity objects fused at different locations and scales is presented and applied to separating arterial and venous trees in 3-D pulmonary multidetector X-ray computed tomography (CT) images. Initialized with seeds, the two isointensity objects (arteries and veins) grow iteratively while maintaining their spatial exclusiveness and eventually form two mutually disjoint objects at convergence. The method is intended to solve the following two fundamental challenges: how to find local size of morphological operators and how to trace continuity of locally separated regions. These challenges are met by combining fuzzy distance transform (FDT), a morphologic feature with a topologic fuzzy connectivity, and a new morphological reconstruction step to iteratively open finer and finer details starting at large scales and progressing toward smaller scales. The method employs efficient user intervention at locations where local morphological separability assumption does not hold due to imaging ambiguities or any other reason. The approach has been validated on mathematically generated tubular objects and applied to clinical pulmonary noncontrast CT data for separating arteries and veins. The tradeoff between accuracy and the required user intervention for the method has been quantitatively examined by comparing with manual outlining. The experimental study, based on a blind seed selection strategy, has demonstrated that above 95% accuracy may be achieved using 25-40 seeds for each of arteries and veins. Our method is very promising for semiautomated separation of arteries and veins in pulmonary CT images even when there is no object-specific intensity variation at conjoining locations.

Fig. 1

Schematic description of the segmentation problem addressed by the proposed multiscale topomorphologic opening method and the challenges met at different steps.

Fig. 2

Modular representation of the multiscale topomorphologic opening algorithm separating two isointensity objects fused at different scales and locations.

Fig. 3

Illustration of intermediate results at different steps of the multiscale topomorphologic opening. (a) 3-D rendition of a computer-generated phantom representing two isointensity objects fused at various scales and locations. (b) Few cross-sectional images of the phantom. (c) FDT image on the central xy plane. Intuitively, it is a union of two FDT maps, one for each cylinder. Although the cylinders are locally separable in the FDT image, no global thresholding serves the purpose. (d) Results of separation of two cylinders after first iteration using FDT-based connectivity. (e) Morphologic reconstruction on the result shown in (d). Regions marked in cyan (or yellow) represent the expansion of the red (respectively, blue) object after morphological reconstruction. (f) and (g) Same as (d) after second (f) and terminal (g) iterations. (h) and (i) 3-D rendition and cross-sectional images of the final result.

Fig. 4

(a)–(k) Results of applying our method to several computer-generated 3-D phantoms after 4 × 4 × 4 downsampling. (a) and (b) 3-D rendition and cross-sectional images of one phantom. (c) Separated cylinders. (d)–(k) Results for other four phantoms. (l)–(v) Results of application of the method after downsampling. Note that this level of downsampling makes separation impossible for the smallest scale features.

Fig. 5

Results of application of the method to a human in vivo pulmonary multidetector CT image. (a) Coronal image slice from a thoracic CT image of a 22-year-old female. (b) Fuzzy segmentation of vasculature. (c) and (d) Original and local-scale normalized FDT maps of the vasculature. (e) 3-D surface rendition of left and right pulmonary vascular trees. (f) Color-coded 3-D rendition of separated arterial and venous trees computed by the proposed method.

Fig. 6

Same as Fig. 5 but for another human subject.

Fig. 7

(a) and (b) Graphical presentations of results of quantitative analysis comparing required user intervention with accomplished sensitivity and false detection for the pulmonary CT data presented in Figs. 5(a) and 6(b). For the example of Fig. 5, the numbers of seeds, false, and miss at 95% and 99% overall sensitivity are: 27, 4.2%, 0.8% and 52, 0.6%, 0.4%, respectively; these numbers for the example of Fig. 6 are 40, 3.7%, 1.3% and 66, 0.5%, 0.5%, respectively. (c)–(f) Qualitative illustrations of artery/vein separation at sensitivity levels of 80%, 90%, 95%, and 99%, respectively. To facilitate visual comparison, the image of Fig. 6(f) is repeated in (g).

Fig. 8

(a) Few examples of mathematical phantoms each containing two tubular objects fused at different locations and scales with significant overlap. (b) Results of separations of two objects using the algorithm by Lei et al. [12], (c) simple FDT-based IRFC [18], [20], and (d) the multi-scale topomorphologic opening algorithm reported here.