Multiscale Opening of Conjoined Fuzzy Objects: Theory and Applications

Abstract

Theoretical properties of a multi-scale opening (MSO) algorithm for two conjoined fuzzy objects are established, and its extension to separating two conjoined fuzzy objects with different intensity properties is introduced. Also, its applications to artery/vein (A/V) separation in pulmonary CT imaging and carotid vessel segmentation in CT angiograms (CTAs) of patients with intracranial aneurysms are presented. The new algorithm accounts for distinct intensity properties of individual conjoined objects by combining fuzzy distance transform (FDT), a morphologic feature, with fuzzy connectivity, a topologic feature. The algorithm iteratively opens the two conjoined objects starting at large scales and progressing toward finer scales. Results of application of the method in separating arteries and veins in a physical cast phantom of a pig lung are presented. Accuracy of the algorithm is quantitatively evaluated in terms of sensitivity and specificity on patients' CTA data sets and its performance is compared with existing methods. Reproducibility of the algorithm is examined in terms of volumetric agreement between two users' carotid vessel segmentation results. Experimental results using this algorithm on patients' CTA data demonstrate a high average accuracy of 96.3% with 95.1% sensitivity and 97.5% specificity and a high reproducibility of 94.2% average agreement between segmentation results from two mutually independent users. Approximately, twenty-five to thirty-five user-specified seeds/separators are needed for each CTA data through a custom designed graphical interface requiring an average of thirty minutes to complete carotid vascular segmentation in a patient's CTA data set.

Keywords: CTA; Fuzzy connectivity; carotid vasculature; fuzzy distance transform; morphology; multi-scale opening; pulmonary vasculature.

Fig. 1

A schematic illustration of the results of different steps in the MSO algorithm—(a) optimal erosion, (b) constrained dilation, and (c) iterative progression to the next iteration.

Fig. 2

A schematic description of challenges in separating bone and vasculature in CTA. (a) Multi-scale fusion of bone (green) and vessel (red) demands local scale-adaptive opening. (b) Intensity-based membership functions for vessel and bone along with pure and shared intensity bands. (c) Color-coded combined vessel and bone membership maps on an axial image slice in a patient's CTA. Regions indicated in pure green are pure bone; here, no pure vessel region is identified and therefore all other regions fall in the shared space. The figures shown in (a) and (b) were previously published by the authors in an IEEE conference paper [31].

Fig. 3

A modular representation of the MSO algorithm.

Fig. 4

A/V separation on a pulmonary pig vessel cast phantom. (a) A photograph of the phantom. (b) An axial image slice from the phantom CT image with different contrast for A/V trees. (c) CT intensity-based A/V classification showing partial voluming effects as thin red films wrapping around blue arteries. (d,e) Same as (b,c) on a coronal image slice. (f) CT intensity histogram of the phantom where the two CT intensity values I_min and I_artery segments the background and pure artery regions. (g) Optimum thresholding and morphological erosion are applied on (b) to separate the core arteries and veins. (h) A/V separation on (b) using the MSO algorithm. (i,j) Same as (g,h) on the matching coronal image slice of (d,e). (k) 3-D rendering of A/V separation using optimum thresholding morphological erosion. (l) Same as (k) but using the MSO algorithm.

Fig. 5

Result of carotid vessel segmentation in a patient's CTA. (a) An axial image slice. (b) Intensity based characterization of pure bone (green) and shared intensity band with red indicating high likelihood for vessels. (c) CTA intensity histogram with I_min and I_bone segmenting the background and the pure bone regions. (d) Axial image slice with the core vasculature marked in red. (e) 3-D rendering of the core vasculature. (f, g) 2-D and 3-D displays of bone-vessel separation using the MSO algorithm.

Fig. 6

Illustration of vascular segmentation results in three patients' CTAs. Here the bone structure is illustrated with partial transparency to depict segmented vessels through soft bones.

Fig. 7

Illustration of comparative results of vessel segmentation in a patient's CTA data using different algorithms – (a,b) MSO, (c) MSVGAR, (d) IRFC-conservative, and (d) IRFC- generous.

Fig. 8

Results of vascular segmentation and bone removal in two patients' CTA data sets as obtained by two mutually blinded trained-users. Reproducibility results shown in the first row are visually almost indistinguishable due to high Agreement (96.9%), while the results in the bottom row have moderate Agreement (94.2%) with apparent differences in segmentation results near the bottom section of the arterial tree