We study a special case of the critical point (Morse) theory of distance functions namely, the gradient flow associated with the distance function to a finite point set in R 3 . The fixed points of this flow are exactly the critical points of the distance function. Our main result is a mathematical characterization and algorithms to compute the stable manifolds, i.e., the inflow regions, of the fixed points. It turns out that the stable manifolds form a polyhedral complex that shares many properties with the Delaunay triangulation of the same point set. We call the latter complex the flow complex of the point set. The flow complex is suited for geometric modeling tasks like surface reconstruction.

The data in the present study demonstrated the localization of the two major respiratory mucin proteins in human nasal mucosa with a similar distribution of expression of MUC5AC and MUC5B in normal upper and lower airways. Mucin protein expression parallels that of mucin messenger RNA expression.

C-arm CT is an emerging imaging technique in transcatheter aortic valve implantation (TAVI) surgery. Automatic aorta segmentation and valve landmark detection in a C-arm CT volume has important applications in TAVI by providing valuable 3D measurements for surgery planning. Overlaying 3D segmentation onto 2D real time fluoroscopic images also provides critical visual guidance during the surgery. In this paper, we present a part-based aorta segmentation approach, which can handle aorta structure variation in case that the aortic arch and descending aorta are missing in the volume. The whole aorta model is split into four parts: aortic root, ascending aorta, aortic arch, and descending aorta. Discriminative learning is applied to train a detector for each part separately to exploit the rich domain knowledge embedded in an expertannotated dataset. Eight important aortic valve landmarks (three aortic hinge points, three commissure points, and two coronary ostia) are also detected automatically in our system. Under the guidance of the detected landmarks, the physicians can deploy the prosthetic valve properly. Our approach is robust under variations of contrast agent. Taking about 1.4 seconds to process one volume, it is also computationally efficient.

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