This paper proposes an efficient algorithm for segmenting the Pulmonary Artery (PA) tree in 3D pulmonary Computed Tomography Angiography (CTA) images. In this algorithm, to reduce the search area the lung regions from the original image are first segmented and the heart region is extracted by selecting the regions between the lungs. A pre-processing algorithm based on Hessian matrix and its eigenvalues is used to remove the connectivity between the pulmonary artery and other nearby pulmonary organs. To extract the pulmonary artery tree, we first use a region growing method initialized by a seed point which is automatically selected within the pulmonary artery trunk in the heart region. In the second step, the segmentation of the pulmonary artery is performed using a 3D level set algorithm, using the output of region grower as the initial contour. We use a new stopping criterion for the used level set algorithm, a consideration often neglected in many level set implementations. To validate and assess the robustness of the method, 20 CT angiography datasets were used (10 free pulmonary embolism scans and 10 CT with pulmonary emboli). A very good agreement with the visual judgment was obtained in both normal and positive pulmonary emboli CT scans.

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In this paper, we introduce a new form of the quadratic reciprocal functional equation. Then, we study the Hyers–Ulam stability for this quadratic reciprocal functional equation in non-Archimedean fields.

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