3D reconstruction of vessels from two uncalibrated mammography images

Abstract

Three dimensional modeling of organs plays a crucial role in the treatment of cancer and radio vascular diseases. The purpose of this work is 3D modeling of breast vessels using only two uncalibrated two-dimensional mammography images in order to have the patient less exposed to X-ray radiation. In the proposed method, we first optimize the internal and external parameters using a nonlinear optimization framework. To this end, we use the data stored in the header of files and key features in the mammography images. Using the optimized parameters, 3D active contours is proposed for 3D modeling of the vessels. Then using the parameters obtained from the previous step, an initial active curve gradually evolves until the energy of active curve is minimized. The surface reconstruction of the vessels is done by employing the methods converting a set of surface points to lattice surface. The proposed method is implied for a set of mammography images. Assuming optimized parameters are achieved, the method can yield promising 3D reconstruction.

Reconstruction of three‐dimensional linear structures in the breast from craniocaudal and mediolateral oblique mammographic views

“…For the purpose of comparison, the approach in [6] reports an average deviation of 1.0 pixel/pixel between their algorithmic reconstruction and the manual reconstruction of the aforesaid synthetic pattern of linear structures.…”

“…Babaee and Nilchi [6] improved the 3D reconstruction of vessels, given two mammograms and an initial estimate of the 3D vessel. This assumption of an initial 3D shape of the vessels is practically not tenable.…”

“…This assumption of an initial 3D shape of the vessels is practically not tenable. In [6], the 3D initial shape is back projected into the CC plane and the MLO plane. The minimisation of the deviation of the position of the back projected vessels in the 2D planes (CC or MLO) from the nearest actual vessel in the CC and MLO mammographic views is done iteratively.…”

“…The minimisation of the deviation of the position of the back projected vessels in the 2D planes (CC or MLO) from the nearest actual vessel in the CC and MLO mammographic views is done iteratively. However, the proof regarding the convergence of this implementation is absent in [6].…”

“…There is an upper bound on the time complexity of the proposed algorithm. In contrast to [6], our proposed methodology does not require any manual initialisation of the 3D position of the linear structures. Stotzka et al [16] and Yam et al [17] perform a 3D reconstruction of micro‐calcifications from two mammograms.…”