3D Reconstruction Using Cubic Bezier Spline Curves and Active Contours (Case Study)

Document Type : Original Paper


1 Department of Applied Mathematics, School of Mathematical sciences, Ferdowsi University, Mashhad, Iran

2 Department of Medical Physics, Faculty of Medicine, Mashhad University of Medical Sciences, Mashhad, Iran Nuclear medicine Research Center, Imam Reza Hospital, Faculty of Medicine, Mashhad University of Medical Sciences, Mashhad, Iran.

3 Department of Medical Physics, Faculty of Medicine, Mashhad University of Medical Sciences, Mashhad, Iran Medical Physics Research Center, Faculty of Medicine, Mashhad University of Medical Sciences, Mashhad, Iran


3D reconstruction of an object from its 2D cross-sections (slices) has many applications in different fields of sciences such as medical physics and biomedical engineering. In order to perform 3D reconstruction, at first, desired boundaries at each slice are detected and then using a correspondence between points of successive slices surface of desired object is reconstructed.
Materials and Methods
In this study, Gradient Vector Flow (GVF) was used in order to trace the boundaries at each slice. Then, cubic Bezier Spline curves were used to approximate each of obtained contours and to approximate the corresponding points of different contours at successive slices. The reconstructed surface was a bi-cubic Bezier Spline surface which was smooth with G2 continuity.
Our presented method was tested on SPECT data of JASZCZAK phantom and human's left ventricle. The results confirmed that the presented method was accurate, promising, applicable, and effective.
Using GVF algorithm to trace boundaries at each slice, and cubic Bezier Spline curves to approximate the obtained rough contours yield to the procedure of reconstruction which was fast and also the final surface was smooth with G2 continuity. So far, some mathematical curves such as spline, cubic spline, and B-spline curves were used to approximate the computed contour during a time consuming procedure. This study presented a 3D reconstruction method based on a combination of GVF algorithm and cubic Bezier Spline curves. There was a good trade-off between speed and accuracy in using cubic Bezier Spline curves which is especially useful for training students.


Main Subjects

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