Using cubic Bezier spline curves and active contours in surface reconstruction (Phantom study)

Introduction: SPECT imagery gives functionality information about the organ with no clue on it's anatomy. This data shows the activity inside with no information about shape. Thus the accurate determination of borders is difficult and perior knowlage of shape is usually required to estimate borders. The reconstruction is a first process that will serve as an important diagnosis tool for hospital. This paper presents a novel surface reconstruction. Method: based on cubic Bezier spline curves and active contours, applied to SPECT image segmentation. Methods: The PHANTOM is a test-method that offers known geometry and volume, allowing us to compare with the obtained results. We use deformable model called GVF snake. GVF snake is based on the energy minimization approach. The use of GVF vector field avoids some of the limitations of traditional snakes related to initial distance to data and robustness in concave regions. This snake like other active contour models often produced rough edgs and protrusions. We use one of the best curve in Computer Aided Design (CAD) called cubic Bezier spline curve to approximate the detected contour at each slices. Then we matched points on every contour with parameter-based match method. After this step we interpolate corresponding points of different contours by using cubic Bezier spline curve, too. Results: We use Matlab 7.8 language. The computer configuration is CPU P4/3.20 GHZ with memory of 1GB. The parameters in the model were determined empirically and were kept constant throughout the experiments. We can extract edge at each slices and then compute volume of phantom. Conclusion: The reconstructed surface is smooth because every two cubic Bezier spline curves is patched with G2 continuity. The reconstruction speed is fast because we can use the forward elimination and backward substitution method to solve the system of tridiagonal equations. Finally, using GVF snake makes high precision for this method. There is a good agreement between experiment results and real values, that shows our method is acceptable. We hopefully applied this method to segmentation of the left ventricle of the heart in SPECT images, in the next stage.