4. Discussion

The aim of this work is not only to make a 3D reconstruction for visualization but also to describe the geometric shape-based fractal interpolation. The benefits of the proposed method to perform 3D reconstruction by 3D fractal interpolation method lies mainly in reducing storage memory for 3D blood vessel images. Indeed, the data-reduction rate ranges from 72 to 94% for the first test image and between 73 and 95% for the second image used, when the tolerance value varies from ε = 0.5 to 2 pixels. This allows us to reduce costs and transmission time. Another advantage in terms of execution time is obtained. This execution time range is varying from 4 to 14 s, according to the iteration number. Furthermore, an accurate form of description is reached since the algorithm does not only interpolate the original points but also determines the interconnection between these points. However, the weakness of our algorithm is the space complexity of algorithm calculation. It requires a specialized computer to minimize the execution time.

In previous works, the result obtained by Guedri et al. [11] offers an innovative approach for 3D reconstruction with fractal calculation time between 4 and 40 s. The execution time of the present method is about 4–14 s for the same number of iterations. Thus, we can note that the present method is faster than other methods.

Regarding the error evolution of the curvature by using the 3D fractal interpolation, Guedri et al. [11] obtained an error between 0.8 and 8%. The new method is indeed better than the other method in terms of error. The error value is between 0.27 and 6.7% and between 0.25 and 6.5% for the first test image and for the second test image, respectively.

This comparison shows that our proposed method can correctly follow all the 3D branches of the blood vessels and reduces the execution time while having a minimal error.
