Multiple ellipse fitting of densely connected contours

Research on the Contour Modeling Method of Peripheral Nerve Internal Fascicular Groups During the Non-Splitting/Merging Phase and Distribution Rules of Model Parameters

Objectives

To investigate benchmark data for docking the same functional nerve bundles based on the mathematical contour model of peripheral nerve internal fascicular groups.

Materials and Methods

First, the discrete points of the original contours of nerve bundles were extracted into a dataset through the image process. Second, two indicators were employed to evaluate the modeling precision. Third, the dataset was modeled by the 3rd-order quasi-uniform B-spline method. Fourth, the dataset was modeled by the Fourier transform method. Fifth, all contours were modeled by the 4th-order Fourier method. Then, the histogram of each parameter from the Fourier model was calculated. Furthermore, the probability density function was fit to each parameter.

Results

First, the optimized sampling number of the 3rd-order quasi-uniform B-spline method is 21. The sampling number is the control point number of the 3rd-order quasi-uniform B-spline, which produces more than 63 parameters in the model. Second, when the Fourier transform model is employed to model the contour of nerve bundles, the optimized order number yields a 4th-order Fourier model, which has 16 parameters. Third, when all contours are modeled by the 4th-order Fourier model, the statistical analysis shows that (1) the pitch parameters a1 and d1 obey the mixed Gaussian distribution; (2) the harmonic parameter b3 obeys the normal distribution; and (3) the pitch parameters b1 and c1 and the remaining harmonic parameters obey the t distribution with position and scale.

Conclusion

This work paves the way for the exploration of the correlation between model parameters and spatial extension.