The traditional ray casting algorithm has the capability to render three-dimensional volume data in the viewable two-dimensional form by sampling the color data along the rays. The speed of the technique relies on the computation incurred by the huge volume of rays. The objective of the paper is to reduce the computations made over the rays by eventually reducing the number of samples being processed throughout the volume data. The proposed algorithm incorporates the grouping strategy based on fuzzy mutual information (FMI) over a group of voxels in the conventional ray casting to achieve the reduction. For the data group, with FMI in a desirable range, a single primary ray is cast into the group as a whole. As data are grouped before casting rays, the proposed algorithm reduces the interpolation calculation and thereby runs with lesser complexity, preserving the image quality.

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The three-dimensional (3D) reconstruction of medical images usually requires hundreds of two-dimensional (2D) scan images. Segmentation, an obligatory part in reconstruction, needs to be performed for all the slices consuming enormous storage space and time. To reduce storage space and time, this paper proposes a three-stage procedure, namely, slice selection, segmentation and interpolation. The methodology will have the potential to 3D reconstruct the human head from minimum selected slices. The first stage of slice selection is based on structural similarity measurement, discarding the most similar slices with none or minimal impact on details. The second stage of segmentation of the selected slices is performed using our proposed phase-field segmentation method. Validation of our segmentation results is done via comparison with other deformable models, and results show that the proposed method provides fast and accurate segmentation. The third stage of interpolation is based on modified curvature registration-based interpolation, and it is applied to re-create the discarded slices. This method is compared to both standard linear interpolation and registration-based interpolation in 100 tomographic data sets. Results show that the modified curvature registration-based interpolation reconstructs missing slices with 96% accuracy and shows an improvement in sensitivity (95.802%) on par with specificity (95.901%).