Freehand three-dimensional (3D) ultrasound imaging enables low-cost and flexible 3D scanning of arbitrary-shaped
organs, where the operator can freely move a two-dimensional (2D) ultrasound probe to acquire a sequence of tracked
cross-sectional images of the anatomy. Often, the acquired 2D ultrasound images are irregularly and sparsely distributed
in the 3D space. Several 3D reconstruction algorithms have been proposed to synthesize 3D ultrasound volumes based
on the acquired 2D images. A challenging task during the reconstruction process is to preserve the texture patterns in the
synthesized volume and ensure that all gaps in the volume are correctly filled. This paper presents an adaptive kernel
regression algorithm that can effectively reconstruct high-quality freehand 3D ultrasound volumes. The algorithm
employs a kernel regression model that enables nonparametric interpolation of the voxel gray-level values. The kernel
size of the regression model is adaptively adjusted based on the characteristics of the voxel that is being interpolated. In
particular, when the algorithm is employed to interpolate a voxel located in a region with dense ultrasound data samples,
the size of the kernel is reduced to preserve the texture patterns. On the other hand, the size of the kernel is increased in
areas that include large gaps to enable effective gap filling. The performance of the proposed algorithm was compared
with seven previous interpolation approaches by synthesizing freehand 3D ultrasound volumes of a benign breast tumor.
The experimental results show that the proposed algorithm outperforms the other interpolation approaches.