New adaptive edge detection algorithms based on volumetric neighborhood size estimation for automatic three or higher dimensional biomedical image analysis are presented in this work. The proposed methods are based on nonparametric three-dimensional kernel functions obtained using the "three-term" orthogonal-type polynomial equations for different types of orthogonal polynomial families. The obtained multidimensional kernels can be of any volumetric neighborhood size and order of approximation. The optimal sizes of volume estimates, produced by the multidimensional convolution of the kernels with the multidimensional biomedical images, are controlled by a switch type variance dependent volume size selector. The proposed methods show excellent results in approximating the true position and shape of the edges of different organs of the human body represented in multidimensional biomedical images, which can have nonuniform voxel size and anisotropic image intensity and noise distribution.