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.
New adaptive varying window size estimation methods for edge detection are presented in this work. The nonparametric Local Polynomial Approximation (LPA) method is used to define gradient estimation kernels or masks, which in conjunction with varying adaptive window size selection, carried out by the Intersection of Confidence Intervals (ICI) for each pixel, let us obtain algorithms which are adaptive to unknown smoothness and nearly optimal in the point-wise risk for estimating the intensity function and its derivatives. Several existing strategies using a constant window size of the convolutional kernel of edge detection have been upgraded to become varying window size techniques, first through the use of LPA for defining the gradient convolutional kernels of different sizes and second through ICI for the selection of the best estimate which balances the bias-variance trade-off in a point wise fashion for the whole stream of data. Comparisons with invariant window size edge detection schemes show the superiority of the presented methods, even over computationally more expensive techniques of edge detection.
New weight functions called filters or masks, have been designed through nonparametric Local Polynomial Approximation methods (LPA) for both, de-Noising and edge detection tasks. These new masks, are combined with the nearest neighborhood interpolators. The produced modified nearest neighborhood interpolation filter structures are incorporated to a new and effective statistical strategy of bandwidth (window size) selection known as the Intersection of Confidence Intervals (ICI), rendering good performance and accuracy when dealing contaminated data. Nonparametric estimation methods (among them LPA) can be considered as being the driving force for the development of bandwidth selection methods (among them ICI).
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