Directional 3D Edge Detection in Anisotropic Data: Detector Design and Performance Assessment

Abstract

A new directional 3D edge detector designed for anisotropic image data is reported. The detector is based on interpolating the image intensity function in a small neighborhood of every voxel by a tri-cubic polynomial. The analytical approximation of the image intensity function is used to compute the intensity function gradients. The developed edge detector uses a maximum average of directional derivatives of the approximated image intensity function over a small neighborhood to determine the gradient direction. Our method is directly applicable to anisotropic image data, and it models the integrative character of data acquisition. With all these features, it remains computationally as expensive as any other convolution-based directional edge detector. Quantitative measures of the 3D edge detection accuracy were employed to compare the performance of our new edge detector to that of the 3D Canny edge detector. 3D edges with step and ramp profiles with varying surface curvatures at the edge point, as well as several levels of noise, were used for the performance testing. The reported edge detector significantly out-performed the Canny edge detector in most experiments in anisotropic data, as well as in data with superimposed noise. Another important property of the new edge detector is the ease of its implementation. Although its design required complex steps, the implementation employs straightforward 3D convolution in the volumetric image data using three precomputed directional masks. A complete description of the gradient implementation is presented.