In remote sensing, modern sensors produce multi-dimensional images. For example, hyperspectral images contain hundreds of spectral images. In many image processing applications, segmentation is an important step. Traditionally, most image segmentation and edge detection methods have been developed for one-dimensional images. For multidimensional images, the output images of spectral band images are typically combined under certain rules or using decision fusions. In this paper, we proposed a new edge detection algorithm for multi-dimensional images using secondorder statistics. First, we reduce the dimension of input images using the principal component analysis. Then we applied multi-dimensional edge detection operators that utilize second-order statistics. Experimental results show promising results compared to conventional one-dimensional edge detectors such as Sobel filter.