This paper proposes a new edge detection method using a $3{ imes}3$ ideal binary pattern and lookup table (LUT) for the mobile robot localization without any parameter adjustments. We take the mean of the pixels within the $3{ imes}3$ block as a threshold by which the pixels are divided into two groups. The edge magnitude and orientation are calculated by taking the difference of average intensities of the two groups and by searching directional code in the LUT, respectively. And also the input image is not only partitioned into multiple groups according to their intensity similarities by the histogram, but also the threshold of each group is determined by fuzzy reasoning automatically. Finally, the edges are determined through non-maximum suppression using edge confidence measure and edge linking. Applying this edge detection method to the mobile robot localization using projective invariance of the cross ratio. we demonstrate the robustness of the proposed method to the illumination changes in a corridor environment.