For superpixel segmentation that partitions an image into multiple homogeneous regions, simple linear iterative clustering (SLIC) has been widely used as a preprocessing step in various image processing and computer vision applications due to its outstanding performance in terms of speed and accuracy. However, determining the segment where each pixel belongs still requires tedious, repeated computation to measure the distance between the pixel and every candidate segment. In this paper, by applying the Cauchy–Schwarz inequality, we derive an approximate distance metric and a simple condition using the metric to get rid of unnecessary computational operations from the cluster inspection procedure. Candidate clusters can be excluded if they satisfy a condition requiring much less computation than the normal cluster inspection involving the distance measure. We refer to the condition as early candidate cluster exclusion (ECCE). To maximize the success rate of ECCE, we propose a method to predict the best cluster for each pixel. In the experimental results, we analyzed various properties of the proposed approximate distance metric, including the required computational operations and the success rate of ECCE. We confirmed that the proposed superpixel segmentation algorithm improves SLIC’s computational efficiency by 219 %, on average, without any degradation in segmentation accuracy.