This article concerns testing the equality of multiple curves in a nonparametric regression context. The proposed test forms an ANOVA type test statistic based on kernel smoothing and examines the ratio of between-and within-group variations. The empirical distribution of the test statistic is derived using a permutation test. Unlike traditional kernel smoothing approaches, the test is conducted in scale-space so that it does not require the selection of an optimal smoothing level, but instead considers a wide range of scales. The proposed method also visualizes its testing results as a color map and graphically summarizes the statistical differences between curves across multiple locations and scales. A numerical study using simulated and real examples is conducted to demonstrate the finite sample performance of the proposed method.