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This paper investigates automatic construction of invariant features using Genetic Programming (GP) for edge detection. Generally, basic features for edge detection, such as gradients, are further manipulated to improve detection performance. In order to improve detection performance, new features are constructed from different local features. In this study, GP is proposed to automatically construct invariant features based on basic invariant features from gradients, image quality (means and standard deviations), and histograms of images. The experimental results show that the invariant features constructed by GP combine advantages from the basic features, reduce drawbacks from basic features alone, and also improve the detection performance.