An elapsed facial emotion involves changes of facial contour due to the motions (such as contraction or stretch) of facial muscles located at the eyes, nose, lips and etc. Thus, the important information such as corners of facial contours that are located in various regions of the face are crucial to the recognition of facial expressions, and even more apparent for micro-expressions. In this paper, we propose the first known notion of employing intrinsic two-dimensional (i2D) local structures to represent these features for micro-expression recognition. To retrieve i2D local structures such as phase and orientation, higher order Riesz transforms are employed by means of monogenic curvature tensors. Experiments performed on micro-expression datasets show the effectiveness of i2D local structures in recognizing micro-expressions.