This paper presents a monotonic invariant intensity descriptor (MIID) via spectral embedding and nonsubsampled contourlet transform (NSCT). To make the proposed descriptor discriminative, NSCT is used for the construction of multiple support regions. Specifically, the directed graph and the spectral feature vectors of the signless Laplacian matrix are exploited to construct the MIID. We theoretically demonstrate that the proposed descriptor is able to tackle monotonic illumination changes and many other geometric and photometric transformations. We conduct extensive experiments on the standard Oxford dataset and the complex illumination dataset to demonstrate the superiority of proposed descriptor over the existing state-of-the-art descriptors in dealing with image blur, viewpoint changes, illumination changes, and JPEG compression.