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In the fields of nanoscience and nanotechnology, it is important to be able to functionalize surfaces chemically for a wide variety of applications. Scanning tunneling microscopes (STMs) are important instruments in this area used to measure the surface structure and chemistry with better than molecular resolution. Self-assembly is frequently used to create monolayers that redefine the surface chemistry in just a single-molecule-thick layer. Indeed, STM images reveal rich information about the structure of self-assembled monolayers since they convey chemical and physical properties of the studied material. In order to assist in and to enhance the analysis of STM and other images, we propose and demonstrate an image-processing framework that produces two image segmentations: one is based on intensities (apparent heights in STM images) and the other is based on textural patterns. The proposed framework begins with a cartoon+texture decomposition, which separates an image into its cartoon and texture components. Afterward, the cartoon image is segmented by a modified multiphase version of the local Chan-Vese model, while the texture image is segmented by a combination of 2D empirical wavelet transform and a clustering algorithm. Overall, our proposed framework contains several new features, specifically in presenting a new application of cartoon+texture decomposition and of the empirical wavelet transforms and in developing a specialized framework to segment STM images and other data. To demonstrate the potential of our approach, we apply it to actual STM images of cyanide monolayers on Au\{111\} and present their corresponding segmentation results.