High-quality astronomical images delivered by modern ground-based and space observatories demand adequate, reliable software for their analysis and accurate extraction of sources, filaments, and other structures, containing massive amounts of detailed information about the complex physical processes in space. The multiwavelength observations with highly variable angular resolutions across wavebands require extraction tools that preserve and use the invaluable high-resolution information. Complex fluctuating backgrounds and filamentary structures appear differently on various scales, calling for multiscale approaches for complete and reliable extraction of sources and filaments. The availability of many extraction tools with varying qualities highlights the need to use standard model benchmarks for choosing the most reliable and accurate method for astrophysical research. This paper presents getsf, a new method for extracting sources and filaments in astronomical images using separation of their structural components, designed to handle multiwavelength sets of images and very complex filamentary backgrounds. The method spatially decomposes the original images and separates the structural components of sources and filaments from each other and from their backgrounds, flattening their resulting images. It spatially decomposes the flattened components, combines them over wavelengths, detects the positions of sources and skeletons of filaments, and measures the detected sources and filaments, creating the output catalogs and images. The fully automated method has a single user-defined parameter (per image), the maximum size of the structures of interest to be extracted, that must be specified by users. This paper presents a realistic multiwavelength set of simulated benchmark images that can serve as the standard benchmark problem to evaluate qualities of source- and filament-extraction methods. This paper describes hires, an improved algorithm for the derivation of high-resolution surface densities from multiwavelength far-infrared Herschel images. The algorithm allows creating the surface densities with angular resolutions that reach 5.6″ when the 70 μm image is used. If the shortest-wavelength image is too noisy or cannot be used for other reasons, slightly lower resolutions of 6.8−11.3″ are available from the 100 or 160 μm images. These high resolutions are useful for detailed studies of the structural diversity in molecular clouds. The codes getsf and hires are illustrated by their applications to a variety of images obtained with ground-based and space telescopes from the X-ray domain to the millimeter wavelengths.