Interatomic and intermolecular forces have been extensively studied, for their ability to understand the processes at the interface between solids and aqueous solutions. In particular, atomic force microscopy (AFM) generates tridimensional images and force profiles at nanometric scale, whatever the nature of the samples (biological, organic, mineral). An AFM microscope affords the measurement of interatomic forces exerting between a probe associated to a cantilever and a chemical sample. A force spectrum f(z) shows the evolution of these forces as a function of the distance z between the probe and the sample. This is a pointwise analysis of the sample, obtained by measuring the cantilever deflection with respect to the probe-sample distance. A reproduction of this pointwise analysis, in conjunction with the scan of the sample surface yields a force-volume image f(x,y,z). This image is composed of the collection of force spectra f(z) on a grid (x,y) representing the sample surface. Today, the analysis and interpretation of a force-volume image remains mainly descriptive. In this paper, we introduce a signal processing formulation, which aims at a precise and automatic characterization of each pixel (xi,yi) of the sample surface. These problems include the decomposition of a force spectrum into elementary patterns, and the factorization of a force-volume image. We discuss the ability of standard signal processing methods to solve these problems, and we illustrate the discussion by means of experimental data.