Polymer latex surfaces were investigated with a new instrument performing mechanical imaging based on the thermal motion of a cantilever of an atomic force microscope. In low-viscosity environments, the power spectral density of the cantilever's Brownian motion is given by resonance curves. From the resonance frequency, the bandwidth, and the amplitude, one obtains the effective spring constant and the drag coefficient of the cantilever. These parameters change when the cantilever makes contact with the sample and provide information on the sample's mechanical properties. The instrument has three-channel nanopositioning capability with feedback-control. The noise power spectra are analyzed in real-time. The imaging capabilities were employed to correlate the surface topography of polymer latex films with the film's ability to produce filaments on pulling with the AFM tip. The film surface has a granular structure due to incomplete coalescence of the neighboring particles. The micromechanical properties of elongated filaments depend on the spatial position of the AFM tip. Most filaments originate from the center of the underlying particle. The mechanical properties of the filaments as a function of pulling distance are characterized by plateaus and steps.