The invention describes a method and a microscopy system for imaging and analysing stochastically and independently blinking point-like emitters. A multiple-order cumulants analysis in conjunction with an established blinking model enables the extraction of super-resolved environment-related parameter maps, such as molecular state lifetimes, concentration and brightness distributions of the emitter. In addition, such parameter maps can be used to compensate for the non-linear brightness and blinking response of higher-order cumulant images - used for example in Super-resolution Optical Fluctuation Imaging (SOFI) - to generate a balanced image contrast. Structures that otherwise would be masked by brighter regions in the conventional cumulant image become visible in the balanced cumulant image. The invention furthermore provides a method for the spectral unmixing of multi- colour samples using spectral cross-cumulants.