Fusion of multiple chemically identical complexes, so-called particles, in localization microscopy, can improve the signal-to-noise ratio and overcome under-labeling. To this end, structural homogeneity of the data must be assumed. Biological heterogeneity, however, could be present in the data originating from distinct conformational variations or (continuous) variations in particle shapes. We present a prior-knowledge-free method for detecting continuous structural variations with localization microscopy. Detecting this heterogeneity leads to more faithful fusions and reconstructions of the localization microscopy data as their heterogeneity is taken into account. In experimental datasets, we show the continuous variation of the height of DNA origami tetrahedrons imaged with 3D PAINT and of the radius of Nuclear Pore Complexes imaged in 2D with STORM. In simulation, we study the impact on the heterogeneity detection pipeline of Degree Of Labeling and of structural variations in the form of two independent modes.