Non-intrusive load monitoring (NILM) systems have gained extensive interest due to their potential role regarding power savings for residential customers. These systems, which are mostly based on stages of detection and classification of transients on aggregated signals, rely heavily on load signatures. In the literature, the image-based voltage–current (V–I) trajectory representation is claimed as the most effective individual steady-state signature for appliance classification. However, this representation inherits some drawbacks from its generation process. This work then proposes two steady-state appliance signatures derived from the curvature scale space of V–I trajectories. These signatures aim to improve the image representations of V–I trajectories by encompassing structural elements related to the general shape of such trajectories as well as some characteristics neglected during their generation. A group of load signatures formed from the proposed signatures was evaluated on direct load classification and load disaggregation scenarios for publicly available datasets. The achieved results surpassed the sole employment of a reference image-based V–I signature for all the test scenarios executed. Also, some of the evaluated signatures outperformed all known proposals that are exclusively based on steady-state signatures for load classification on a given benchmarking dataset.