The existing lens correction methods deal with the distortion correction by one or more specific image distortion models. However, distortion determination may fail when an unsuitable model is used. So, methods based on the distortion model would have some drawbacks. A model-free lens distortion correction based on the phase analysis of fringe-patterns is proposed in this paper. Firstly, the mathematical relationship of the distortion displacement and the modulated phase of the sinusoidal fringe-pattern are established in theory. By the phase demodulation analysis of the fringe-pattern, the distortion displacement map can be determined point by point for the whole distorted image. So, the image correction is achieved according to the distortion displacement map by a model-free approach. Furthermore, the distortion center, which is important in obtaining an optimal result, is measured by the instantaneous frequency distribution according to the character of distortion automatically. Numerical simulation and experiments performed by a wide-angle lens are carried out to validate the method.

The integration of renewable energy and rising electricity demand strain system flexibility. While price-based demand response (PBDR) improves flexibility through pricing signals, its efficacy hinges critically on accurate consumer modeling. Recognizing this pivotal role, this paper provides a comprehensive review of consumer models in PBDR and their applications to electric vehicles (EVs). First, a unified conceptual framework is presented, delineating the energy, information and financial flows among the system operator (SO), load aggregators (LAs), and end-users, and highlighting the central position of consumer modeling. Second, existing modeling approaches are systematically classified into four categories, namely rule-based, optimization-based, data-driven, and hybrid, to facilitate the selection of appropriate models by researchers and stakeholders for diverse scenarios. Furthermore, the application and adaptation of these models to EVs are critically analyzed, accounting for unique vehicular constraints. Subsequently, a systematic summary of the key characteristics and existing research gaps is provided. Finally, key directions for future research are proposed accordingly, aimed at incorporating bounded rationality into behavioral models, developing individualized consumer modeling coupled with user-specific dynamic pricing, and extending consumer modeling to residential multi-energy prosumers in integrated energy systems.