Fluid-structure interactions turn quite complicated and intricately coupled when the structure is flexible. Moreover, these are typical examples of unsteady flows. To fully understand such intricate interactions and flow dynamics, we need the kinematic information of the deformed geometry of the structure at very finely resolved time steps. Usually, this information is retrieved from the raw images obtained from the experiments. Thus, the challenge is twofold: first, to extract geometric data from noisy images, and second, to extract data from numerous images. This daunts manual extraction, which is laborious and time-intensive, and demands automated techniques. We present the steps to extract the coordinate data and thus, the geometry of flexible surfaces (flaps), from noisy PIV images using three state-of-the-art deep learning architectures and models. These models can learn specific patterns from images. We present a sequence of these models that can help extract the features from the images. In this paper, we discuss how flap extraction problems can be related to edge detection problems and how we use models built for deep-sky imagery and biomedical segmentation for our problem. Further, these algorithms can be extended to extract the 3D deformed geometry of flexible fins in fish and wings in insects and birds which would provide more insights on flapping wing/fin kinematics in natural organisms.