Ultrasound imaging is common for surgical training and development of medical robotics systems. Recent advancements in surgical training often utilize soft-tissue phantoms based on gelatin, with additional objects inserted to represent different, typically fluid-based pathologies. Segmenting these objects from the images is an important step in the development of training and robotic systems. The current study proposes a simple and fast algorithm for segmenting convex cyst-like structures from phantoms under very low training sample scenarios. The algorithm is based on a custom two-step thresholding procedure with additional post-processing with two trainable parameters. Two large phantoms with convex cysts are created and used to train the algorithm and evaluate its performance. The train/test procedure are repeated 60 times with different dataset splits and prove the viability of the solution with only 4 training images. The DICE coefficients were on average at 0.92, while in the best cases exceeded 0.95, all with fast performance in single-thread operation. The algorithm might be useful for development of surgical training systems and medical robotic systems in general.