State-of-the-art automated segmentation algorithms are not 100% accurate especially when segmenting difficult to interpret datasets like those with severe osteoarthritis (OA). We present a novel interactive method called just-enough interaction (JEI), which adds a fast correction step to the automated layered optimal graph segmentation of multiple objects and surfaces (LOGISMOS). After LOGISMOS segmentation in knee MRI, the JEI user interaction does not modify boundary surfaces of the bones and cartilages directly. Local costs of underlying graph nodes are modified instead and the graph is re-optimized, providing globally optimal corrected results. Significant performance improvement ($p ll 0.001$) was observed when comparing JEI-corrected results to the automated. The algorithm was extended from 3D JEI to longitudinal multi-3D (4D) JEI allowing simultaneous visualization and interaction of multiple-time points of the same patient.