Plane detection from depth images is a crucial subtask with broad robotic applications, often accomplished by iterative methods such as Random Sample Consensus (RANSAC). While RANSAC is a robust strategy with strong probabilistic guarantees, the ambiguity of its inlier threshold criterion makes it susceptible to false positive plane detections. This issue is particularly prevalent in complex real-world scenes, where the true number of planes is unknown and multiple planes coexist. In this paper, we aim to address this limitation by proposing a generalised framework for plane detection based on model information optimization. Building on previous works, we treat the observed depth readings as discrete random variables, with their probability distributions constrained by the ground truth planes. Various models containing different candidate plane constraints are then generated through repeated random sub-sampling to explain our observations. By incorporating the physics and noise model of the depth sensor, we can calculate the information for each model, and the model with the least information is accepted as the most likely ground truth. This information optimization process serves as an objective mechanism for determining the true number of planes and preventing false positive detections. Additionally, the quality of each detected plane can be ranked by summing the information reduction of inlier points for each plane. We validate these properties through experiments with synthetic data and find that our algorithm estimates plane parameters more accurately compared to the default Open3D RANSAC plane segmentation. Furthermore, we accelerate our algorithm by partitioning the depth map using neural network segmentation, which enhances its ability to generate more realistic plane parameters in real-world data.