This paper presents several adaptive linear predictive coding techniques based upon extension of recursive ladder filters to two and three dimensions (2-D/3-D). A 2-D quarter-plane autoregressive ladder filter is developed using a least square criterion in an exact recursive fashion. The 2-D recursive ladder filter is extended to a 3-D case which can adaptively track the variation of both spatial and temporal changes of moving images. Using the 2-D/3-D ladder filters and a previous frame predictor, two types of adaptive predictor-control schemes are proposed in which the prediction error at each pel can be obtained at or close to a minimum level. We also investigate several modifications of the basic encoding methods. Performance of the 2D/3-D ladder filters, their adaptive control schemes, and variations in coding methods are evaluated by computer simulations on two real sequences and compared to the results of motion compensation and frame differential coders. As a validity test of the ladder filters developed, the error signals for the different predictors are compared and the visual quality of output images is verified.