Human visual perception is a fundamentally relational process: Lightness perception depends on luminance ratios, and depth perception depends on occlusion (difference of depth) cues. Neurons in low-level visual cortex are sensitive to the difference (but not the value itself) of signals, and these differences have to be used to reconstruct the input. This process can be regarded as a 2-dimensional differentiation and integration process: First, differentiated signals for depth and lightness are created at an earlier stage of visual processing and then 2-dimensionally integrated at a later stage to construct surfaces. The subjective filling in of physically missing parts of input images (completion) can be explained as a property that emerges from this surface construction process. This approach is implemented in a computational model, called DISC (Differentiation-Integration for Surface Completion). In the DISC model, border ownership (the depth order at borderlines) is computed based on local occlusion cues (L- and T-junctions) and the distribution of borderlines. Two-dimensional integration is then applied to construct surfaces in the depth domain, and lightness values are in turn modified by these depth measurements. Illusory percepts emerge through the surface-construction process with the development of illusory border ownership and through the interaction between depth and lightness perception. The DISC model not only produces a central surface with the correctly modified lightness values of the original Kanizsa figure but also responds to variations of this figure such that it can distinguish between illusory and nonillusory configurations in a manner that is consistent with human perception.