Objects and activities (temporal objects) are composed of a recursive hierarchy of perceptual wholes and parts, whose properties, such as shape, reflectance, and color, constitute a hierarchy of intrinsic causal factors of object appearance.However, object appearance is the compositional consequence of both an object’s intrinsic and extrinsic causal factors, where the extrinsic causal factors are related to illumination, and imaging conditions.We propose a unified tensor model of wholes and parts that statistically models the mechanism of data formation. We derive a compositional hierarchical block tensor factorization that computes a disentangled representation of the causal factors of object image formation by optimizing simultaneously across wholes and parts. Given computational efficiency considerations,we introduce an incremental bottom-up computational alternative that employs the lower level part representations to represent the higher level of abstractions, the parent wholes. This incremental computational approach may also be employed to update the causal model representation when data that becomes available incrementally. The resulting object representation is an interpretable combinatorial choice of intrinsic causal factor representations related to an object’s recursive hierarchy of wholes and parts that renders object recognition robust to occlusion and reduces training data requirements.