DSAD: Dynamic Soft Anisotropic Diagrams for Reduced-Order Video Representation

Efficient video representations should do more than predict pixels: for a long video to be trainable, decodable, and budgeted, appearance and motion must be assigned to explicit units. Group-of-Pictures (GoP) primitive representations provide such units by fitting short blocks with canonical local elements, but their deformation is often still predicted by a neural head. Conversely, implicit neural representations achieve compact global fits without exposing local units that can be moved, ranked, or pruned. We observe that a short GoP contains many primitives but only a few independent motion patterns, suggesting that the same local ownership system used for appearance should also define the motion basis. We introduce Dynamic Soft Anisotropic Diagrams (DSAD), an explicit representation built from three layers over a shared soft-distance geometry. First, a Soft Anisotropic Diagram (SAD), defined as a top-$K$-masked softmax over anisotropic-Apollonius sites, provides a canonical coordinate family in which dense sites encode local RGB ownership. Second, a coarser anchor set reuses the SAD geometry so that anchor weights form a partition-of-unity motion basis without an additional neural module. Third, a reduced-order model (ROM) factorizes deformation into this spatial motion basis and knot-based temporal coefficients. This construction unifies appearance and motion within a single diagram while decoupling spatial ownership from temporal dynamics. On Bunny, UVG, and DAVIS, DSAD attains the highest PSNR among primitive representations and competitive performance among all compared methods, while using a leaner per-GoP deformation module and fewer fine-stage training iterations than state-of-the-art baselines. Ablations show that the gain is a matched-budget trade-off: a compact anchor-ROM motion head reallocates parameters to anchored appearance. RAFT spectra further suggest that the largest gains occur when GoP motion is close to low-rank. Code and models will be released.