Cell migration plays an essential role in many of physiological and pathological processes, including morphogenesis, inflammation, wound healing, and tumor metastasis. It is a complex process that involves multi-scale interactions between the cell and the extracellular matrix (ECM). Cells migrate through stromal ECM with native and cell-derived curvature at micron-meter scale are context-specific. How does the curvature of ECM mechanically change cell morphology and motility? Can the diverse migration behaviors from genetically identical cells be predictively using cell migrating data? We address these questions using an integrated computational and experimental approach: we developed three-dimensional biomechanical cell model and measured and analyzed a large number of cell migration images over time. Our findings suggest that 1. substrate curvature determines cell shape through contact and regulating protrusion dynamics; 2. effective cell migration is characterized with long cellular persistence time, low-speed variation, spatial-temporally coordinated protrusion and contraction; 3. the cell shape variation space is low dimensional; and 4. migration behavior can be determined by a single image projected in the low dimensional cell shape variation space.